% Alphabetic order

@article{Abdulle2020,
  title={Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration},
  author={Abdulle, A. and Garegnani, G.},
  journal={Statistics and Computing},
  pages={1--26},
  year={2020},
  publisher={Springer}
}

@book{Adams2003,
  title={Sobolev spaces},
  author={Adams, R. A. and Fournier, J. J.F.},
  volume={140},
  year={2003},
  publisher={Elsevier}
}

@article{Akaike1974,
  title={A new look at the statistical model identification},
  author={Akaike, H.},
  journal={IEEE Transactions on Automatic Control},
  volume={19},
  number={6},
  pages={716--723},
  year={1974},
  publisher={IEEE}
}

@book{Amari2007,
  title={Translations of Mathematical Monographs: Methods of {I}nformation {G}eometry},
  author={Amari, S. and Nagaoka, H.},
  volume={191},
  year={2007},
  publisher={American Mathematical Society}
}

@book{Amari2012,
  title={Differential-{G}eometrical {M}ethods in {S}tatistics},
  author={Amari, S.},
  volume={28},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@article{Arasaratnam2007,
  title={Discrete-time nonlinear filtering algorithms using {Gauss--Hermite} quadrature},
  author={Arasaratnam, I. and Haykin, S. and Elliott, R. J.},
  journal={Proceedings of the IEEE},
  volume={95},
  number={5},
  pages={953--977},
  year={2007},
  publisher={IEEE}
}

@article{Arasaratnam2009,
  title={Cubature {K}alman filters},
  author={Arasaratnam, I. and Haykin, S.},
  journal={IEEE Transactions on Automatic Control},
  volume={54},
  number={6},
  pages={1254--1269},
  year={2009},
  publisher={IEEE}
}

@article{Aravkin2017,
  title={Generalized {K}alman smoothing: Modeling and algorithms},
  author={Aravkin, A. and Burke, J. V. and Ljung, L. and Lozano, A. and Pillonetto, G.},
  journal={Automatica},
  volume={86},
  pages={63--86},
  year={2017},
  publisher={Elsevier}
}

@article{Arcangeli2007,
  title={An extension of a bound for functions in {S}obolev spaces, with applications to (m, s)-spline interpolation and smoothing},
  author={Arcang{\'e}li, R. and de Silanes, M. C. L. and Torrens, J. J.},
  journal={Numerische Mathematik},
  volume={107},
  number={2},
  pages={181--211},
  year={2007},
  publisher={Springer}
}

@book{Arnold1992,
  title={Ordinary Differential Equations},
  author={Arnol'd, V. I.},
  year={1992},
  publisher={Springer-Verlag Berlin Heidelberg}
}

@ARTICLE{Arulampalam2002,
    author = {M. S. Arulampalam and S. Maskell and N. Gordon},
    title = {A tutorial on particle filters for online nonlinear/non-{G}aussian {B}ayesian tracking},
    journal = {IEEE Transactions Signal Processing},
    year = {2002},
    volume = {50},
    pages = {174--188}
}

@article{Alahmadi2020,
  title={A comparison of approximate versus exact techniques for {B}ayesian parameter inference in nonlinear ordinary differential equation models},
  author={Alahmadi, A. A. and Flegg, J. A. and Cochrane, D. G. and Drovandi, C. C. and Keith, J. M.},
  journal={Royal Society open science},
  volume={7},
  number={3},
  year={2020},
  publisher={The Royal Society}
}

@article{Ala-Luhtala2015,
title = {Gaussian filtering and variational approximations for {B}ayesian smoothing in continuous-discrete stochastic dynamic systems},
journal = {Signal Processing},
volume = {111},
pages = {124--136},
year = {2015},
author = {Ala-Luhtala, J. and S\"arkk\"a, S. and Piché, R.}
}

@incollection{Archambeau2007,
title = {Variational Inference for Diffusion Processes},
author = {Archambeau, C. and Opper, M. and Shen, Y. and Cornford, D. and Shawe-taylor, J. S.},
booktitle = {Advances in Neural Information Processing Systems 20},
pages = {17--24},
year = {2008},
crossref = {NIPS2007},
}

@article{Astrom1971,
  title={System identification -- a survey},
  author={{\AA}str{\"o}m, K. J. and Eykhoff, P.},
  journal={Automatica},
  volume={7},
  number={2},
  pages={123--162},
  year={1971},
  publisher={Elsevier}
}

@article{Anderson1972,
  title={Fixed interval smoothing for nonlinear continuous time systems},
  author={Anderson, B. D. O.},
  journal={Information and Control},
  volume={20},
  number={3},
  pages={294--300},
  year={1972},
  publisher={Academic Press}
}

@book{AndersonMoore1979,
	  author="Anderson, B. D. O. and Moore, J. B.",
	  title="Optimal Filtering",
	  publisher="Prentice--Hall",
  	  series = "Information and System Sciences Series",
	  year = "1979"
}

@article{Anderson1981,
  title={Detectability and stabilizability of time-varying discrete-time linear systems},
  author={Anderson, B. D. O. and Moore, J. B.},
  journal={SIAM Journal on Control and Optimization},
  volume={19},
  number={1},
  pages={20--32},
  year={1981},
  publisher={SIAM}
}

@book{Anderson2007,
  title={Optimal Control: Linear Quadratic Methods},
  author={Anderson, B. D. O. and Moore, J. B.},
  year={1989},
  publisher={Prentice--Hall},
  series = {Information and System Sciences Series}
}

@article{Agamennoni2014,
  title={Robust estimation in non-linear state-space models with state-dependent noise},
  author={Agamennoni, Gabriel and Nebot, Eduardo M},
  journal={IEEE Transactions on Signal Processing},
  volume={62},
  number={8},
  pages={2165--2175},
  year={2014},
  publisher={IEEE}
}

@article{Benson1979,
  title={Parameter fitting in dynamic models},
  author={Benson, M},
  journal={Ecological Modelling},
  volume={6},
  number={2},
  pages={97--115},
  year={1979},
  publisher={Elsevier}
}

@book{Bar2004,
  title={Estimation with Applications to Tracking and Navigation: Theory Algorithms and Software},
  author={Bar-Shalom, Y. and Li, X. R. and Kirubarajan, T.},
  year={2004},
  publisher={John Wiley \& Sons}
}

@book{Barfoot2017,
  title={State Estimation for Robotics},
  author={Barfoot, T. D.},
  year={2017},
  publisher={Cambridge University Press}
}

@article{Bauer2015,
  title={Diffeomorphic density matching by optimal information transport},
  author={Bauer, M. and Joshi, S. and Modin, K.},
  journal={SIAM Journal on Imaging Sciences},
  volume={8},
  number={3},
  pages={1718--1751},
  year={2015},
  publisher={SIAM}
}

@book{Bard1974,
  title={Nonlinear parameter estimation},
  author={Bard, Y.},
  year={1974},
  publisher={Academic Press}
}
@inproceedings{Barber2014,
  title={Gaussian processes for {B}ayesian estimation in ordinary differential equations},
  author={Barber, D. and Wang, Y.},
  booktitle={International Conference on Machine Learning},
  pages={1485--1493},
  year={2014},
  organization={PMLR}
}

@article{Biegler1986,
  title={Nonlinear parameter estimation: a case study comparison},
  author={Biegler, L. T. and Damiano, J. J. and Blau, G. E.},
  journal={AIChE Journal},
  volume={32},
  number={1},
  pages={29--45},
  year={1986},
  publisher={Wiley Online Library}
}

@book{Beal2003,
  title={Variational algorithms for approximate Bayesian inference},
  author={Beal, M. J.},
  year={2003},
  publisher={University of {L}ondon}
}

@article{Benevs1981,
  title={Exact finite-dimensional filters for certain diffusions with nonlinear drift},
  author={Bene{\v{s}}, V. E.},
  journal={Stochastics: An International Journal of Probability and Stochastic Processes},
  volume={5},
  number={1-2},
  pages={65--92},
  year={1981},
  publisher={Taylor \& Francis}
}

@inproceedings{Bosch2021,
  title={Calibrated adaptive probabilistic {ODE} solvers},
  author={Bosch, N. and Hennig, P. and Tronarp, F.},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={3466--3474},
  year={2021},
  organization={PMLR}
}

@InProceedings{Bosch2021b,
  title = 	 { Pick-and-Mix Information Operators for Probabilistic {ODE} Solvers },
  author =       {Bosch, Nathanael and Tronarp, Filip and Hennig, Philipp},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages = 	 {10015--10027},
  year={2022},
  organization={PMLR}
}

@book{Boyd2004,
  title={Convex optimization},
  author={Boyd, S. and Vandenberghe, L.},
  year={2004},
  publisher={Cambridge university press}
}

@article{Boyd2011,
  title={Distributed optimization and statistical learning via the alternating direction method of multipliers},
  author={Boyd, S. and Parikh, N. and Chu, E. and Peleato, B. and Eckstein, J.},
  journal={Foundations and Trends in Machine learning},
  volume={3},
  number={1},
  pages={1--122},
  year={2011}
}

@article{Brigo1998,
  title={A differential geometric approach to nonlinear filtering: the projection filter},
  author={Brigo, D. and Hanzon, B. and LeGland, F.},
  journal={IEEE Transactions on Automatic Control},
  volume={43},
  number={2},
  pages={247--252},
  year={1998},
  publisher={IEEE}
}

@article{Brigo1999,
  title={Approximate nonlinear filtering by projection on exponential manifolds of densities},
  author={Brigo, D. and Hanzon, B. and Le Gland, F.},
  journal={Bernoulli},
  volume={5},
  number={3},
  pages={495--534},
  year={1999},
  publisher={Bernoulli Society for Mathematical Statistics and Probability}
}

@article{Briol2019,
  title={Probabilistic integration: A role in statistical computation?},
  author={Briol, F-X. and Oates, C. J. and Girolami, M. and Osborne, M. A. and Sejdinovic, D.},
  journal={Statistical Science},
  volume={34},
  number={1},
  pages={1--22},
  year={2019},
  publisher={Institute of Mathematical Statistics}
}

@article{Borisov2018,
  title={The conditionally minimax nonlinear filtering method and modern approaches to state estimation in nonlinear stochastic systems},
  author={Borisov, Andrey Vladimirovich and Bosov, Alexey V and Kibzun, Andrei Ivanovich and Miller, GB and Semenikhin, Konstantin Vladimirovich},
  journal={Automation and Remote Control},
  volume={79},
  number={1},
  pages={1--11},
  year={2018},
  publisher={Springer}
}


@ARTICLE{Bell1993,
    author = {B. M. Bell and F. W. Cathey},
    title = {The iterated {K}alman filter update as a {G}auss--{N}ewton method},
    journal = {IEEE Transaction on Automatic Control},
    year = {1993},
    volume = {38},
    number = {2},
    pages = {294--297}
}

@article{Bell1994,
  title={The iterated {K}alman smoother as a {G}auss--{N}ewton method},
  author={Bell, B. M.},
  journal={SIAM Journal on Optimization},
  volume={4},
  number={3},
  pages={626--636},
  year={1994},
}

@article{Bourdaud2010,
  title={Superposition in homogeneous and vector valued {S}obolev spaces},
  author={Bourdaud, G.},
  journal={Transactions of the American Mathematical Society},
  volume={362},
  number={11},
  pages={6105--6130},
  year={2010}
}

@article{Bourdaud2011,
  title={Composition Operators on Function Spaces with Fractional Order of Smoothness (Harmonic Analysis and Nonlinear Partial Differential Equations)},
  author={Bourdaud, G. and Sickel, W.},
  year={2011},
  publisher={京都大学数理解析研究所}
}

@inproceedings{Bukal2017,
  title={Score matching based assumed density filtering with the von {M}ises--{F}isher distribution},
  author={Bukal, M. and Markovi{\'c}, I. and Petrovi{\'c}, I.},
  booktitle={20th International Conference on Information Fusion},
  year={2017},
  crossref ={FUSION2017},
}

