Adaptive mixture modeling metropolis methods for bayesian analysis of nonlinear state-space models

Journal of Computational and Graphical Statistics

Volumn 19, Issue 2, 2010, Pages 260-280

  Niemi, Jarad ^a   West, Mike ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Duke University   (United States)

Author keywords

Bayesian computation; Forward filtering, backward sampling; Regenerating mixture procedure; Smoothing in state space models; Systems biology

Indexed keywords

EID: 77956652910     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2010.08117     Document Type: Article

References (40)

1. Alspach, D. L., and Sorenson, H. W. (1972), "Non-Linear Bayesian Estimation Using Gaussian Sum Approximations," IEEE Transactions on Automatic Control, AC-17, 439-448. [263]
2. Andrade Netto, M. L., Gimeno, L., and Mendes, M. J. (1978), "A New Spline Algorithm for Non-Linear Filtering of Discrete Time Systems," in Proceedings of the 4th IFAC Symposium on Identification and System Parameter Estimation, Tbilisi, U.S.S.R., pp. 2123-2130. [269]
3. Bild, A. H., Yao, G., Chang, J. T., Wang, Q., Potti, A., Chasse, D., Joshi, M., Harpole, D., Lancaster, J. M., Berchuck, A., Olson, J. A., Marks, J. R., Dressman, H. K., West, M., and Nevins, J. (2006), "Oncogenic Pathway Signatures in Human Cancers as a Guide to Targeted Therapies," Nature, 439, 353-357. [273]
4. Carlin, B. P., Polson, N. G., and Stoffer, D. S. (1992), "A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling," Journal of the American Statistical Association, 87, 493-500. [261,270,271,276]
5. Carter, C. K., and Kohn, R. (1994), "On Gibbs Sampling for State-Space Models," Biometrika, 81, 541-553. [261]
6. Chen, R., and Liu, J. S. (2000), "Mixture Kalman Filters," Journal of the Royal Statistical Society, Ser. B, 62, 493-508. [261,276,277]
7. Doucet, A., deFreitas, N., and Gordon, N. (eds.) (2001), Sequential Monte Carlo Methods in Practice, New York: Springer-Verlag. [261]
8. Doucet, A., Godsill, S., and Andrieu, C. (2000), "On Sequential Monte Carlo Sampling Methods for Bayesian Filtering," Statistics and Computing, 10, 197-208. [261,269]
9. Fearnhead, P., and Meligkotsidou, L. (2007), "Filtering Methods for Mixture Models," Journal of Computational and Graphical Statistics, 16, 586-607. [263]
10. Frühwirth-Schnatter, S. (1994), "Data Augmentation and Dynamic Linear Models," Journal of Time Series Analysis, 15, 183-202. [261]
11. Gadkar, K. G., Gunawan, R., and Doyle, F. J. (2005), "Iterative Approach to Model Identification of Biological Networks," BMC Bioinformatics, 6, 155. [271]
12. Gadkar, K. G., Varner, J., and Doyle, F. J. (2005), "Model Identification of Signal Transduction Networks From Data Using a State Regulator Problem," IEE Systems Biology, 2, 17-30. [271]
13. Geweke, J., and Tanizaki, H. (1999), "On Markov Chain Monte Carlo Methods for Nonlinear and Non-Gaussian State-Space Models," Communications in Statistics: Simulation and Computation, 28, 867-894. [261]
14. Godsill, S. J., Doucet, A., and West, M. (2004), "Monte Carlo Smoothing for Nonlinear Time Series," Journal of the American Statistical Association, 99, 156-168. [261,271]
15. Golightly, A., and Wilkinson, D. J. (2005), "Bayesian Inference for Stochastic Kinetic Models Using a Diffusion Approximation," Biometrics, 61, 781-788. [261,271]
16. - (2006a), "Bayesian Sequential Inference for Nonlinear Multivariate Diffusions," Statistics and Comput ing, 16, 323-338. [271]
17. - (2006b), "Bayesian Sequential Inference for Stochastic Kinetic Biochemical Network Models," Journal of Computational Biology, 13, 838-851. [271]
18. Gordon, N. J., Salmond, D. J., and Smith, A. F. M. (1993), "Novel Approach to Non-Linear/Non-Gaussian Bayesian State Estimation," IEE Proceedings Part F: Communications, Radar and Signal Processing, 140, 107-113. [261,269]
