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Vectorized and parallel particle filter SMC parameter estimation for stiff ODEs
1. | Department of Mathematics, North Carolina State University, Campus Box 8205, 2311 Stinson Drive, 2108 SAS Hall, Raleigh, NC 27695-8205, United States |
2. | Case Western Reserve University, Department of Mathematics and Center for Modelling Integrated Metabolic Systems, 10900 Euclid Avenue, Cleveland, OH 44106 |
3. | Case Western Reserve University, Department of Mathematics, Applied Mathematics, and Statistics, Cleveland, OH 44106 |
References:
[1] |
A. Arnold, Sequential Monte Carlo Parameter Estimation for Differential Equations, Ph.D thesis, Case Western Reserve University, 2014. |
[2] |
A. Arnold, D. Calvetti and E. Somersalo, Linear multistep methods, particle filtering and sequential Monte Carlo, Inverse Problems, 29 (2013), 085007. |
[3] |
O. Brun, V. Teuliere and J.-M. Garcia, Parallel particle filtering, Journal of Parallel and Distributed Computing, 62 (2002), 1186-1202. |
[4] |
B. Calderhead, M. Girolami and N. D. Lawrence, Accelerating Bayesian inference over nonlinear differential equations with Gaussian processes, Adv. Neural Inf. Process. Syst., 21 (2009), 217-224. |
[5] |
D. Calvetti and E. Somersalo, Large scale statistical parameter estimation in complex systems with an application to metabolic models, Multiscale Model. Simul., 5 (2006), 1333-1366. |
[6] |
N. Chopin, P. E. Jacob and O. Papaspiliopoulos, SMC$^2$: an efficient algorithm for sequential analysis of state space models, J. R. Stat. Soc. Ser. B Stat. Methodol., 75 (2013), 397-426. |
[7] |
A. Golightly and D. J. Wilkinson, Bayesian parameter inference for stochastic biochemical network models using particle MCMC, J. R. Soc. Interface Focus, 1 (2011), 807-820. |
[8] |
A. Iserles, A First Course in the Numerical Analysis of Differential Equations, $2^{nd}$ edition, Cambridge Texts in Applied Mathematics, Cambridge University Press, New York, 2009. |
[9] |
A. Lee, C. Yau, M. B. Giles, A. Doucet and C. C. Holmes, On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods, J. Comput. Graph. Statist., 19 (2010), 769-789. |
[10] |
R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, Philadelphia, 2007. |
[11] |
C. Lieberman and K. Willcox, Goal-oriented inference: approach, linear theory, and application to advection diffusion, SIAM Review, 55 (2013), 493-519. |
[12] |
J. Liu and M. West, Combined parameter and state estimation in simulation-based filtering, in Sequential Monte Carlo Methods in Practice (eds. A. Doucet, J. F. G. de Freitas and N. J. Gordon), Springer, New York (2001), 197-223. |
[13] |
S. Maskell, B. Alun-Jones and M. Macleod, A single instruction multiple data particle filter, Nonlinear Statistical Signal Processing Workshop 2006 IEEE, (2006), 51-54. |
[14] |
L. M. Murray, Bayesian state-space modelling on high-performance hardware using LibBi, preprint, arXiv:1306.3277. |
[15] |
M. Pitt and N. Shephard, Filtering via simulation: auxiliary particle filters, J. Amer. Statist. Assoc., 94 (1999), 590-599. |
[16] |
R. Ren and G. Orkoulas, Parallel Markov chain Monte Carlo simulations, The Journal of Chemical Physics, 126 (2007), 211102. |
[17] |
L. R. Scott, T. Clark and B. Bagheri, Scientific Parallel Computing, Princeton, Princeton, NJ, 2005. |
[18] |
M. West, Approximating posterior distributions by mixtures, J. R. Stat. Soc. Ser. B Stat. Methodol., 55 (1993), 409-422. |
[19] |
M. West, Mixture models, Monte Carlo, Bayesian updating and dynamic models, in Computing Science and Statistics: Proceedings of the 24th Symposium on the Interface (ed. J. H. Newton), Interface Foundation of America, Fairfax Station, VA (1993), 325-333. |
[20] |