@Book{Butcher2008,
	author= "Butcher, J. C.",
	title = "Numerical Methods for Ordinary Differential Equations",
	edition = {2nd},
	publisher = {John Wiley \& Sons, Inc.},
	year = "2008",
}

@article{Byrne1975,
  title={A polyalgorithm for the numerical solution of ordinary differential equations},
  author={Byrne, G. D. and Hindmarsh, A. C.},
  journal={ACM Transactions on Mathematical Software (TOMS)},
  volume={1},
  number={1},
  pages={71--96},
  year={1975},
  publisher={ACM New York, NY, USA}
}

@inproceedings{Calderhead2009,
  title={Accelerating {B}ayesian inference over nonlinear differential equations with {G}aussian processes},
  author={Calderhead, B. and Girolami, M. and Lawrence, N. D.s},
  booktitle={Advances in Neural Information Processing Systems},
  pages={217--224},
  year={2009}
}

@article{Cao2011,
  title={Robust estimation for ordinary differential equation models},
  author={Cao, J. and Wang, L. and Xu, J.},
  journal={Biometrics},
  volume={67},
  number={4},
  pages={1305--1313},
  year={2011},
  publisher={Wiley Online Library}
}

@book{Cappe2006,
  title={Inference in hidden {M}arkov models},
  author={Capp{\'e}, O. and Moulines, E. and Ryd{\'e}n, T.},
  year={2006},
  publisher={Springer Science \& Business Media}
}

@ARTICLE{Cappe2007,
    author = {O. Cappe and S. J. Godsill and E. Moulines},
    title = {An Overview of Existing Methods and Recent Advances in Sequential {M}onte {C}arlo},
    journal = {Proceedings of the {IEEE}},
    year = {2007},
    volume = {95},
    number = {2},
    pages = {899--924}
}


@article{Chkrebtii2016,
	author = "Chkrebtii, O. A. and Campbell, D. A. and Calderhead, B. and Girolami, M. A.",
	journal = "Bayesian Analysis",
	month = "12",
	number = "4",
	pages = "1239--1267",
	publisher = "International Society for Bayesian Analysis",
	title = "{Bayesian} Solution Uncertainty Quantification for Differential Equations",

	volume = "11",
	year = "2016"
}

@article{Chkrebtii2019a,
  title={Adaptive step-size selection for state-space probabilistic differential equation solvers},
  author={Chkrebtii, O. A. and Campbell, D. A.},
  journal={Statistics and Computing},
  volume={29},
  number={6},
  pages={1285--1295},
  year={2019},
  publisher={Springer}
}

@book{CrassidisJunkins2004,
	author="J. L. Crassidis and J. L. Junkins",
	title="Optimal Estimation of Dynamic Systems",
	publisher="Chapman \& Hall/CRC",
	year = "2004"
}

@article{Crisan2002,
  title={A survey of convergence results on particle filtering methods for practitioners},
  author={Crisan, D. and Doucet, A.},
  journal={IEEE Transactions on Signal Processing},
  volume={50},
  number={3},
  pages={736--746},
  year={2002},
  publisher={IEEE}
}

@article{Cockayne2019a,
  title={Bayesian probabilistic numerical methods},
  author={Cockayne, J. and Oates, C. J and Sullivan, T. J. and Girolami, M.},
  journal={SIAM Review},
  volume={61},
  number={4},
  pages={756--789},
  year={2019},
  publisher={SIAM}
}


@Article{Conrad2017,
author="Conrad, P. R.
and Girolami, M.
and S{\"a}rkk{\"a}, S.
and Stuart, A.
and Zygalakis, K.",
title="Statistical analysis of differential equations: introducing probability measures on numerical solutions",
journal="Statistics and Computing",
year="2017",
month="Jul",
day="01",
volume="27",
number="4",
pages="1065--1082",
}

@article{Cox1990,
  title={Asymptotic analysis of penalized likelihood and related estimators},
  author={Cox, D. D. and O'Sullivan, F.},
  journal={The Annals of Statistics},
  pages={1676--1695},
  year={1990}
}

@article{Cox1994,
  title={On the {S}obolev class of a composite function},
  author={Cox, D. D. and O’Sullivan, F.},
  journal={Proceedings of the American Mathematical Society},
  volume={122},
  number={3},
  pages={727--732},
  year={1994}
}

@article{Cseke2016,
  title={Expectation propagation for continuous time stochastic processes},
  author={Cseke, B. and Schnoerr, D. and Opper, M. and Sanguinetti, G.},
  journal={Journal of Physics A: Mathematical and Theoretical},
  volume={49},
  number={49},
  pages={494002},
  year={2016},
  publisher={IOP Publishing}
}

@book{Curtain1977,
  title={Functional analysis in modern applied mathematics},
  author={Curtain, Ruth F and Pritchard, Anthony J},
  volume={132},
  year={1977},
  publisher={Academic press}
}

@article{Dahlquist1963,
  title={A special stability problem for linear multistep methods},
  author={Dahlquist, G. },
  journal={BIT Numerical Mathematics},
  volume={3},
  number={1},
  pages={27--43},
  year={1963},
  publisher={Springer}
}

@article{Dass2017,
  title={Laplace based approximate posterior inference for differential equation models},
  author={Dass, S. C. and Lee, J. and Lee, K. and Park, J.},
  journal={Statistics and Computing},
  volume={27},
  number={3},
  pages={679--698},
  year={2017},
  publisher={Springer}
}

@inproceedings{Daum1984,
  title={Exact finite dimensional nonlinear filters for continuous time processes with discrete time measurements},
  author={Daum, F. E.},
  booktitle = {The 23rd IEEE Conference on Decision and Control},
  pages={16--22},
  year={1984},
  crossref = {CDC1984},
}


@article{DelMoral2006,
  title={Sequential {M}onte {C}arlo samplers},
  author={Del Moral, P. and Doucet, A. and Jasra, A.},
  journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume={68},
  number={3},
  pages={411--436},
  year={2006},
  publisher={Wiley Online Library}
}

@article{Del2015a,
  title={Sequential {M}onte {C}arlo with highly informative observations},
  author={Del Moral, P. and Murray, L. M.},
  journal={SIAM/ASA Journal on Uncertainty Quantification},
  volume={3},
  number={1},
  pages={969--997},
  year={2015},
  publisher={SIAM}
}

@inproceedings{DesbouvriesPetitinMonfrini2011,
    author = {Francois Desbouvries and Yohan Petitin and Emmanuel Monfrini},
    title = {OPTIMAL {SIR} ALGORITHM VS. FULLY ADAPTED AUXILLIARY PARTICLE FILTER: A MATTER OF CONDITIONAL INDEPENDENCE},
    Booktitle = "Acoustics, Speech and Signal Procesisng (ICASSP), 2011 {IEEE} International Conference on",
    year = {2011},
    pages = {3992--3995}
}

@book{Deuflhard2002,
	author = {Deuflhard, P. and Bornemann, F.},
	publisher = {Springer},
	title = {Scientific Computing with Ordinary Differential Equations},
	year = 2002
}

@inproceedings{Dondelinger2013,
  title={{ODE} parameter inference using adaptive gradient matching with {G}aussian processes},
  author={Dondelinger, F. and Husmeier, D. and Rogers, S. and Filippone, M.},
  booktitle={Artificial intelligence and Statistics},
  pages={216--228},
  year={2013}
}

@inproceedings{Douc2005,
  title={Comparison of resampling schemes for particle filtering},
  author={Douc, R. and Capp{\'e}, O.},
  booktitle={ISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis},
  pages={64--69},
  year={2005},
  crossref = {ISPA2005},
}

@article{Doucet2000,
  title={On sequential {M}onte {C}arlo sampling methods for {B}ayesian filtering},
  author={Doucet, A. and Godsill, S. and Andrieu, C.},
  journal={Statistics and computing},
  volume={10},
  number={3},
  pages={197--208},
  year={2000},
  publisher={Springer}
}
@incollection{Doucet2001,
  title={An introduction to sequential {Monte} {Carlo} methods},
  author={Doucet, A. and De Freitas, N. and Gordon, N.},
  booktitle={Sequential Monte Carlo methods in practice},
  pages={3--14},
  year={2001},
  publisher={Springer}
}

@ARTICLE{DoucetJacobRubethaler2013,
    author = {A. Doucet and P. E. Jacob and S. Rubenthaler},
    title = {Derivative-free estimation of the score vector and observed information matrix},
    journal = {arXiv preprint 1304.5768},
    year = {2013}
}

@article{Dutra2014,
  title={Maximum a posteriori state path estimation: Discretization limits and their interpretation},
  author={Dutra, Dimas Abreu and Teixeira, Bruno Ot{\'a}vio Soares and Aguirre, Luis Antonio},
  journal={Automatica},
  volume={50},
  number={5},
  pages={1360--1368},
  year={2014},
  publisher={Elsevier}
}

@article{Friston2002,
  title={Bayesian estimation of dynamical systems: an application to f{MRI}},
  author={Friston, K. J.},
  journal={NeuroImage},
  volume={16},
  number={2},
  pages={513--530},
  year={2002},
  publisher={Elsevier}
}

@article{Gao2019a,
  title={Iterated Extended {K}alman Smoother-based Variable Splitting for ${L}_1$-Regularized State Estimation},
  author={Gao, R. and Tronarp, F. and S{\"a}rkk{\"a}, S.},
  journal={IEEE Transactions on Signal Processing},
  volume={67},
  number={19},
  pages={5078--5092},
  year={2019},
  publisher={IEEE}
}

@inproceedings{Garcia2014,
    title = {Iterated statistical linear regression for {B}ayesian updates},
    author = {Garc{\'\i}a-Fern{\'a}ndez, {\'A}. F. and Svensson, L. and Morelande, M. R.},
    booktitle = {17th International Conference on Information Fusion},
    pages = {1--8},
    year = {2014},
    crossref = {FUSION2014},
}

@article{Garcia2015,
author={Garc{\'\i}a-Fern{\'a}ndez, {\'A}. F. and Svensson, L. and Morelande, M. R. and S\"arkk\"a, S.},
journal={IEEE Transactions on Signal Processing},
title={Posterior Linearization Filter: Principles and Implementation Using Sigma Points},
year={2015},
volume={63},
number={20},
pages={5561--5573},
}

@article{Garcia2017,
author={Garc{\'\i}a-Fern{\'a}ndez, {\'A}. F. and L. Svensson and S. S\"arkk\"a},
journal={IEEE Transactions on Automatic Control},
title={Iterated posterior linearisation smoother},
year={2017},
volume={62},
number={4},
pages={2056--2063},
}

@article{Garcia2019a,
  title={Gaussian Process Classification Using Posterior Linearization},
  author={Garc{\'\i}a-Fern{\'a}ndez, {\'A}. F. and Tronarp, F. and S{\"a}rkk{\"a}, S.},
  journal={IEEE Signal Processing Letters},
  volume={26},
  number={5},
  pages={735--739},
  year={2019},
  publisher={IEEE}
}

@article{Garcia2019b,
  title={Gaussian Target Tracking With Direction-of-Arrival von {M}ises--{F}isher Measurements},
  author={Garc{\'\i}a-Fern{\'a}ndez, {\'A}. F. and Tronarp, F. and S{\"a}rkk{\"a}, S.},
  journal={IEEE Transactions on Signal Processing},
  volume={67},
  number={11},
  pages={2960--2972},
  year={2019},
  publisher={IEEE}
}

@book{Gelb1974,
  title={Applied Optimal Estimation},
  author={Gelb, A.},
  year={1974},
  publisher={MIT press}
}

@article{Gelman1996,
  title={Physiological pharmacokinetic analysis using population modeling and informative prior distributions},
  author={Gelman, A. and Bois, F. and Jiang, J.},
  journal={Journal of the American Statistical Association},
  volume={91},
  number={436},
  pages={1400--1412},
  year={1996},
  publisher={Taylor \& Francis}
}

@book{Gine2016,
  title={Mathematical Foundations of Infinite-Dimensional Statistical Models},
  author={Gin{\'e}, E. and Nickl, R.},
  year={2016},
  publisher={Cambridge University Press}
}