19. Harrison, P., and Stevens, C. (1971), "A Bayesian Approach to Short-Term Forecasting," Operations Research Quarterly, 22, 341-362. [263]
20. - (1976), "Bayesian Forecasting," Journal of the Royal Statistical Society, Ser. B, 38, 205-247. [263]
21. He, F, Yeung, L. F, and Brown, M. (2007), "Discrete-Time Model Representation for Biochemical Pathway Systems," IAENG International Journal of Computer Science, 34, 111-118. [271]
22. - (2008), "Discrete-Time Model Representations for Biochemical Pathways," in Trends in Intelligent Systems and Computer Engineering, New York: Springer, pp. 255-271. [271]
23. Hürzeler, M., and Künsch, H. R. (1998), "Monte Carlo Approximations for General State-Space Models," Journal of Computational and Graphical Statistics, 7, 175-193. [261,269]
24. Kitagawa, G. (1987), "Non-Gaussian State-Space Modeling of Nonstationary Time Series (C/R: P1041-1063; C/R: V83 P1231)," Journal of the American Statistical Association, 82, 1032-1041. [269-271]
25. - (1996), "Monte Carlo Filter and Smoother for Non-Gaussian Non-Linear State Space Models," Journal of Computational and Graphical Statistics, 5, 1-25. [261]
26. Liu, J., and West, M. (2001), "Combined Parameter and State Estimation in Simulation-Based Filtering," in Sequential Monte Carlo Methods in Practice, eds. A. Doucet, J. De Freitas, and N. Gordon, New York: Springer-Verlag, pp. 197-217. [261]
27. Nevins, J. (1998), "Toward an Understanding of the Functional Complexity of the E2F and Retinoblastoma Families," Cell Growth and Differentiation, 9, 585-593. [273]
28. Niemi, J. (2009), "Bayesian Analysis and Computational Methods for Dynamic Modeling," Ph.D. thesis, Duke University. [271]
29. Ravines, R. R., Migon, H. S., and Schmidt, A. M. (2007), "An Efficient Sampling Scheme for Dynamic Generalized Models," Technical Report 201/2007, Departamento de Métodos Estatísticos, UFRJ. [261,267]
30. Rosenfeld, N., Young, J., Alon, U., Swain, P., and Elowitz, M. (2005), "Gene Regulation at the Single-Cell Level,"Science, 307, 1962-1965. [261]
31. Sears, R., Ohtani, K., and Nevins, J. R. (1997), "Identification of Positively and Negatively Acting Elements Regulating Expression of the E2F2 Gene in Response to Cell Growth Signals," Molecular and Cellular Biology, 17, 5227-5235. [273]
32. Sorenson, H. W., and Alspach, D. L. (1971), "Recursive Bayesian Estimation Using Gaussian Sums," Automatica, 7, 465-479. [263]
33. Stroud, J. R., Müller, P., and Polson, N. G. (2003), "Nonlinear State-Space Models With State-Dependent Variances," Journal of the American Statistical Association, 98, 377-386. [261]
34. Tan, C, Song, H., Niemi, J., and You, L. (2007), "A Synthetic Biology Challenge: Making Cells Compute," Molecular BioSystems, 3, 343-353. [261]
35. Wang, Q., Niemi, J., Tan, C, You, L., and West, M. (2010), "Image Segmentation and Dynamic Lineage Analysis in Single-Cell Fluorescent Microscopy," Cytometry, Part A, 77, 101-110. [261]
36. West, M. (1992), "Modelling With Mixtures" (with discussion), in Bayesian Statistics 4, eds. J. Bernardo, J. Berger, A. Dawid, and A. Smith, Oxford: Clarendon Press, pp. 503-524. [261,263,277]
37. - (1993a), "Approximating Posterior Distributions by Mixtures," Journal of the Royal Statistical Society, Ser. B, 54, 553-568. [263,277]
38. - (1993b), "Mixture Models, Monte Carlo, Bayesian Updating and Dynamic Models," Computing Science and Statistics, 24, 325-333. [261,263,269,277]
39. West, M., and Harrison, J. (1997), Bayesian Forecasting and Dynamic Models (2nd ed.), New York: Springer-Verlag. [261-263,267,276]
40. Wilkinson, D. (2006), Stochastic Modelling for Systems Biology, London: Chapman & Hall/CRC. [261,271]