Grupo de Tratamiento de Señal y Aprendizaje
http://hdl.handle.net/10016/9041
Mon, 20 Nov 2017 00:13:45 GMT2017-11-20T00:13:45ZNested particle filters for online parameter estimation in discrete-time state-space Markov models
http://hdl.handle.net/10016/25879
Nested particle filters for online parameter estimation in discrete-time state-space Markov models
Crisan, Dan; Míguez Arenas, Joaquín
We address the problem of approximating the posterior probability distribution of the fixed parameters of a state-space dynamical system using a sequential Monte Carlo method. The proposed approach relies on a nested structure that employs two layers of particle filters to approximate the posterior probability measure of the static parameters and the dynamic state variables of the system of interest, in a vein similar to the recent "sequential Monte Carlo square" (SMC2) algorithm. However, unlike the SMC2 scheme, the proposed technique operates in a purely recursive manner. In particular, the computational complexity of the recursive steps of the method introduced herein is constant over time. We analyse the approximation of integrals of real bounded functions with respect to the posterior distribution of the system parameters computed via the proposed scheme. As a result, we prove, under regularity assumptions, that the approximation errors vanish asymptotically in Lp (p≥1) with convergence rate proportional to 1N√+1M√, where N is the number of Monte Carlo samples in the parameter space and N×M is the number of samples in the state space. This result also holds for the approximation of the joint posterior distribution of the parameters and the state variables. We discuss the relationship between the SMC2 algorithm and the new recursive method and present a simple example in order to illustrate some of the theoretical findings with computer simulations.
Documento depositado en el repositorio arXiv.org. Versión: arXiv:1308.1883v5 [stat.CO]
Wed, 10 May 2017 00:00:00 GMThttp://hdl.handle.net/10016/258792017-05-10T00:00:00ZA comparison of nonlinear population Monte Carlo and particle Markov chain Monte Carlo algorithms for Bayesian inference in stochastic kinetic models
http://hdl.handle.net/10016/25878
A comparison of nonlinear population Monte Carlo and particle Markov chain Monte Carlo algorithms for Bayesian inference in stochastic kinetic models
Koblents Lapteva, Eugenia; Míguez Arenas, Joaquín
In this paper we address the problem of Monte Carlo approximation of posterior probability distributions in stochastic kinetic models (SKMs). SKMs are multivariate Markov jump processes that model the interactions among species in biochemical systems according to a set of uncertain parameters. Markov chain Monte Carlo (MCMC) methods have been typically preferred for this Bayesian inference problem. Specifically, the particle MCMC (pMCMC) method has been recently shown to be an effective, while computationally demanding, method applicable to this problem. Within the pMCMC framework, importance sampling (IS) has been used only as the basis of the sequential Monte Carlo (SMC) approximation of the acceptance ratio in the Metropolis-Hastings kernel. However, the recently proposed nonlinear population Monte Carlo (NPMC) algorithm, based on an iterative IS scheme, has also been shown to be effective as a Bayesian inference tool for low dimensional (predator-prey) SKMs. In this paper, we provide an extensive performance comparison of pMCMC versus NPMC, when applied to the challenging prokaryotic autoregulatory network. We show how the NPMC method can greatly outperform the pMCMC algorithm in this scenario, with an overall moderate computational effort. We complement the numerical comparison of the two techniques with an asymptotic convergence analysis of the nonlinear IS scheme at the core of the proposed method when the importance weights can only be computed approximately
Documento depositado en el repositorio arXiv.org. Versión: arXiv:1404.5218v1 [stat.ME]
Mon, 21 Apr 2014 00:00:00 GMThttp://hdl.handle.net/10016/258782014-04-21T00:00:00ZA simple scheme for the parallelization of particle filters and its application to the tracking of complex stochastic systems
http://hdl.handle.net/10016/25877
A simple scheme for the parallelization of particle filters and its application to the tracking of complex stochastic systems
Crisan, Dan; Míguez Arenas, Joaquín; Rios Muñoz, Gonzalo Ricardo
We investigate the use of possibly the simplest scheme for the parallelisation of the standard particle filter, that consists in splitting the computational budget into M fully independent particle filters with N particles each, and then obtaining the desired estimators by averaging over the M independent outcomes of the filters. This approach minimises the parallelisation overhead yet displays highly desirable theoretical properties. Under very mild assumptions, we analyse the mean square error (MSE) of the estimators of 1-dimensional statistics of the optimal filtering distribution and show explicitly the effect of parallelisation scheme on the convergence rate. Specifically, we study the decomposition of the MSE into variance and bias components, to show that the former decays as 1/MN, i.e., linearly with the total number of particles, while the latter converges towards 0 as 1/N². Parallelisation, therefore, has the obvious advantage of dividing the running times while preserving the (asymptotic) performance of the particle filter. Following this lead, we propose a time-error index to compare schemes with different degrees of parallelisation. Finally, we provide two numerical examples. The first one deals with the tracking of a Lorenz 63 chaotic system with dynamical noise and partial (noisy) observations, while the second example involves a dynamical network of modified FitzHugh-Nagumo (FH-N) stochastic nodes. The latter is a large dimensional system (≈3,000 state variables in our computer experiments) designed to numerically reproduce typical electrical phenomena observed in the atria of the human heart. In both examples, we show how the proposed parallelisation scheme attains the same approximation accuracy as a centralised particle filter with only a small fraction of the running time, using a standard multicore computer.
Documento depositado en el repositorio arXiv.org. Versión: arXiv:1407.8071v2 [stat.CO]
Fri, 09 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10016/258772015-10-09T00:00:00ZAnalysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models
http://hdl.handle.net/10016/25753
Analysis of a nonlinear importance sampling scheme for Bayesian parameter estimation in state-space models
Míguez Arenas, Joaquín; Pérez Mariño, Inés; Vázquez López, Manuel Alberto
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 [superíndice - ½]. 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.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10016/257532018-01-01T00:00:00Z