@article{Girosi1995,
  title={Regularization theory and neural networks architectures},
  author={Girosi, Federico and Jones, Michael and Poggio, Tomaso},
  journal={Neural computation},
  volume={7},
  number={2},
  pages={219--269},
  year={1995},
  publisher={MIT Press}
}


@article{Godsill2004,
    author = {S. J. Godsill and A. Doucet and M. West},
    title = {{M}onte {C}arlo smoothing for nonlinear time series},
    journal = {Journal of the American Statistical Association},
    year = {2004},
    volume = {99},
    number = {465},
    pages = {156--168}
}

@article{Golomb1971,
  title={Linear ordinary differential equations with boundary conditions on arbitrary point sets},
  author={Golomb, M. and Jerome, J.},
  journal={Transactions of the American Mathematical Society},
  volume={153},
  pages={235--264},
  year={1971}
}

@article{Golub1969,
  title={Calculation of {Gauss} quadrature rules},
  author={Golub, G. H. and Welsch, J. H.},
  journal={Mathematics of Computation},
  volume={23},
  number={106},
  pages={221--230},
  year={1969}
}

@inproceedings{Gorbach2017,
  title={Scalable variational inference for dynamical systems},
  author={Gorbach, N. S. and Bauer, S. and Buhmann, J. M.},
  booktitle={Advances in Neural Information Processing Systems},
  pages={4806--4815},
  year={2017}
}

@article{Gustafsson2012,
  title={Some relations between extended and unscented {K}alman filters},
  author={Gustafsson, F. and Hendeby, G.},
  journal={IEEE Transactions on Signal Processing},
  volume={60},
  number={2},
  pages={545--555},
  year={2012},
  publisher={IEEE}
}

@ARTICLE{ekfukftoolbox,
    author = {Simo S\"arkk\"a and Jouni Hartkainen and Arno Solin},
    title = { {EKF/UKF} Toolbox},
    note = {http://becs.aalto.fi/en/research/bayes/ekfukf/}
}

@book{GodsillRayner1998,
	author="S. J. Godsill and P. J. Rayner",
	title="Digital Audio Restoration: A Statistical Model Based Approach",
	publisher="Springer",
	year = "1998"
}

@inproceedings{Glover2014,
        author={J. Glover and L. P. Kaelbling},
        booktitle =        {2014 IEEE International Conference on Robotics and Automation (ICRA)},
        Pages = {4133--4140},
        title = {Tracking the Spin on a Ping Pong Ball with the Quaternion {B}ingham Filter},
        crossref = {ICRA2014},
}

@article{Gilitschenski2016,
	author = {I. Gilitschenski and G. Kurz and S. J. Julier and U. D. Hanebeck},
	title = {Unscented orientation Estimation Based on the {B}ingham Distribution},
	journal = {IEEE Transactions on Automatic Control},
	volume = {61},
	number = {1},
	pages= {172--177},
	year = {2016},
	publisher = {IEEE},
}

@inproceedings{Gilitschenski2014,
        author={I. Gilitschenski and G. Kurz and  and S. J. Julier and U. D. Hanebeck},
        booktitle = {17th International Conference on Information Fusion},
        title = {Efficient {B}ingham Filtering Based on Saddlepoint Approximations},
        Year = {2014},
    crossref = {FUSION2014},
}

@article{Goebel1991,
  title={On {F}r{\'e}chet-differentiability of {N}emytskij operators acting in {H}{\"o}lder spaces},
  author={Goebel, M.},
  journal={Glasgow Mathematical Journal},
  volume={33},
  number={1},
  pages={1--5},
  year={1991},
  publisher={Cambridge University Press}
}

@article{Gomez2016,
  title={Online Algorithms For Parameter Mean And Variance Estimation In Dynamic Regression Models},
  author={Gomez-Uribe, Carlos Alberto},
  journal={arXiv preprint arXiv:1605.05697},
  year={2016}
}

@article{Gomez2018a,
  title={The decoupled extended Kalman filter for dynamic exponential-family factorization models},
  author={Gomez-Uribe, Carlos Alberto and Karrer, Brian},
  journal={arXiv preprint arXiv:1806.09976},
  year={2018}
}

@article{Gordon1993,
    author = {N. J. Gordon and D. J. Salmond and A. F. M. Smith},
    title = {Novel approach to nonlinear/non-{G}aussian {B}ayesian state estimation},
    journal = {IEE Proceedings F - Radar and Signal Processing},
    year = {1993},
    volume = {140},
    pages = {107--113}
}

@article{Gugushvili2012,
  title={$\sqrt{n}$-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing},
  author={Gugushvili, S. and Klaassen, C. A. J.},
  journal={Bernoulli},
  volume={18},
  number={3},
  pages={1061--1098},
  year={2012},
  publisher={Bernoulli Society for Mathematical Statistics and Probability}
}

@book{Hairer1996,
  title={Solving Ordinary Differential Equations {II}: Stiff and Differential-Algebraic Problems},
  author={Hairer, E. and Wanner, G.},
  year={1996},
  publisher={Springer}
}

@book{Hairer87,
	author = {E. Hairer and S.P. N{\o}rsett and G. Wanner},
	publisher = {Springer},
	title = {{Solving Ordinary Differential Equations I: Nonstiff Problems}},
	year = 1987
}

@inproceedings{Hartikainen2010,
  title={Kalman filtering and smoothing solutions to temporal {G}aussian process regression models},
  author={Hartikainen, J. and S{\"a}rkk{\"a}, S.},
  booktitle={2010 IEEE international workshop on machine learning for signal processing},
  pages={379--384},
  year={2010},
  organization={IEEE}
}

@inproceedings{Heinonen2018a,
  title={Learning unknown ODE models with {G}aussian processes},
  author={Heinonen, M. and Yildiz, C. and Mannerstr{\"o}m, H. and Intosalmi, J. and L{\"a}hdesm{\"a}ki, H.},
  booktitle={International Conference on Machine Learning},
  year={2018},
  organization={PMLR}
}

@inproceedings{Hennig2014,
	author = {P. Hennig and S. Hauberg},
	booktitle = {{Proc. of the 17th int. Conf. on Artificial Intelligence and
Statistics ({AISTATS})}},
	publisher = {JMLR, W\&CP},
	title = {Probabilistic Solutions to Differential Equations and their
Application to {Riemannian} Statistics},
	volume = {33},
	year = {2014}
}

@article{Hennig2015,
  title={Probabilistic numerics and uncertainty in computations},
  author={Hennig, P. and Osborne, M. A. and Girolami, M.},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  volume={471},
  number={2179},
  pages={20150142},
  year={2015},
  publisher={The Royal Society Publishing}
}

@inproceedings{Huang2016,
  title={A robust {S}tudent's t based cubature filter},
  author={Huang, Y. and Zhang, Y. and Li, N. and Naqvi, S. M. and Chambers, J.},
  booktitle={19th International Conference on Information Fusion},
  pages={9--16},
  year={2016},
  crossref = {FUSION2016},
}

@article{Isserlis1918,
    Author = "Isserlis, L.",
    Title = "On a Formula for the Product-Moment Coefficient of any Order of a Normal Frequency Distribution in any Number of Variables",
    Journal = "Biometrika",
    Volume = "12",
    Number = "1/2",
    Pages = "134--139",
    Year = "1918"
}

@article{ItoXiong2000,
    Author = "Ito, K. and Xiong, K.",
    Title = "{G}aussian Filters for Nonlinear Filtering Problems",
    Journal = "IEEE Transactions on Automatic Control",
    Volume = "45",
    Number = "5",
    Pages = "910--927",
    Year = "2000",
    Month = "May"
}

@book{Jakobsson2013,
	author = {A. Jakobsson},
	title = {An Introduction to Time Series Modeling},
	publisher = {Studentlitteratur},
	year = {2013},
}

@Book{Jazwinski1970,
  author     = {Jazwinski, A. H.},
  title      = {Stochastic Processes and Filtering Theory},
  publisher  = {Academic Press},
  year       = {1970}
}
F
@inproceedings{JulierUhlmannDurrant1995,
    author = {Julier, S. J. and Uhlmann, J. K. and Durrant-Whyte, H. F.},
    title = {A New Approach for Filtering Nonlinear Systems},
    booktitle = {Proceedings of the 1995 American Control Conference},
    pages = {1628--1632},
    year = {1995},
    crossref = {ACC1995},
}



@article{JulierUhlmannDurrant2000,
    Author = {Julier, S. J. and Uhlmann, J. K. and Durrant-Whyte, H. F.},
    Title = {A new method for the nonlinear transformation of means and covariances in filters and estimators},
    Journal = {IEEE Transactions on Automatic Control},
    Volume = {45},
    Number = {3},
    Pages = {477--482},
    Year = {2000},
    Month = {Mar}
}

@article{Julier2004,
  title={Unscented filtering and nonlinear estimation},
  author={Julier, S. J. and Uhlmann, J. K.},
  journal={Proceedings of the IEEE},
  volume={92},
  number={3},
  pages={401--422},
  year={2004},
  publisher={IEEE}
}

@article{Kantas2009,
  title={An overview of sequential {M}onte {C}arlo methods for parameter estimation in general state-space models},
  author={Kantas, N. and Doucet, A. and Singh, S. S. and Maciejowski, J. M.},
  journal={IFAC Proceedings Volumes},
  volume={42},
  number={10},
  pages={774--785},
  year={2009},
  publisher={Elsevier}
}

@book{Karatzas1988,
  author={Karatzas, I. and Shreve, S. E.},
  title={Brownian Motion and Stochastic Calculus},
  year={1988},
  publisher={Springer}
}

@article{Kallianpur1968,
    Author = {G. Kallianpur and C. Striebel},
    Title = {Estimation of stochatic systems: arbitrary system process with additive white noise observation errors},
    Journal = {Annals of Mathematical Statistics},
    Volume = {39},
    Number = {3},
    Pages = {785--801},
    Year = {1968}
}

@article{Kalman1960,
  title={A new approach to linear filtering and prediction problems},
  author={Kalman, R. E.},
  journal={Journal of Basic Engineering},
  volume={82},
  number={1},
  pages={35--45},
  year={1960}
}

@article{KalmanBucy1961,
    Author = "R.E. Kalman and R.S. Bucy",
    Title = "New results in linear filtering and prediction theory",
    Journal = "Transactions of the ASME, Journal of Basic Engineering",
    Volume = "83",
    Pages = "95--108",
    Year = "1961"
}

@article{Kanagawa2018a,
  title={Gaussian processes and kernel methods: A review on connections and equivalences},
  author={Kanagawa, M. and Hennig, P. and Sejdinovic, D. and Sriperumbudur, B. K.},
  journal={arXiv preprint arXiv:1807.02582},
  year={2018}
}

@article{Kanagawa2020a,
  title={Convergence analysis of deterministic kernel-based quadrature rules in misspecified settings},
  author={Kanagawa, M. and Sriperumbudur, B. K. and Fukumizu, K.},
  journal={Foundations of Computational Mathematics},
  volume={20},
  pages={155--194},
  year={2020},
  publisher={Springer}
}

@inproceedings{Karvonen2016,
  title={Approximate state-space {G}aussian processes via spectral transformation},
  author={Karvonen, T. and Sarkk{\"a}, S.},
  booktitle={2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP)},
  year={2016}
}

@inproceedings{Karvonen2017,
  title={Classical quadrature rules via {G}aussian processes},
  author={Karvonen, T. and S{\"a}rkk{\"a}, S.},
  booktitle={27th International Workshop on Machine Learning for Signal Processing},
  year={2017},
  crossref = {MLSP2017},
}

@article{Karvonen2020,
  title={Maximum likelihood estimation and uncertainty quantification for {G}aussian process approximation of deterministic functions},
  author={Karvonen, T. and Wynne, G. and Tronarp, F. and Oates, C. J. and S{\"a}rkk{\"a}, S.},
  journal={arXiv preprint arXiv:2001.10965},
  year={2020}
}

