2020
Crisan, Dan; López-Yela, Alberto; Miguez, Joaquín
Stable Approximation Schemes for Optimal Filters Artículo de revista
En: SIAM/ASA Journal on Uncertainty Quantification, vol. 8, no. 1, pp. 483-509, 2020.
Enlaces | BibTeX | Etiquetas: optimal filters, stability analysis, State space models, truncated filters
@article{JMiguez20b,
title = {Stable Approximation Schemes for Optimal Filters},
author = {Dan Crisan and Alberto L\'{o}pez-Yela and Joaqu\'{i}n Miguez},
doi = {10.1137/19M1255410},
year = {2020},
date = {2020-03-26},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
volume = {8},
number = {1},
pages = {483-509},
keywords = {optimal filters, stability analysis, State space models, truncated filters},
pubstate = {published},
tppubtype = {article}
}
2018
Crisan, Dan; Míguez, Joaquín
Nested particle filters for online parameter estimation in discrete-time state-space Markov models Artículo de revista
En: Bernoulli, vol. 24, no. 4A, pp. 3039 – 3086, 2018.
Enlaces | BibTeX | Etiquetas: error bounds, model inference, Monte Carlo, Parameter estimation, Particle filtering, recursive algorithms, State space models
@article{10.3150/17-BEJ954,
title = {Nested particle filters for online parameter estimation in discrete-time state-space Markov models},
author = {Dan Crisan and Joaqu\'{i}n M\'{i}guez},
url = {https://doi.org/10.3150/17-BEJ954},
doi = {10.3150/17-BEJ954},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Bernoulli},
volume = {24},
number = {4A},
pages = {3039 -- 3086},
publisher = {Bernoulli Society for Mathematical Statistics and Probability},
keywords = {error bounds, model inference, Monte Carlo, Parameter estimation, Particle filtering, recursive algorithms, State space models},
pubstate = {published},
tppubtype = {article}
}
Míguez, Joaquín; Mariño, Inés P.; Vázquez, Manuel A
Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models Artículo de revista
En: Signal Processing, vol. 142, pp. 281-291, 2018, ISSN: 0165-1684.
Resumen | Enlaces | BibTeX | Etiquetas: Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models
@article{MIGUEZ2018281,
title = {Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models},
author = {Joaqu\'{i}n M\'{i}guez and In\'{e}s P. Mari\~{n}o and Manuel A V\'{a}zquez},
url = {https://www.sciencedirect.com/science/article/pii/S0165168417302761},
doi = {https://doi.org/10.1016/j.sigpro.2017.07.030},
issn = {0165-1684},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Signal Processing},
volume = {142},
pages = {281-291},
abstract = {The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.},
keywords = {Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models},
pubstate = {published},
tppubtype = {article}
}
The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.
Míguez, Joaquín; Mariño, Inés P.; Vázquez, Manuel A
Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models Artículo de revista
En: Signal Processing, vol. 142, pp. 281-291, 2018, ISSN: 0165-1684.
Resumen | Enlaces | BibTeX | Etiquetas: Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models
@article{MIGUEZ2018281b,
title = {Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models},
author = {Joaqu\'{i}n M\'{i}guez and In\'{e}s P. Mari\~{n}o and Manuel A V\'{a}zquez},
url = {https://www.sciencedirect.com/science/article/pii/S0165168417302761},
doi = {https://doi.org/10.1016/j.sigpro.2017.07.030},
issn = {0165-1684},
year = {2018},
date = {2018-01-01},
urldate = {2018-01-01},
journal = {Signal Processing},
volume = {142},
pages = {281-291},
abstract = {The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.},
keywords = {Adaptive importance sampling, Bayesian inference, Importance sampling, Parameter estimation, population Monte Carlo, State space models},
pubstate = {published},
tppubtype = {article}
}
The Bayesian estimation of the unknown parameters of state-space (dynamical) systems has received considerable attention over the past decade, with a handful of powerful algorithms being introduced. In this paper we tackle the theoretical analysis of the recently proposed nonlinear population Monte Carlo (NPMC). This is an iterative importance sampling scheme whose key features, compared to conventional importance samplers, are (i) the approximate computation of the importance weights (IWs) assigned to the Monte Carlo samples and (ii) the nonlinear transformation of these IWs in order to prevent the degeneracy problem that flaws the performance of conventional importance samplers. The contribution of the present paper is a rigorous proof of convergence of the nonlinear IS (NIS) scheme as the number of Monte Carlo samples, M, increases. Our analysis reveals that the NIS approximation errors converge to 0 almost surely and with the optimal Monte Carlo rate of M−12. Moreover, we prove that this is achieved even when the mean estimation error of the IWs remains constant, a property that has been termed exact approximation in the Markov chain Monte Carlo literature. We illustrate these theoretical results by means of a computer simulation example involving the estimation of the parameters of a state-space model typically used for target tracking.
2011
Miguez, Joaquin; Crisan, Dan; Djuric, Petar M
On the Convergence of Two Sequential Monte Carlo Methods for Maximum a Posteriori Sequence Estimation and Stochastic Global Optimization Artículo de revista
En: Statistics and Computing, vol. 23, no. 1, pp. 91–107, 2011, ISSN: 0960-3174.
Resumen | Enlaces | BibTeX | Etiquetas: Global optimization, MAP sequence estimation, Sequential Monte Carlo, State space models
@article{Miguez2011,
title = {On the Convergence of Two Sequential Monte Carlo Methods for Maximum a Posteriori Sequence Estimation and Stochastic Global Optimization},
author = {Joaquin Miguez and Dan Crisan and Petar M Djuric},
url = {http://www.researchgate.net/publication/225447686_On_the_convergence_of_two_sequential_Monte_Carlo_methods_for_maximum_a_posteriori_sequence_estimation_and_stochastic_global_optimization},
issn = {0960-3174},
year = {2011},
date = {2011-01-01},
journal = {Statistics and Computing},
volume = {23},
number = {1},
pages = {91--107},
abstract = {This paper addresses the problem of maximum a posteriori (MAP) sequence estimation in general state-space models. We consider two algorithms based on the sequential Monte Carlo (SMC) methodology (also known as particle filtering). We prove that they produce approximations of the MAP estimator and that they converge almost surely. We also derive a lower bound for the number of particles that are needed to achieve a given approximation accuracy. In the last part of the paper, we investigate the application of particle filtering and MAP estimation to the global optimization of a class of (possibly non-convex and possibly non-differentiable) cost functions. In particular, we show how to convert the cost-minimization problem into one of MAP sequence estimation for a state-space model that is “matched” to the cost of interest. We provide examples that illustrate the application of the methodology as well as numerical results.},
keywords = {Global optimization, MAP sequence estimation, Sequential Monte Carlo, State space models},
pubstate = {published},
tppubtype = {article}
}
This paper addresses the problem of maximum a posteriori (MAP) sequence estimation in general state-space models. We consider two algorithms based on the sequential Monte Carlo (SMC) methodology (also known as particle filtering). We prove that they produce approximations of the MAP estimator and that they converge almost surely. We also derive a lower bound for the number of particles that are needed to achieve a given approximation accuracy. In the last part of the paper, we investigate the application of particle filtering and MAP estimation to the global optimization of a class of (possibly non-convex and possibly non-differentiable) cost functions. In particular, we show how to convert the cost-minimization problem into one of MAP sequence estimation for a state-space model that is “matched” to the cost of interest. We provide examples that illustrate the application of the methodology as well as numerical results.