Coupling the SAEM algorithm and the extended Kalman filter for maximum likelihood estimation in mixed-effects diffusion models

Statistics and its Interface

Volumn 6, Issue 4, 2013, Pages 519-532

  Delattre, Maud ^a   Lavielle, Marc ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Extended kalman filter; Mixed effects models; SAEM; Stochastic differential equations

Indexed keywords

EID: 84893350019     PISSN: 19387989     EISSN: 19387997     Source Type: Journal    
DOI: 10.4310/SII.2013.v6.n4.a10     Document Type: Article

References (25)

1. Allassonniere, S., Kuhn, E. and Trouvé, A. (2010). Construction of Bayesian deformable models via a stochastic approximation algorithm: A convergence study. Bernoulli 16 641-678. MR2730643
2. Andrieu, C., Doucet, A. and Holenstein, R. (2010). Particle markov chain Monte Carlo. Journal of the Royal Statistical Society: Series B 72 269-342. MR2758115
3. Bergstrand, M., Hooker, A., Wallin, J. E. and Karlsson, M. O. (2011). Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models. AAPS J. 13 143-151.
4. Bleakley, K. and Lavielle, M. (2011). Automatic data binning for improved visual diagnosis of pharmacometric models. Journal of Pharmacokinetics and Pharmacodynamics 38 861-871.
5. Cappé, O., Godsill, S. J. and Moulines, E. (2007). An overview of existing methods and recent advances in sequential Monte Carlo. Proceedings of the IEEE 95 899-924.
6. Delattre, M., Genon-Catalot, V. and Samson, A. (2013). Maximum likelihood estimation for stochastic differential equations with random effects. Scandinavian Journal of Statistics, to appear.
7. Delyon, B., Lavielle, M. and Moulines, E. (1999). Convergence of a stochastic approximation version of the EM algorithm. The Annals of Statistics 27 94-128. MR1701103
8. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society - Series B 39 1-38. MR0501537
9. Ditlevsen, S. and Gaetano, A. D. (2005). Mixed effects in stochastic differential equation models. REVSTAT Statistical Journal 3 137-153. MR2259358
10. Donnet, S. and Samson, A. (2008). Parametric inference for mixed models defined by stochastic differential equations. ESAIM: Probability and Statistics 12 196-218. MR2374638
11. Donnet, S. and Samson, A. (2010). EM algorithm coupled with particle filter for maximum likelihood parameter estimation of stochastic differential mixed-effects models. Technical report. http://hal.archives-ouvertes.fr/hal-00519576/.
12. Doucet, A., de Freitas, N. and Gordon, N. (2001). Sequential Monte Carlo Methods in Practice. Springer. MR1847783
13. Faugeras, O., Touboul, J. and Cessac, B. (2009). A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs. Frontiers in Computational Neuroscience 3 1-28.
14. Grewal, M. S. and Andrews, A. P. (2008). Kalman Filtering: Theory and Practice Using MATLAB, Third ed. Wiley.
15. Klim, S., Mortensen, S. B., Kristensen, N. R., Overgaard, R. V. and Madsen, H. (2009). Population stochastic modelling (PSM)-an R package for mixed-effects models based on stochastic differential equations. Computer Methods and Programs in Biomedicine 94 279-289.
16. Kuhn, E. and Lavielle, M. (2004). Coupling a stochastic approximation version of EM with an MCMC procedure. ESAIM: Probability and Statistics 8 115-131. MR2085610
17. Kuhn, E. and Lavielle, M. (2005). Maximum likelihood estimation in nonlinear mixed effects models. Computational Statistics and Data Analysis 49 1020-1038. MR2143055
18. Lixoft, (2013). Monolix 4.2.1 User Guide. http://www.lixoft.eu/monolix/documentation.
19. Mazzoni, T. (2008). Computational aspects of continuousdiscrete extended Kalman-filtering. Computational Statistics 23 519-539. MR2448180
20. Mbalawata, I. S., Särkkä, S. and Haario, H. (2012). Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering. Computational Statistics 1-29.
21. Overgaard, R. V., Jonsson, N., TornØe, C. W. and Madsen, H. (2005). Non-linear mixed-effects models with stochastic differential equations: Implementation of an estimation algorithm. Journal of Pharmacokinetics and Pharmacodynamics 32 85-107.
22. Picchini, U. and Ditlevsen, S. (2011). Practical estimation of high dimensional stochastic differential mixed-effects models. Computational Statistics and Data Analysis 55 1426-1444. MR2741425
23. Picchini, U., Gaetano, A. D. and Ditlevsen, S. (2010). Stochastic differential mixed-effects models. Scandinavian Journal of Statistics 37 67-90. MR2675940
24. Pinheiro, J. C. and Bates, D. M. (2000). Mixed-Effects Models in S and S-PLUS. Springer Verlag.
25. TornØe, C. W., Overgaard, R. V., AgersØ, H., Nielsen, H. A., Madsen, H. and Jonsson, E. N. (2005). Stochastic differential equations in NONMEM: Implementation, application, and comparison with ordinary differential equations. Pharmaceutical Research 22 1247-1258.