@inproceedings{Kersting2016,
	author = {{Kersting}, H. and {Hennig}, P.},
	booktitle = {{Uncertainty in Artificial Intelligence (UAI) 2016}},
	title = {Active Uncertainty Calibration in {Bayesian} {ODE} Solvers},
	year = {2016},
        crossref = {UAI2016},
}

@article{Kersting2020a,
  title={Convergence rates of {G}aussian {ODE} filters},
  author={Kersting, H. and Sullivan, T. J. and Hennig, P.},
  journal={Statistics and computing},
  volume={30},
  number={6},
  pages={1791--1816},
  year={2020},
  publisher={Springer}
}

@inproceedings{Kersting2020b,
  title={Differentiable likelihoods for fast inversion of ’likelihood-free’ dynamical systems},
  author={Kersting, H. and Kr{\"a}mer, N. and Schiegg, M. and Daniel, C. and Tiemann, M. and Hennig, P.},
  booktitle={International Conference on Machine Learning},
  pages={5198--5208},
  year={2020},
  organization={PMLR}
}

@book{King1998,
  title={Unifying political methodology: The likelihood theory of statistical inference},
  author={King, G.},
  year={1998},
  publisher={University of Michigan Press}
}

@article{Kimeldorf1970,
  title={A correspondence between {B}ayesian estimation on stochastic processes and smoothing by splines},
  author={Kimeldorf, G. S. and Wahba, G.},
  journal={The Annals of Mathematical Statistics},
  volume={41},
  number={2},
  pages={495--502},
  year={1970}
}

@article{Kimeldorf1971,
  title={Some results on {T}chebycheffian spline functions},
  author={Kimeldorf, George and Wahba, Grace},
  journal={Journal of mathematical analysis and applications},
  volume={33},
  number={1},
  pages={82--95},
  year={1971},
  publisher={Elsevier}
}

@article{Kitagawa1996,
  title={Monte {C}arlo filter and smoother for non-{G}aussian nonlinear state space models},
  author={Kitagawa, G.},
  journal={Journal of {C}omputational and {G}raphical {S}tatistics},
  volume={5},
  number={1},
  pages={1--25},
  year={1996}
}

@book{Kloeden2013,
  title={Numerical Solution of Stochastic Differential Equations},
  author={Kloeden, P. E. and Platen, E.},
  volume={23},
  year={2013},
  publisher={Springer Science \& Business Media}
}

@article{Knoth1989,
  title={A globalization scheme for the generalized {G}auss--{N}ewton method},
  author={Knoth, O},
  journal={Numerische Mathematik},
  volume={56},
  number={6},
  pages={591--607},
  year={1989},
  publisher={Springer}
}

@article{KokkalaSolinSarkka2015,
  author = {Juho Kokkala and Arno Solin and Simo S\"arkk\"a},
  title = {Sigma-Point Filtering and Smoothing Based Parameter Estimation
           in Nonlinear Dynamic Systems},
  journal = {Journal of Advances in Information Fusion},
  year = {to appear},
}

@article{Koyama2018,
  title={Projection smoothing for continuous and continuous-discrete stochastic dynamic systems},
  author={Koyama, S.},
  journal={Signal Processing},
  volume={144},
  pages={333--340},
  year={2018},
  publisher={Elsevier}
}

@article{Kurz2014a,
	author = {G. Kurz and I. Gilitschenski and S. Julier and U. D. Hanebeck},
	title = {Recursive {B}ingham Filter for Directional Estimation Involving 180 Degree Symmetry},
	journal = {Journal on Advances in Information Fusion},
	volume = {9},
	number = {2},
	pages= {90--105},
	year = {2014},
	publisher = {ISIF?},
}


@inproceedings{Kurz2013,
        author={G. Kurz and I. Gilitschenski and S. Julier and U. D. Hanebeck},
        booktitle =    {16th International Conference on Information Fusion},
        title = {Recursive Estimation of Orientation Based on the {B}ingham Distribution},
        year = {2013},
        crossref = {FUSION2013},
}

@proceedings{FUSION2013,
  title =        {16th International Conference on Information Fusion},
  booktitle =    {16th International Conference on Information Fusion},
  publisher = {IEEE},
  address = {Istanbul, Turkey},
  month =        {July 9 - 12},
  year =         {2013},
  organization = {ISIF},
}

@article{Kramer2020a,
  title={Stable implementation of probabilistic {ODE} solvers},
  author={Kr{\"a}mer, N. and Hennig, P.},
  journal={arXiv preprint arXiv:2012.10106},
  year={2020}
}

@article{Kramer2021a,
  title={Probabilistic {ODE} Solutions in Millions of Dimensions},
  author={Kr{\"a}mer, N. and Bosch, N. and Schmidt, J. and Hennig, P.},
  journal={arXiv preprint arXiv:2110.11812},
  year={2021}
}

@article{Kurz2016a,
	author = {Kurz, G. and Gilitschenski, I. and Hanebeck, U. D.},
	title = {Unscented von {M}ises--{F}isher Filtering},
	journal = {IEEE Signal Processing Letters},
	volume = {23},
	number = {4},
	pages= {463--467},
	year = {2016},
	publisher = {IEEE},
}


@article{Kushner1967,
  title={Approximations to optimal nonlinear filters},
  author={Kushner, H.},
  journal={IEEE Transactions on Automatic Control},
  volume={12},
  number={5},
  pages={546--556},
  year={1967},
  publisher={IEEE}
}


@article{Lefebvre2002,
  title={Comment on ``{A} new method for the nonlinear transformation of means and covariances in filters and estimators'' [with authors' reply]},
  author={Lefebvre, T. and Bruyninckx, H. and De Schuller, J.},
  journal={IEEE Transactions on Automatic Control},
  volume={47},
  number={8},
  pages={1406--1409},
  year={2002},
  publisher={IEEE}
}

@article{Lie2019,
  title={Strong convergence rates of probabilistic integrators for ordinary differential equations},
  author={Lie, H. C. and Stuart, A. M. and Sullivan, T. J.},
  journal={Statistics and Computing},
  volume={29},
  number={6},
  pages={1265--1283},
  year={2019},
  publisher={Springer}
}

@article{Lindsten2014,
  title={Particle {G}ibbs with ancestor sampling},
  author={Lindsten, F. and Jordan, M. I. and Sch{\"o}n, T. B.},
  journal={The Journal of Machine Learning Research},
  volume={15},
  number={1},
  pages={2145--2184},
  year={2014}
}

@phdthesis{Luo2006,
  title={Wiener chaos expansion and numerical solutions of stochastic partial differential equations},
  author={Luo, W.},
  year={2006},
  school={California Institute of Technology}
}

@article{Lyons2014,
  title={Series expansion approximations of {B}rownian motion for non-linear {K}alman filtering of diffusion processes},
  author={Lyons, S. M. J. and S{\"a}rkk{\"a}, S. and Storkey, A. J.},
  journal={IEEE Transactions on Signal Processing},
  volume={62},
  number={6},
  pages={1514--1524},
  year={2014},
  publisher={IEEE}
}

@inproceedings{Liu2013a,
  title={Generalized linear minimum mean-square error estimation},
  author={Liu, Yu and Li, X Rong},
  booktitle={2013 16th International Conference on Information Fusion},
  pages={1819--1826},
  year={2013},
  organization={IEEE}
}

@inproceedings{Liu2013b,
  title={Generalized linear minimum mean-square error estimation with application to space-object tracking},
  author={Liu, Yu and Li, X Rong and Chen, Huimin},
  booktitle={Signals, Systems and Computers, 2013 Asilomar Conference on},
  pages={2133--2137},
  year={2013},
  organization={IEEE}
}

@article{Lan2015a,
  title={Nonlinear estimation by {LMMSE}-based estimation with optimized uncorrelated augmentation},
  author={Lan, Jian and Li, X Rong},
  journal={IEEE Transactions on Signal Processing},
  volume={63},
  number={16},
  pages={4270--4283},
  year={2015},
  publisher={IEEE}
}

@inproceedings{Lan2014a,
  title={Nonlinear estimation by linear estimation with augmentation of uncorrelated conversion},
  author={Lan, Jian and Li, X Rong},
  booktitle={2014 17th International Conference on Information Fusion},
  pages={1--8},
  year={2014},
  organization={IEEE}
}

@inproceedings{Lee2018a,
  title={Bayesian Attitude Estimation with Approximate Matrix {F}isher Distributions on {SO}(3)},
  author={Lee, T.},
  booktitle={2018 IEEE Conference on Decision and Control (CDC)},
  pages={5319--5325},
  year={2018},
  crossref = {CDC2018},
}

@article{Lee2018b,
  title={Bayesian Attitude Estimation With the matrix {F}isher distribution on {SO}(3)},
  author={Lee, T.},
  journal={IEEE Transactions on Automatic Control},
  volume={63},
  number={10},
  pages={3377--3392},
  year={2018},
  publisher={IEEE}
}

@article{Leondes1970,
  title={Nonlinear smoothing theory},
  author={Leondes, C. T. and Peller, J. B. and Stear, E. B.},
  journal={IEEE Transactions on System Science and Cybernetics},
  volume={6},
  number={1},
  pages={63--71},
  year={1970},
  publisher={IEEE}
}

@inproceedings{LiKimMourikis2013,
    Author = "M. Li and B. H. Kim and A. I. Mourikis",
    Title = "Real-time motion tracking on a cellphone using inertial sensing and a rolling-shutter camera",
    Booktitle = "IEEE International Conference on Robotics and Automation (ICRA)",
    Pages = "4712--4719",
    Month = "May",
    Year = "2013"
}

@book{LindstromMadsenNielsen2015,
	  author="E. Lindstr{\"o}m and H. Madsen and J. N. Nielsen",
	  title="Statistics for Finance",
	  publisher="Chapman and Hall/{CRC}",
	  year = "2015"
}

@article{Ljung1979,
  title={Asymptotic behavior of the extended {K}alman filter as a parameter estimator for linear systems},
  author={Ljung, L.},
  journal={IEEE Transactions on Automatic Control},
  volume={24},
  number={1},
  pages={36--50},
  year={1979},
  publisher={IEEE}
}

@book{Mardia2000,
        Author = {Mardia, K. V. and Jupp, P. E.},
        Publisher = {Wiley},
        Title = {Directional Statistics},
        Year = {2000}
}

@article{Magnani2017,
	author = {E. Magnani and H. Kersting and M. Schober and P. Hennig},
	journal = {{arXiv:1709.08471 [cs.NA]}},
	month = sep,
	title = {{Bayesian Filtering for ODEs with Bounded Derivatives}},
	year = {2017}
}

@article{Marcus1973,
  title={Nemytsky operators on {S}obolev spaces},
  author={M. Marcus and V. J. Mizel},
  journal={Arch. Rational Mech. Anal.},
  volume={51},
  pages={347--370},
  year={1973}
}

@INPROCEEDINGS{Markovic2014a,
author={I. Marković and F. Chaumette and I. Petrović},
booktitle={2014 IEEE International Conference on Robotics and Automation (ICRA)},
title={Moving object detection, tracking and following using an omnidirectional camera on a mobile robot},
year={2014},
pages={5630-5635},
crossref = {ICRA2014},
}


@INPROCEEDINGS{Markovic2014b,
author={I. Marković and M. Bukal and J. Ćesić and I. Petrović},
booktitle={17th International Conference on Information Fusion},
title={Direction-only tracking of moving objects on the unit sphere via probabilistic data association},
year={2014},
crossref = {FUSION2014},
}

@article{Matsuda2021,
  title={Estimation of ordinary differential equation models with discretization error quantification},
  author={Matsuda, T. and Miyatake, Y.},
  journal={SIAM/ASA Journal on Uncertainty Quantification},
  volume={9},
  number={1},
  pages={302--331},
  year={2021},
  publisher={SIAM}
}

@book{Maybeck1982,
	author= {Maybeck, P. S.},
	title= {Stochastic Models, Estimation and Control},
        volume={1-3},
	publisher={Academic Press},
	year = {1979,1982,1982}
}