D. J. Wilkinson, Parallel Bayesian computation, in Handbook of Parallel Computing and Statistics (ed. E. J. Kontoghiorghes), Chapman & Hall/CRC, Boca Raton, FL (2005), 477-508. |
[21] |
Y. Zhou, vSMC: Parallel sequential Monte Carlo in C++, preprint, arXiv:1306.5583. |
show all references
References:
[1] |
A. Arnold, Sequential Monte Carlo Parameter Estimation for Differential Equations, Ph.D thesis, Case Western Reserve University, 2014. |
[2] |
A. Arnold, D. Calvetti and E. Somersalo, Linear multistep methods, particle filtering and sequential Monte Carlo, Inverse Problems, 29 (2013), 085007. |
[3] |
O. Brun, V. Teuliere and J.-M. Garcia, Parallel particle filtering, Journal of Parallel and Distributed Computing, 62 (2002), 1186-1202. |
[4] |
B. Calderhead, M. Girolami and N. D. Lawrence, Accelerating Bayesian inference over nonlinear differential equations with Gaussian processes, Adv. Neural Inf. Process. Syst., 21 (2009), 217-224. |
[5] |
D. Calvetti and E. Somersalo, Large scale statistical parameter estimation in complex systems with an application to metabolic models, Multiscale Model. Simul., 5 (2006), 1333-1366. |
[6] |
N. Chopin, P. E. Jacob and O. Papaspiliopoulos, SMC$^2$: an efficient algorithm for sequential analysis of state space models, J. R. Stat. Soc. Ser. B Stat. Methodol., 75 (2013), 397-426. |
[7] |
A. Golightly and D. J. Wilkinson, Bayesian parameter inference for stochastic biochemical network models using particle MCMC, J. R. Soc. Interface Focus, 1 (2011), 807-820. |
[8] |
A. Iserles, A First Course in the Numerical Analysis of Differential Equations, $2^{nd}$ edition, Cambridge Texts in Applied Mathematics, Cambridge University Press, New York, 2009. |
[9] |
A. Lee, C. Yau, M. B. Giles, A. Doucet and C. C. Holmes, On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods, J. Comput. Graph. Statist., 19 (2010), 769-789. |
[10] |
R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, Philadelphia, 2007. |
[11] |
C. Lieberman and K. Willcox, Goal-oriented inference: approach, linear theory, and application to advection diffusion, SIAM Review, 55 (2013), 493-519. |
[12] |
J. Liu and M. West, Combined parameter and state estimation in simulation-based filtering, in Sequential Monte Carlo Methods in Practice (eds. A. Doucet, J. F. G. de Freitas and N. J. Gordon), Springer, New York (2001), 197-223. |
[13] |
S. Maskell, B. Alun-Jones and M. Macleod, A single instruction multiple data particle filter, Nonlinear Statistical Signal Processing Workshop 2006 IEEE, (2006), 51-54. |
[14] |
L. M. Murray, Bayesian state-space modelling on high-performance hardware using LibBi, preprint, arXiv:1306.3277. |
[15] |
M. Pitt and N. Shephard, Filtering via simulation: auxiliary particle filters, J. Amer. Statist. Assoc., 94 (1999), 590-599. |
[16] |
R. Ren and G. Orkoulas, Parallel Markov chain Monte Carlo simulations, The Journal of Chemical Physics, 126 (2007), 211102. |
[17] |
L. R. Scott, T. Clark and B. Bagheri, Scientific Parallel Computing, Princeton, Princeton, NJ, 2005. |
[18] |
M. West, Approximating posterior distributions by mixtures, J. R. Stat. Soc. Ser. B Stat. Methodol., 55 (1993), 409-422. |
[19] |
M. West, Mixture models, Monte Carlo, Bayesian updating and dynamic models, in Computing Science and Statistics: Proceedings of the 24th Symposium on the Interface (ed. J. H. Newton), Interface Foundation of America, Fairfax Station, VA (1993), 325-333. |
[20] |
D. J. Wilkinson, Parallel Bayesian computation, in Handbook of Parallel Computing and Statistics (ed. E. J. Kontoghiorghes), Chapman & Hall/CRC, Boca Raton, FL (2005), 477-508. |
[21] |
Y. Zhou, vSMC: Parallel sequential Monte Carlo in C++, preprint, arXiv:1306.5583. |
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