Abstract
We develop a Metropolis algorithm to perform Bayesian inference for models given by coupled stochastic differential equations. A key challenge in developing practical algorithms is the computation of the likelihood. We address this problem through the use of a fast method to track the probability density function of the stochastic differential equation. The method applies quadrature to the Chapman–Kolmogorov equation associated with a temporal discretization of the stochastic differential equation. The inference method can be adapted to scenarios in which we have multiple observations at one time, multiple time series, or observations with large and/or irregular temporal spacing. Computational tests show that the resulting Metropolis algorithm is capable of efficient inference for an electrical oscillator model.
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References
Archambeau, C., Cornford, D., Opper, M., Shawe-Taylor, J.: Gaussian process approximations of stochastic differential equations. J. Mach. Learn. Res. Workshop Conf. Proc. 1, 1–16 (2007)
Archambeau, C., Opper, M., Shen, Y., Cornford, D., Shawe-Taylor, J.: Variational inference for diffusion processes. Adv. Neural Inf. Process. Syst. 20, 17–24 (2007)
Bhat, H.S., Madushani, R.W.M.A.: Density tracking by quadrature for stochastic differential equations, arXiv:1610.09572 [stat.CO] (2016)
Fuchs, C.: Inference for Diffusion Processes: With Applications in Life Sciences. Springer, Berlin (2013)
Iacus, S.M.: Simulation and Inference for Stochastic Differential Equations: With R Examples. Springer Series in Statistics. Springer, New York (2009)
King, A.A., Nguyen, D., Ionides, E.L., et al.: Statistical inference for partially observed Markov processes via the R package pomp. J. Stat. Softw. 69, 1–43 (2016)
Picchini, U.: Inference for SDE models via approximate Bayesian computation. J. Comput. Graph. Stat. 23(4), 1080–1100 (2014)
Ruttor, A., Batz, P., Opper, M.: Approximate Gaussian process inference for the drift function in stochastic differential equations. Adv. Neural Inf. Process. Syst. 26, 2040–2048 (2013)
Sørensen, H.: Parametric inference for diffusion processes observed at discrete points in time: a survey. Int. Stat. Rev. 72(3), 337–354 (2004)
Vrettas, M.D., Opper, M., Cornford, D.: Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations. Phys. Rev. E 91(012148) (2015)
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Bhat, H.S., Madushani, R.W.M.A., Rawat, S. (2017). Bayesian Inference of Stochastic Pursuit Models from Basketball Tracking Data. In: Argiento, R., Lanzarone, E., Antoniano Villalobos, I., Mattei, A. (eds) Bayesian Statistics in Action. BAYSM 2016. Springer Proceedings in Mathematics & Statistics, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-319-54084-9_12
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DOI: https://doi.org/10.1007/978-3-319-54084-9_12
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