@article{Maggiar2018,
  title={A derivative-free trust-region algorithm for the optimization of functions smoothed via gaussian convolution using adaptive multiple importance sampling},
  author={Maggiar, A. and Wachter, A. and Dolinskaya, I. S. and Staum, J.},
  journal={SIAM Journal on Optimization},
  volume={28},
  number={2},
  pages={1478--1507},
  year={2018},
  publisher={SIAM}
}

@article{Martens2014a,
  title={New insights and perspectives on the natural gradient method},
  author={Martens, James},
  journal={arXiv preprint arXiv:1412.1193},
  year={2014}
}

@article{Masreliez1975,
        Author = {C. J. Masereliez},
        Journal = {Automatic Control, IEEE Transactions on},
        Pages = {107--},
        Title = {Approximate Non-Gaussian Filtering With Linear State and Observation Relations},
        Volume = {107-110},
        Year = {1975}
}

@article{McNameeStenger1967,
        Author = {J. McNamee and F. Stenger},
        Journal = {Numerische Mathematik},
        Pages = {327--344},
        Title = {Construction of Fully Symmetric Numerical Integration Formulas},
        Volume = {10},
        Year = {1967}
}

@article{Menda2020,
  title={Scalable Identification of Partially Observed Systems with Certainty-Equivalent {EM}},
  author={Menda, K. and de Becdeli{\`e}vre, J. and Gupta, J. K. and Kroo, I. and Kochenderfer, M. J. and Manchester, Z.},
  journal={arXiv preprint arXiv:2006.11615},
  year={2020}
}

@book{MarkleyCrassidis2014,
	author="Markley, F. L. and Crassidis, J. L.",
	title="Fundamentals of Spacecraft Attitude Determination",
	publisher="Springer",
	year = "2014"
}

@article{Mobahi2012,
  title={Gaussian smoothing and asymptotic convexity},
  author={Mobahi, H. and Ma, Y.},
  journal={Coordinated Science Laboratory Report no. UILU-ENG-12-2201, DC-254},
  year={2012},
  publisher={Coordinated Science Laboratory, University of Illinois at Urbana-Champaign}
}

@article{MorelandeGarciaFernandez2013,
    Author = "Morelande, M. R. and García-Fernández, {\'A}. F.",
    Title = "Analysis of {K}alman Filter Approximations for Nonlinear Measurements",
    Journal = "IEEE Transactions on Signal Processing",
    Volume = "61",
    Number = "22",
    Pages = "5477--5484",
    Year = "2013"
}

@book{Nielson1997,
  title={An Introduction to Integration and Measure Theory},
  author={Nielson, O. A.},
  year={1997},
  publisher={John Wiley \& Sons, Inc., New York.}
}

@article{Nielsen2009,
  title={Statistical exponential families: A digest with flash cards},
  author={Nielsen, F. and Garcia, V.},
  journal={arXiv preprint arXiv:0911.4863},
  year={2009}
}

@article{NielsenMadsen2001,
    Author = "Henrik Aa. Nielsen and Henrik Madsen",
    Title = "A generalization of some classical time seris tools",
    Journal = "Computaitonal Statistics \& Data Analysis",
    Volume = "31",
    Pages = "13--31",
    Year = "2001"
}

@article{Nordsieck1962,
  title={On numerical integration of ordinary differential equations},
  author={Nordsieck, A.},
  journal={Mathematics of Computation},
  volume={16},
  number={77},
  pages={22--49},
  year={1962}
}

@article{Nugari1988,
  title={Continuity and differentiability properties of the {N}emitskii operator in {H}{\"o}lder spaces},
  author={Nugari, R.},
  journal={Glasgow Mathematical Journal},
  volume={30},
  number={1},
  pages={59--65},
  year={1988},
  publisher={Cambridge University Press}
}

@article{Macdonald2015,
  title={Controversy in mechanistic modelling with {G}aussian processes},
  author={Macdonald, B. and Higham, C. and Husmeier, D.},
  journal={Proceedings of Machine Learning Research},
  volume={37},
  pages={1539--1547},
  year={2015},
  publisher={PMLR}
}

@article{Matsuda2019,
  title={Estimation of ordinary differential equation models with discretization error quantification},
  author={Matsuda, T. and Miyatake, Y.},
  journal={arXiv preprint arXiv:1907.10565},
  year={2019}
}

@inproceedings{Morelande2006,
    Author = "Morelande, M. R.",
    Title = "Tracking multiple targets with a sensor network",
    Booktitle = "9th International Conference on Information Fusion ({FUSION})",
    publisher="IEEE",
    Year = "10-13 July 2006"
}

@article{Oates2019a,
  title={A modern retrospective on probabilistic numerics},
  author={Oates, C. J. and Sullivan, T. J.},
  journal={Statistics and Computing},
  volume={29},
  number={6},
  pages={1335--1351},
  year={2019},
  publisher={Springer}
}

@article{Oates2019b,
  title={Optimality criteria for probabilistic numerical methods},
  author={Oates, C. and Cockayne, J. and Prangle, D. and Sullivan, T. J. and Girolami, M.},
  journal={arXiv preprint arXiv:1901.04326},
  year={2019}
}

@book{Oksendal2003,
	  author="B. {\O}ksendal",
	  title="Stochastic Differential Equations - An Introduction with Applications",
	  publisher="Springer",
	  year = "2003"
}

@article{Ollivier2017a,
  title={Online Natural Gradient as a Kalman Filter},
  author={Ollivier, Yann},
  journal={arXiv preprint arXiv:1703.00209},
  year={2017}
}

@techreport{Platanioti2005,
  title={A review of stochastic volatility: univariate and multivariate models},
  author={Platanioti, K and McCoy, EJ and Stephens, DA},
  year={2005},
}

@article{Price1983,
  title={Rolling with “slipping”: I},
  author={Price, G. C. and Williams, D.},
  journal={S{\'e}minaire de probabilit{\'e}s de Strasbourg},
  volume={17},
  pages={194--197},
  year={1983}
}


@inproceedings{Pruher2017b,
  title={Student-t process quadratures for filtering of non-linear systems with heavy-tailed noise},
  author={Pr{\"u}her, J. and Tronarp, F. and Karvonen, T. and S{\"a}rkk{\"a}, S. and Straka, O.},
  booktitle={20th International Conference on Information Fusion},
  year={2017},
  crossref = {FUSION2017},
}

@article{Pruher2017,
  title={Gaussian process quadrature moment transform},
  author={Pr{\"u}her, J. and Straka, O.},
  journal={IEEE Transactions on Automatic Control},
  volume={63},
  number={9},
  pages={2844--2854},
  year={2017},
  publisher={IEEE}
}

@inproceedings{PruherSimandl2016,
    author = {Prüher, J. and {\v{S}}imandl, M.},
    title = {{B}ayesian Quadrature Variance in Sigma-Point Filtering},
    booktitle = {Informatics in Control, Automation and Robotics 12th International Conference, ICINCO, Revised Selected Papers},
    pages = {355--370},
    crossref = {ICINCO2015},
}

@proceedings{ICINCO2015,
  editor = {Filipe, J. and Madani, K. and Gusikhin, O. and Sasiadek, J.},
  title =        {Informatics in Control, Automation and Robotics 12th International Conference, ICINCO},
  booktitle =    {Informatics in Control, Automation and Robotics 12th International Conference, ICINCO},
  publisher = {Springer},
  address = {Colmar, France},
  month =        {July 21 - 23},
  year =         {2015},
}


@article{Li2003,
  title={Survey of maneuvering target tracking. {P}art {I}. Dynamic models},
  author={Li, X. R. and Jilkov, V. P.},
  journal={IEEE Transactions on Aerospace and Electronic Systems},
  volume={39},
  number={4},
  pages={1333--1364},
  year={2003},
  publisher={IEEE}
}

@article{Ramsay2007,
  title={Parameter estimation for differential equations: a generalized smoothing approach},
  author={Ramsay, J. O. and Hooker, G. and Campbell, D. and Cao, J.},
  journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume={69},
  number={5},
  pages={741--796},
  year={2007},
  publisher={Wiley Online Library}
}

@article{RauchTungStriebel1965,
    Author = "H. E. Rauch and F. Tung and C. T. Striebel",
    Title = "Maximum likelihood estimates of linear dynamic system",
    Journal = "AIAA Journal",
    Volume = "3",
    Number = "8",
    Pages = "1445--1450",
    Year = "1965",
    Month = "Aug"
}

@article{ReifGuntherYazUnbehauen1999,
    Author = "Reif, K. and Günther, S. and Yaz, E. and Unbehauen, R.",
    Title = "Stochastic Stability of the Discrete-Time Extended {K}alman Filter",
    Journal = "IEEE Transactions on Automatic Control",
    Volume = "44",
    Number = "4",
    Pages = "714--728",
    Year = "1999",
    Month = "Apr"
}

@inproceedings{RothOzkan2013,
         title = {A {S}tudent's $t$ filter for heavy tailed process and measurement noise},
        author = {Roth, M. and {\"O}zkan, E. and Gustafsson, F.},
     booktitle = {2013 IEEE International Conference on Acoustics, Speech and Signal Processing},
         pages = {5770--5774},
          year = {2013},
         crossref = {ICASSP2013},
}

@book{Rall1969,
  title={Computational solution of nonlinear operator equations},
  author={Rall, L. B.},
  year={1969},
  publisher={Wiley}
}

@book{Rogers2000,
  title={Diffusions, Markov Processes and Martingales},
  author={Rogers, L. C. G. and Williams, D.},
  volume={1,2,3},
  year={2000},
  publisher={Cambridge university press}
}

@article{RueMartinoChopin2009,
    Author = "Rue, H. and Martino, S. and Chopin, N.",
    Title = "Approximate {B}ayesian inference for latent {G}aussian models by using integrated nested {L}aplace apprxomiations (with discussion)",
    Journal = "J.R. Statist. Soc.",
    Volume = "B",
    Number = "71",
    Pages = "319-392",
    Year = "2009"
}


@book{Rasmussen2006,
author = {C. E. Rasmussen and C. K. I. Williams},
title = {Gaussian Processes for Machine learning},
publisher ={{MIT} {P}ress},
year = {2006}
}

@book{RogersWilliams2000,
	author={Rogers, L. C. G. and Williams, D},
	title={Diffusions, {M}arkov Processes and Martingales, Volume I: Foundations},
	publisher={Cambridge university Press},
	year = {2000}
}

@inproceedings{Schober2014,
  title={Probabilistic {ODE} solvers with {R}unge-{K}utta means},
  author={Schober, M. and Duvenaud, D. K. and Hennig, P.},
booktitle = {Advances in Neural Information Processing Systems 27},
  pages={739--747},
  year={2014},
  crossref = {NIPS2014},
}

@article{Schober2019,
  title={A probabilistic model for the numerical solution of initial value problems},
  author={Schober, M. and S{\"a}rkk{\"a}, S. and Hennig, P.},
  journal={Statistics and Computing},
  volume={29},
  number={1},
  pages={99--122},
  month={January},
  year={2019},
  publisher={Springer}
}

@InProceedings{John2019,
  title = 	 {{GOODE}: A {G}aussian Off-The-Shelf Ordinary Differential Equation Solver},
  author = 	 {John, D. and Heuveline, V. and Schober, M.},
  booktitle = 	 {Proceedings of the 36th International Conference on Machine Learning},
  pages = 	 {3152--3162},
  year = 	 {2019},
  editor = 	 {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
  volume = 	 {97},
  series = 	 {Proceedings of Machine Learning Research},
  address = 	 {Long Beach, California, USA},
  month = 	 {09--15 Jun},
  publisher = 	 {PMLR},
}

@article{SandblomSvensson2012,
    Author = "Sandblom, F. and Svensson, L.",
    Title = "Moment Estimation Using a Marginalized Transform",
    Journal = "IEEE Transactions on Signal Processing",
    Volume = "60",
    Number = "2",
    Pages = "6138--6150",
    Year = "2012",
    Month = "Dec"
}

@PhDThesis{Sarkka:2006,
  title  = {Recursive {B}ayesian Inference on Stochastic
            Differential Equations},
  author = {Simo S\"arkk\"a},
  year   = {2006},
  school = {Helsinki University of Technology},
  type   = {Doctoral dissertation}
}

@Article{Sarkka2007,
  author  = {S. S\"arkk\"a},
  title   = {On Unscented {K}alman Filtering for State Estimation of
             Continuous-Time Nonlinear Systems},
  journal = {IEEE Transactions on Automatic Control},
   volume = {52(9)},
    pages = {1631--1641},
  year    = {2007},
}

@article{Sarkka2008,
    Author = {S\"arkk\"a, S.},
    Title = {Unscented {R}auch--{T}ung--{S}triebel {S}moother},
    Journal = {IEEE Transactions on Automatic Control},
    Volume = "53",
    Number = "3",
    Pages = "845--849",
    Year = "2008",
    Month = "April"
}

@article{Sarkka2008b,
  title={Application of {G}irsanov theorem to particle filtering of discretely observed continuous-time non-linear systems},
  author={S{\"a}rkk{\"a}, S. and Sottinen, T.},
  journal={Bayesian Analysis},
  volume={3},
  number={3},
  pages={555--584},
  year={2008},
  publisher={International Society for Bayesian Analysis}
}

@article{Sarkka2010a,
  title={Continuous-time and continuous--discrete-time unscented {R}auch--{T}ung--{S}triebel smoothers},
  author={S{\"a}rkk{\"a}, S.},
  journal={Signal Processing},
  volume={90},
  number={1},
  pages={225--235},
  year={2010},
  publisher={Elsevier}
}

@article{Sarkka2010b,
  title={On {G}aussian optimal smoothing of non-linear state space models},
  author={S\"arkk\"a, S. and Hartikainen, J.},
  journal={IEEE Transactions on Automatic Control},
  volume={55},
  number={8},
  pages={1938--1941},
  year={2010},
  publisher={IEEE}
}

@book{Sarkka2013,
        Author = {S. S\"arkk\"a},
        Publisher = {Cambridge University Press},
        Title = {{B}ayesian Filtering and Smoothing},
        Year = {2013}
}

@book{Sarkka2019,
        Author = {S. S\"arkk\"a and A. Solin},
        Publisher = {Cambridge University Press},
        Title = {Applied Stochastic Differential Equations},
        Year = {2019}
}



@article{SarkkaSarmavuori2013,
    Author = "S. S{\"a}rkk{\"a} and J. Sarmavuori",
    Title = "{G}aussian filtering and smoothing for continuous-discrete dynamic systems",
    Journal = "Signal Processing",
    Volume = "93",
    Pages = "500--510",
    Year = "2013",
}

@article{Sarkka2013a,
  title={Spatiotemporal learning via infinite-dimensional {B}ayesian filtering and smoothing: A look at {G}aussian process regression through {K}alman filtering},
  author={S\"arkk\"a, S. and Solin, A. and Hartikainen, J.},
  journal={IEEE Signal Processing Magazine},
  volume={30},
  number={4},
  pages={51--61},
  year={2013},
  publisher={IEEE}
}

@article{Sarkka2015,
  title={On the relation between {G}aussian process quadratures and sigma-point methods},
  author={S{\"a}rkk{\"a}, S. and Hartikainen, J. and Svensson, L. and Sandblom, F.},
  journal={arXiv preprint arXiv:1504.05994},
  year={2015}
}

@article{SarkkaHartikainenSvenssonSandblom2016,
    Author = "Särkkä, S. and Hartikainen, J. and Svensson, L. and Sandblom, F.",
    Title = "On the relation between {G}aussian process quadratures and sigma-point methods",
    Journal = "Journal of Advances in Information Fusion",
    Volume = "11",
    Number = "1",
    Pages = "31--46",
    Year = "2016",
}

@inproceedings{Sarkka2020a,
  title={Levenberg--{M}arquardt and Line-Search Extended {K}alman Smoothers},
  author={S{\"a}rkk{\"a}, S. and Svensson, L.},
  booktitle =  {2020 IEEE International Conference on Acoustics, Speech and Signal Processing},
  year = {2020},
  crossref = {ICASSP2020},
}

@article{Sidhu1979,
  title={Vector-valued {L}g-splines {I}. Interpolating splines},
  author={Sidhu, G. S. and Weinert, H. L.},
  journal={Journal of Mathematical Analysis and Applications},
  volume={70},
  number={2},
  pages={505--529},
  year={1979},
  publisher={Elsevier}
}

@inproceedings{Schmidt2021,
title={A Probabilistic State Space Model for Joint Inference from Differential Equations and Data},
author={J. Schmidt and N. Kr{\"a}mer and P. Hennig},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021}
}

@article{Schultz1970,
  title={Error bounds for polynomial spline interpolation},
  author={Schultz, M. H.},
  journal={Mathematics of Computation},
  volume={24},
  number={111},
  pages={507--515},
  year={1970}
}

@incollection{Schumaker1982,
  title={Optimal spline solutions of systems of ordinary differential equations},
  author={Schumaker, L. L.},
  booktitle={Differential Equations},
  pages={272--283},
  year={1982},
  publisher={Springer}
}

@article{Schon2005,
  title={Marginalized particle filters for mixed linear/nonlinear state-space models},
  author={Sch\"on, T. and Gustafsson, F. and Nordlund, P. J.},
  journal={IEEE Transactions on Signal Processing},
  volume={53},
  number={7},
  pages={2279--2289},
  year={2005},
  publisher={IEEE}
}

@article{Schweppe1965,
  title={Evaluation of likelihood functions for {G}aussian signals},
  author={Schweppe, F.},
  journal={IEEE Transactions on Information Theory},
  volume={11},
  number={1},
  pages={61--70},
  year={1965},
  publisher={IEEE}
}

@inproceedings{Steinbring2014,
  title={Progressive {G}aussian filtering using explicit likelihoods},
  author={Steinbring, J. and Hanebeck, U. D.},
  booktitle={17th International Conference on Information Fusion},
  year={2014},
    crossref = {FUSION2014},
}

@article{Stoica2004,
  title={Model-order selection: a review of information criterion rules},
  author={Stoica, P. and Selen, Y.},
  journal={IEEE Signal Processing Magazine},
  volume={21},
  number={4},
  pages={36--47},
  year={2004},
  publisher={IEEE}
}

@book{StoneStreitCorwinBell2014,
	author = {L. D. Stone and R. L. Streit and T. L. Corwin and K. L. Bell},
	title = {{B}ayesian Multiple Target Tracking},
	publisher = {Artech House},
	year = {2014},
}

@article{Storvik2002,
  title={Particle filters for state-space models with the presence of unknown static parameters},
  author={Storvik, G.},
  journal={IEEE Transactions on Signal Processing},
  volume={50},
  number={2},
  pages={281--289},
  year={2002},
  publisher={IEEE}
}

@book{Simon2006,
     author = {Simon, D.},
      title = {Optimal State Estimation: {K}alman, $\text{H}_\infty$, and Nonlinear Approaches},
  publisher = {John Wiley \& Sons},
       year = {2006},
}

@incollection{Skilling1991,
  title={Bayesian solution of ordinary differential equations},
  author={Skilling, J.},
  booktitle={Maximum entropy and Bayesian methods},
  pages={23--37},
  year={1992},
  publisher={Springer}
}

%    Year = "6-9 July 2015"
@inproceedings{SkoglundHendebyAxehill2015,
    Author = {Skoglund, M. and Hendeby, G. and Axehill, D.},
    Title = {Extended {K}alman Filter Modifications based on an Optimization View Point},
    Booktitle = {18th International Conference on Information Fusion},
    year = {2015},
    crossref = {FUSION2015},
}

@inproceedings{Solin2014,
  title={Gaussian quadratures for state space approximation of scale mixtures of squared exponential covariance functions},
  author={Solin, A. and S{\"a}rkk{\"a}, S.},
  booktitle={2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)},
  year={2014},
}

@article{Stein1981,
    Author = "C. M. Stein",
    Title = "Estimation of the mean of a multivariate {N}ormal distribution",
    Journal = "The Annals of Statistics",
    Volume = "9",
    Number = "6",
    Pages = "1135--1151",
    Year = "1981"
}

@article{Striebel1965,
    author = {Striebel, C. T.},
    title = {Partial Differential Equations for the Conditional Distribution of a {M}arkov Process Given Noisy Observations},
    journal = {Journal of Mathematical Analysis and Applications},
    volume = {11},
    pages = {151--159},
    year = {1965},
}

@inproceedings{Sun2017a,
  title={Nonlinear estimation by {H}ermite polynomial-based uncorrelated conversion within LMMSE framework},
  author={Sun, Tao and Xin, Ming},
  booktitle={American Control Conference (ACC), 2017},
  pages={4583--4588},
  year={2017},
  organization={IEEE}
}

@inproceedings{Sun2017b,
  title={Kernel based filter for nonlinear estimation},
  author={Sun, Haoyuan and Lan, Jian and Li, X Rong},
  booktitle={20th International Conference on Information Fusion},
  pages={1--8},
  year={2017},
  organization={IEEE}
}

@inproceedings{Solo2014,
  title={An approach to stochastic system identification in {R}iemannian manifolds},
  author={Solo, V.},
  booktitle={53rd IEEE Conference on Decision and Control},
  pages={6510--6515},
  year={2014},
  organization={IEEE}
}

@article{Sutter2016,
  title={A variational approach to path estimation and parameter inference of hidden diffusion processes},
  author={Sutter, T. and Ganguly, A. and Koeppl, H.},
  journal={The Journal of Machine Learning Research},
  volume={17},
  number={1},
  pages={6544--6580},
  year={2016},
  publisher={JMLR. org}
}

@article{Sarkka2020b,
  title={Temporal parallelization of {B}ayesian smoothers},
  author={S{\"a}rkk{\"a}, S. and Garc{\'\i}a-Fern{\'a}ndez, {\'A}. F.},
  journal={IEEE Transactions on Automatic Control},
  volume={66},
  number={1},
  pages={299--306},
  year={2020},
  publisher={IEEE}
}

@inproceedings{Teymur2016,
	title = {Probabilistic Linear Multistep Methods},
	author = {Teymur, Onur and Zygalakis, Kostas and Calderhead, Ben},
	booktitle = {Advances in Neural Information Processing Systems (NIPS)},
	year = {2016},
}

@inproceedings{Teymur2018a,
  title={Implicit Probabilistic Integrators for {ODEs}},
  author={Teymur, O. and Lie, H. C. and Sullivan, T. and Calderhead, B.},
	booktitle = {{Advances in Neural Information Processing Systems (NIPS)}},
  year={2018}
}

@book{TittertonWeston2004,
	author="D. H. Titterton and J. L. Weston",
	title="Strapdown Inertial Navigation Technology",
	publisher="The Institute of Electrical Engineers",
	year = "2004"
}

@article{Toni2009,
  title={Approximate {B}ayesian computation scheme for parameter inference and model selection in dynamical systems},
  author={Toni, T. and Welch, D. and Strelkowa, N. and Ipsen, A. and Stumpf, M. P. H.},
  journal={Journal of the Royal Society Interface},
  volume={6},
  number={31},
  pages={187--202},
  year={2009},
  publisher={The Royal Society London}
}

@INPROCEEDINGS{Traa2014,
author={J. Traa and P. Smaragdis},
booktitle={2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)},
title={Multiple speaker tracking with the Factorial von {M}ises--{F}isher Filter},
crossref = {MLSP2014},
}


% 5-8 July
@inproceedings{Tronarp2016,
	title = {Sigma-Point Filtering for Nonlinear Systems with Non-Additive heavy-Tailed Noise},
	author = {Tronarp, F. and Hostettler, R. and S\"arkk\"a, S.},
        booktitle =    {19th International Conference on Information Fusion},
	year = {2016},
        crossref = {FUSION2016},
}

@ARTICLE{Tronarp2018a,
author={Tronarp, F. and Garcia-Fernandez, A. F. and S{\"a}rkk{\"a}, S.},
journal={IEEE Signal Processing Letters},
title={Iterative Filtering and Smoothing In Non-Linear and Non-{G}aussian Systems Using Conditional Moments},
year={2018},
volume={25},
number={3},
pages={408-412},
ISSN={1070-9908},
month={March},
}

@inproceedings{Tronarp2018b,
  title={Continuous-Discrete von {M}ises--{F}isher Filtering on $\mathrm{S}^2$ for Reference Vector Tracking},
  author={Tronarp, F. and Hostettler, R. and S{\"a}rkk{\"a}, S.},
  booktitle={21st International Conference on Information Fusion},
  pages={1345--1352},
  year={2018},
  crossref = {FUSION2018},
}

%10-13 July
@inproceedings{Tronarp2018c,
  title={Non-Linear Continuous-Discrete Smoothing by Basis Function Expansions of {B}rownian Motion},
  author={Tronarp, F. and S{\"a}rkk{\"a}, S.},
  booktitle = {21th International Conference on Information Fusion},
  pages={1114--1121},
  year={2018},
  crossref = {FUSION2018},
}

@inproceedings{Tronarp2018d,
  title={Mixture representation of the {M}at{\'e}rn class with applications in state space approximations and {B}ayesian quadrature},
  author={Tronarp, F. and Karvonen, T. and S{\"a}rkk{\"a}, S.},
  booktitle={2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)},
  year={2018},
}

@article{Tronarp2019a,
  title={Iterative statistical linear regression for {G}aussian smoothing in continuous-time non-linear stochastic dynamic systems},
  author={Tronarp, F. and S{\"a}rkk{\"a}, S.},
  journal={Signal Processing},
  volume={159},
  pages={1--12},
  year={2019},
  publisher={Elsevier}
}

%12-17 May
@inproceedings{Tronarp2019b,
  title={Updates in {B}ayesian Filtering by Continuous Projections on a Manifold of Densities},
  author={Tronarp, F. and S{\"a}rkk{\"a}, S.},
  booktitle =    {2019 IEEE International Conference on Acoustics, Speech and Signal Processing},
  pages={5032--5036},
  year={2019},
  crossref = {ICASSP2019},
}

@article{Tronarp2019c,
  title={Probabilistic solutions to ordinary differential equations as nonlinear {B}ayesian filtering: a new perspective},
  author={Tronarp, F. and Kersting, H. and S{\"a}rkk{\"a}, S. and Hennig, P.},
  journal={Statistics and Computing},
  volume={29},
  number={6},
  pages={1297--1315},
  year={2019},
  publisher={Springer}
}


@article{Tronarp2019d,
  title={Student's $ t $-Filters for Noise Scale Estimation},
  author={Tronarp, F. and Karvonen, T. and S{\"a}rkk{\"a}, S.},
  journal={IEEE Signal Processing Letters},
  volume={26},
  number={2},
  pages={352--356},
  year={2019},
  publisher={IEEE}
}

@article{Tronarp2021a,
  title={Bayesian {ODE} solvers: The maximum a posteriori estimate},
  author={Tronarp, F. and S{\"a}rkk{\"a}, S. and Hennig, P.},
  journal={Statistics and Computing},
  volume={31},
  number={3},
  pages={1--18},
  year={2021},
  publisher={Springer}
}

@article{Tsagris2014,
  title={On the folded normal distribution},
  author={Tsagris, M. and Beneki, C. and Hassani, H.},
  journal={Mathematics},
  volume={2},
  number={1},
  pages={12--28},
  year={2014},
  publisher={Multidisciplinary Digital Publishing Institute}
}

@article{Valent1985,
  title={A property of multiplication in {S}obolev spaces. {S}ome applications},
  author={Valent, T.},
  journal={Rendiconti del Seminario Matematico della Universit{\`a} di Padova},
  volume={74},
  pages={63--73},
  year={1985}
}

@book{Valent2013,
  title={Boundary value problems of finite elasticity: local theorems on existence, uniqueness, and analytic dependence on data},
  author={Valent, T.},
  volume={31},
  year={2013},
  publisher={Springer Science \& Business Media}
}

@article{VanDenBergLewis1985,
  title={Brownian motion on a hypersurface},
  author={Van Den Berg, M. and Lewis, J. T.},
  journal={Bulletin of the London Mathematical Society},
  volume={17},
  number={2},
  pages={144--150},
  year={1985},
  publisher={Wiley Online Library}
}

@article{Varah1982,
  title={A spline least squares method for numerical parameter estimation in differential equations},
  author={Varah, J. M.},
  journal={SIAM Journal on Scientific and Statistical Computing},
  volume={3},
  number={1},
  pages={28--46},
  year={1982},
  publisher={SIAM}
}

@incollection{VanDerVaart2008,
  title={Reproducing kernel {H}ilbert spaces of {G}aussian priors},
  author={van der Vaart, Aad W. and van Zanten, J. Harry },
  booktitle={Pushing the limits of contemporary statistics: contributions in honor of Jayanta K. Ghosh},
  pages={200--222},
  year={2008},
  publisher={Institute of Mathematical Statistics}
}

@book{Voit2000,
  title={Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists},
  author={Voit, E. O.},
  year={2000},
  publisher={Cambridge University Press}
}

@article{Wahba1973,
  title={A class of approximate solutions to linear operator equations},
  author={Wahba, G.},
  journal={Journal of Approximation Theory},
  volume={9},
  number={1},
  pages={61--77},
  year={1973},
  publisher={Elsevier}
}

@article{wahba1973b,
  title={Convergence rates of certain approximate solutions to {F}redholm integral equations of the first kind},
  author={Wahba, G.},
  journal={Journal of Approximation Theory},
  volume={7},
  number={2},
  pages={167--185},
  year={1973},
  publisher={Academic Press}
}

@article{Wahba1978a,
  title={Improper priors, spline smoothing and the problem of guarding against model errors in regression},
  author={Wahba, G.},
  journal={Journal of the Royal Statistical Society: Series B (Methodological)},
  volume={40},
  number={3},
  pages={364--372},
  year={1978},
  publisher={Wiley Online Library}
}

@inproceedings{Wang2017,
  title={Laplace {$\ell_1$}  robust {K}alman filter based on majorization minimization},
  author={Wang, H. and Li, H. and Zhang, W. and Wang, H.},
  booktitle={20th International Conference on Information Fusion},
  year={2017},
  organization={IEEE}
}


@article{Wang2018,
  title={A Role for Symmetry in the {B}ayesian Solution of Differential Equations},
  author={Wang, J. and Cockayne, J. and Oates, C. J.},
  journal={Bayesian Analysis},
  year={2018},
  publisher={International Society for Bayesian Analysis}
}

@incollection{WanVanDerMerwe2001,
    Author = "Wan, E. A. and van der Merwe, R.",
    Editor = "Haykin, Simon",
    Title = "The Unscented {K}alman Filtering",
    Booktitle = "Kalman Filtering and Neural Networks",
    Publisher = "John Wiley \& Sons",
    Pages = "221--280",
    Chapter = "7",
    Year = "2001"
}

@article{Weinert1974,
  title={Stochastic interpretations and recursive algorithms for spline functions},
  author={Weinert, H. L. and Kailath, T.},
  journal={The Annals of Statistics},
  volume={2},
  number={4},
  pages={787--794},
  year={1974},
  publisher={Institute of Mathematical Statistics}
}

@article{Wendland2005,
  title={Approximate interpolation with applications to selecting smoothing parameters},
  author={Wendland, Holger and Rieger, Christian},
  journal={Numerische Mathematik},
  volume={101},
  number={4},
  pages={729--748},
  year={2005},
  publisher={Springer}
}

@article{Weinert1978,
  title={A stochastic framework for recursive computation of spline functions--Part {I}: Interpolating splines},
  author={Weinert, H. L. and Sidhu, G. S.},
  journal={IEEE Transactions on Information Theory},
  volume={24},
  number={1},
  pages={45--50},
  year={1978},
  publisher={IEEE}
}

@article{Weinert1979,
  title={Arma {S}plines, {S}ystem {I}nverses, and {L}east-{S}quares {E}stimates},
  author={Weinert, H. L. and Desai, U. B. and Sidhu, G. S.},
  journal={SIAM Journal on Control and Optimization},
  volume={17},
  number={4},
  pages={525--536},
  year={1979},
  publisher={SIAM}
}

@inproceedings{Wenk2019,
  title={Fast {G}aussian process based gradient matching for parameter identification in systems of nonlinear {ODE}s},
  author={Wenk, P. and Gotovos, A. and Bauer, S. and Gorbach, N. S. and Krause, A. and Buhmann, J. M.},
  booktitle={The 22nd International Conference on Artificial Intelligence and Statistics},
  pages={1351--1360},
  year={2019},
  organization={PMLR}
}

@inproceedings{Wenk2020,
  title={ {ODIN}: {ODE}-informed regression for parameter and state inference in time-continuous dynamical systems},
  author={Wenk, P. and Abbati, G. and Osborne, M. A. and Sch{\"o}lkopf, B. and Krause, A. and Bauer, S.},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  pages={6364--6371},
  year={2020}
}

@article{West1985,
  title={Dynamic generalized linear models and {B}ayesian forecasting},
  author={West, M. and Harrison, P. J. and Migon, H. S.},
  journal={Journal of the American Statistical Association},
  volume={80},
  number={389},
  pages={73--83},
  year={1985},
  publisher={Taylor \& Francis Group}
}

@article{Westfall2014,
        Author = {Peter H. Westfall},
        Journal = {The American Statistician},
        Pages = {191--195},
        Title = {Kurtosis as {P}eakedness, 1905-2014. {R.I.P.}},
        Volume = {68},
        Year = {2014}
}

@inproceedings{Wigren2019,
  title={Parameter elimination in particle {G}ibbs sampling},
  author={Wigren, A. and Risuleo, R. S. and Murray, L. and Lindsten, F.},
  booktitle={Advances in Neural Information Processing Systems},
  pages={8916--8927},
  year={2019}
}

@article{WongZakai1965,
       title = {On the convergence of ordinary integrals to stochastic integrals},
      author = {Wong, E. and Zakai, M.},
        year = {1965},
     journal = {The Annals of Mathematical Statistics},
      volume = {36},
      number = {5},
       pages = {1560--1564}
}

@incollection{WuKundu1989,
    Author = "Wu, W.R and Kundu, A",
    Title = "Kalman filtering in non-Gaussian environment using efficient score function approximation",
    Booktitle = "Proceedings of 1989 {IEEE} Symposium on Circuits and Systems",
    Pages = "413-416",
    Year = "1989"
}

@article{WuHuWuHu2006,
    Author = "Wu, Y. and Hu, D. and Wu, M. and Hu, X.",
    Title = "A Numerical-Integration Perspective on {G}aussian Filters",
    Journal = "IEEE Transactions on Signal Processing",
    Volume = "54",
    Number = "8",
    Pages = "2910--2921",
    Year = "2006",
    Month = "Aug"
}

@inproceedings{Wuthrich2016a,
  title={Robust {G}aussian filtering using a pseudo measurement},
  author={W{\"u}thrich, Manuel and Cifuentes, Cristina Garcia and Trimpe, Sebastian and Meier, Franziska and Bohg, Jeannette and Issac, Jan and Schaal, Stefan},
  booktitle={American Control Conference (ACC), 2016},
  pages={3606--3613},
  year={2016},
  organization={IEEE}
}

@article{Wuthrich2016b,
  title={A new perspective and extension of the {G}aussian Filter},
  author={W{\"u}thrich, Manuel and Trimpe, Sebastian and Garcia Cifuentes, Cristina and Kappler, Daniel and Schaal, Stefan},
  journal={The International Journal of Robotics Research},
  volume={35},
  number={14},
  pages={1731--1749},
  year={2016},
  publisher={SAGE Publications Sage UK: London, England}
}

@article{Zhou2014,
  title={Gradient-based adaptive stochastic search for non-differentiable optimization},
  author={Zhou, E. and Hu, J.},
  journal={IEEE Transactions on Automatic Control},
  volume={59},
  number={7},
  pages={1818--1832},
  year={2014},
  publisher={IEEE}
}

@article{Zhao2004,
  title={Best linear unbiased filtering with nonlinear measurements for target tracking},
  author={Zhao, Zhanlue and Li, TX Rong and Jilkov, Vesselin P},
  journal={IEEE Transactions on Aerospace and electronic systems},
  volume={40},
  number={4},
  pages={1324--1336},
  year={2004},
  publisher={IEEE}
}

@inproceedings{Zhang2017a,
  title={Gaussian sum filtering using uncorrelated conversion for nonlinear estimation},
  author={Zhang, Yingjie and Lan, Jian},
  booktitle={2017 20th International Conference on Information Fusion},
  pages={1--8},
  year={2017},
  organization={IEEE}
}


%%%
%%% LIST OF PROCEEDINGS FOR CROSSREF
%%%

@proceedings{ACC1995,
  title =        {Proceedings of 1995 American Control Conference},
  booktitle =    {Proceedings of 1995 American Control Conference},
  publisher = {IEEE},
  address = {Seattle, WA, USA},
  month =        {June 21 - 23},
  year =         {1995},
  organization = {AACC},
}

@proceedings{CDC1984,
  title = {The 23rd IEEE Conference on Decision and Control},
  booktitle = {The 23rd IEEE Conference on Decision and Control},
  publisher = {IEEE},
  address = {Las Vegas, Nevada, USA},
  month = {December 12 - 14},
  year =  {1984},
}

@proceedings{CDC2018,
  title = {2018 IEEE Conference on Decision and Control (CDC)},
  booktitle = {2018 IEEE Conference on Decision and Control (CDC)},
  publisher = {IEEE},
  address = {Miami Beach, FL, USA},
  month = {December 17 - 19},
  year =  {2014},
}

@proceedings{FUSION2014,
  title =        {17th International Conference on Information Fusion},
  booktitle =    {17th International Conference on Information Fusion},
  publisher = {IEEE},
  address = {Salamanca, Spain},
  month =        {July 7 - 10},
  year =         {2014},
  organization = {ISIF},
}

@proceedings{FUSION2015,
  title =        {18th International Conference on Information Fusion},
  booktitle =    {18th International Conference on Information Fusion},
  publisher = {IEEE},
  address = {Washington, DC, USA},
  month =        {July 6 - 9},
  year =         {2014},
  organization = {ISIF},
}

@proceedings{FUSION2016,
  title =        {19th International Conference on Information Fusion},
  booktitle =    {19th International Conference on Information Fusion},
  publisher = {IEEE},
  address = {Heidelberg, Germany},
  month =        {July 5 - 8},
  year =         {2016},
  organization = {ISIF},
}

@proceedings{FUSION2017,
  title =        {20th International Conference on Information Fusion},
  booktitle =    {20th International Conference on Information Fusion},
  publisher = {IEEE},
  address = {Xi'an, China},
  month =        {July 10 - 13},
  year =         {2017},
  organization = {ISIF},
}

@proceedings{FUSION2018,
  title =        {21th International Conference on Information Fusion},
  booktitle =    {21th International Conference on Information Fusion},
  publisher = {IEEE},
  address = {Cambridge, United Kingdom},
  month =        {July 10 - 13},
  year =         {2018},
  organization = {ISIF},
}

@proceedings{ICASSP2013,
  title =        {2013 IEEE International Conference on Acoustics, Speech and Signal Processing},
  booktitle =    {2013 IEEE International Conference on Acoustics, Speech and Signal Processing},
  publisher = {IEEE},
  address = {Vancouver, B.C, Canada},
  month =        {May 26 - 31},
  year =         {2013},
}

@proceedings{ICASSP2019,
  title =        {2019 IEEE International Conference on Acoustics, Speech and Signal Processing},
  booktitle =    {2019 IEEE International Conference on Acoustics, Speech and Signal Processing},
  publisher = {IEEE},
  address = {Brighton, United Kingdom},
  month =        {May 12 - 17},
  year =         {2019},
}

@proceedings{ICASSP2020,
  title =        {2020 IEEE International Conference on Acoustics, Speech and Signal Processing},
  booktitle =    {2020 IEEE International Conference on Acoustics, Speech and Signal Processing},
  publisher = {IEEE},
  address = {Virtual location},
  month =        {May 4 - 8},
  year =         {2020},
}

@proceedings{ICRA2014,
  title =        {2014 IEEE International Conference on Robotics and Automation (ICRA)},
  booktitle =    {2014 IEEE International Conference on Robotics and Automation (ICRA)},
  publisher = {IEEE},
  address = {Hong Kong, China},
  month =        {May 31 - June 7},
  year =         {2014},
}

@proceedings{ISPA2005,
  title =        {Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis},
  booktitle =    {Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis},
  publisher = {IEEE},
  address = {Zagreb, Croatia},
  month =        {September 15 - 17},
  year =         {2005},
}

@proceedings{MLSP2014,
  title={2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)},
  booktitle={2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)},
  publisher = {IEEE},
  address = {Reims, France},
  month =        {September 21 - 24},
  year =         {2014},
}

@proceedings{MLSP2017,
  title =        {27th International Workshop on Machine Learning for Signal Processing},
  booktitle =    {27th International Workshop on Machine Learning for Signal Processing},
  publisher = {IEEE},
  address = {Tokyo, Japan},
  month =        {September 25 - 28},
  year =         {2017},
  organization = {IEEE},
}

@proceedings{NIPS2007,
  editor = {J. C. Platt and D. Koller and Y. Singer and S. T. Roweis},
  title =        {Advances in Neural Information Processing Systems 20},
  booktitle =    {Advances in Neural Information Processing Systems 20},
  publisher = {Curran Associates, Inc.},
  address = {Vancouver, B.C., Canada},
  month =        {December 3 - 5},
  year =         {2007},
}

@proceedings{NIPS2014,
  editor = {Z. Ghahramani and M. Welling and C. Cortes and N. D. Lawrence and K. Q. Weinberger},
  booktitle = {Advances in Neural Information Processing Systems 27},
  title = {Advances in Neural Information Processing Systems 27},
  publisher = {Curran Associates, Inc.},
  address = {Montr\'eal, Canada},
  month =        {December 8 - 13},
  year =         {2007},
}

@proceedings{UAI2016,
	booktitle = {{Uncertainty in Artificial Intelligence (UAI) 2016}},
	title = {{Uncertainty in Artificial Intelligence (UAI) 2016}},
  address = {New York City, NY, USA},
  month =        {June 25 - 29},
  year =         {2016},
  organization = {AUAI},
}

@article{Menda2021,
  author={Menda, Kunal and Laird, Lucas and Kochenderfer, Mykel J. and Caceres, Rajmonda S.},
  title={Explaining {COVID}-19 outbreaks with reactive {SEIRD} models},
  journal={Scientific Reports},
  year={2021},
  month={Sep},
  day={09},
  volume={11},
  number={1},
  pages={17905},
}

@article{lauer2020incubation,
  title={The incubation period of coronavirus disease 2019 ({COVID}-19) from publicly reported confirmed cases: estimation and application},
  author={Lauer, Stephen A and Grantz, Kyra H and Bi, Qifang and Jones, Forrest K and Zheng, Qulu and Meredith, Hannah R and Azman, Andrew S and Reich, Nicholas G and Lessler, Justin},
  journal={Annals of internal medicine},
  volume={172},
  number={9},
  pages={577--582},
  year={2020},
  publisher={American College of Physicians}
}

@article{Bi2020,
  author={Bi, Qifang and Wu, Yongsheng and Mei, Shujiang and Ye, Chenfei and Zou, Xuan and Zhang, Zhen and Liu, Xiaojian and Wei, Lan and Truelove, Shaun A. and Zhang, Tong and Gao, Wei and Cheng, Cong and Tang, Xiujuan and Wu, Xiaoliang and Wu, Yu and Sun, Binbin and Huang, Suli and Sun, Yu and Zhang, Juncen and Ma, Ting and Lessler, Justin and Feng, Tiejian},
  title={Epidemiology and transmission of {COVID}-19 in 391 cases and 1286 of their close contacts in {S}henzhen, {C}hina: a retrospective cohort study},
  journal={The Lancet. Infectious diseases},
  year={2020},
  month={Aug},
  edition={2020/04/27},
  publisher={Elsevier Ltd.},
  volume={20},
  number={8},
  pages={911-919},
}

@article{rackauckas2017differentialequations,
  title={Differential{E}quations.jl--a performant and feature-rich ecosystem for solving differential equations in julia},
  author={Rackauckas, Christopher and Nie, Qing},
  journal={Journal of Open Research Software},
  volume={5},
  number={1},
  year={2017},
  publisher={Ubiquity Press}
}

@article{Bezanson_Julia_A_fresh_2017,
  author = {Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and Shah, Viral B.},
  doi = {10.1137/141000671},
  journal = {SIAM Review},
  month = {9},
  number = {1},
  pages = {65--98},
  title = {{Julia: A fresh approach to numerical computing}},
  volume = {59},
  year = {2017}
}

@article{Optim.jl-2018,
  author  = {Mogensen, Patrick Kofod and Riseth, Asbj{\o}rn Nilsen},
  title   = {Optim: A mathematical optimization package for {Julia}},
  journal = {Journal of Open Source Software},
  year    = {2018},
  volume  = {3},
  number  = {24},
  pages   = {615},
  doi     = {10.21105/joss.00615}
}

@Book{NoceWrig06,
  author    = {Jorge Nocedal and Stephen J. Wright},
  publisher = {Springer},
  title     = {Numerical Optimization},
  year      = {2006},
  address   = {New York, NY, USA},
  edition   = {2e},
}

@article{hagerzhang2006,
  author = {Hager, William W. and Zhang, Hongchao},
  title = {Algorithm 851: {CG\_DESCENT}, a Conjugate Gradient Method with Guaranteed Descent},
  year = {2006},
  publisher = {Association for Computing Machinery},
  address = {New York, NY, USA},
  volume = {32},
  number = {1},
  journal = {ACM Trans. Math. Softw.},
  pages = {113–137},
  numpages = {25},
}

@article{hethcote2000mathematics,
  title={The mathematics of infectious diseases},
  author={Hethcote, Herbert W},
  journal={SIAM review},
  volume={42},
  number={4},
  pages={599--653},
  year={2000},
  publisher={SIAM}
}
@article{volterra,
    author = {Volterra, Vito},
    title = "{Variations and Fluctuations of the Number of Individuals in Animal Species living together}",
    journal = {ICES Journal of Marine Science},
    volume = {3},
    number = {1},
    pages = {3-51},
    year = {1928},
}

@book{lotka,
  title={Elements of Physical Biology},
  author={Lotka, A.J.},
  lccn={25006649},
  year={1925},
  publisher={Williams \& Wilkins}
}

@Article{FitzHugh1955,
  author={FitzHugh, Richard},
  title={Mathematical models of threshold phenomena in the nerve membrane},
  journal={The bulletin of mathematical biophysics},
  year={1955},
  volume={17},
  number={4},
  pages={257-278},
}

@ARTICLE{Nagumo1962,
  author={Nagumo, J. and Arimoto, S. and Yoshizawa, S.},
  journal={Proceedings of the IRE},
  title={An Active Pulse Transmission Line Simulating Nerve Axon},
  year={1962},
  volume={50},
  number={10},
  pages={2061-2070},
}

@article{tsit5,
 title={Runge--{K}utta pairs of order 5 (4) satisfying only the first column simplifying assumption},
 author={Tsitouras, Ch},
 journal={Computers \& Mathematics with Applications},
 volume={62},
 year={2011},
 publisher={Elsevier}
}

@article{radau,
  title={Stiff differential equations solved by {R}adau methods},
  author={Hairer, Ernst and Wanner, Gerhard},
  journal={Journal of Computational and Applied Mathematics},
  volume={111},
  year={1999},
  publisher={Elsevier}
}
