533 research outputs found
Fast smoothing in switching approximations of non-linear and non-Gaussian models
International audienceStatistical smoothing in general non-linear non-Gaussian systems is a challenging problem. A new smoothing method based on approximating the original system by a recent switching model has been introduced. Such switching model allows fast and optimal smoothing. The new algorithm is validated through an application on stochastic volatility and dynamic beta models. Simulation experiments indicate its remarkable performances and low processing cost. In practice, the proposed approach can overcome the limitations of particle smoothing methods and may apply where their usage is discarded
Fast exact filtering in generalized conditionally observed Markov switching models with copulas
International audienceWe deal with the problem of statistical filtering in the context of Markov switching models. For X_1^N hidden continuous process, R_1^N hidden finite Markov process, and Y_1^N observed continuous one, the problem is to sequentially estimate X_1^N and R_1^N from Y_1^N. In the classical " conditional Gaussian Linear state space model " (CGLSSM), where (R_1^N, X_1^N) is a hidden Gaussian Markov chain, fast exact filtering is not workable. Recently, " conditionally Gaussian observed Markov switching model " (CGOMSM) has been proposed, in which (R_1^N, Y_1^N) is a hidden Gaussian Markov chain instead. This model allows fast exact filtering. In this paper, using copula, we extend CGOMSM to a more general one, in which (R_1^N, Y_1^N) is a hidden Markov chain (HMC) with noise of any form and the regimes are no need to be all Gaussian, while the exact filtering is still workable. Experiments are conducted to show how the exact filtering results based on CGOMSM can be improved by the use of the new model
A class of fast exact Bayesian filters in dynamical models with jumps
In this paper, we focus on the statistical filtering problem in dynamical
models with jumps. When a particular application relies on physical properties
which are modeled by linear and Gaussian probability density functions with
jumps, an usualmethod consists in approximating the optimal Bayesian estimate
(in the sense of the Minimum Mean Square Error (MMSE)) in a linear and Gaussian
Jump Markov State Space System (JMSS). Practical solutions include algorithms
based on numerical approximations or based on Sequential Monte Carlo (SMC)
methods. In this paper, we propose a class of alternative methods which
consists in building statistical models which share the same physical
properties of interest but in which the computation of the optimal MMSE
estimate can be done at a computational cost which is linear in the number of
observations.Comment: 21 pages, 7 figure
Efficient Gibbs Sampling for Markov Switching GARCH Models
We develop efficient simulation techniques for Bayesian inference on
switching GARCH models. Our contribution to existing literature is manifold.
First, we discuss different multi-move sampling techniques for Markov Switching
(MS) state space models with particular attention to MS-GARCH models. Our
multi-move sampling strategy is based on the Forward Filtering Backward
Sampling (FFBS) applied to an approximation of MS-GARCH. Another important
contribution is the use of multi-point samplers, such as the Multiple-Try
Metropolis (MTM) and the Multiple trial Metropolize Independent Sampler, in
combination with FFBS for the MS-GARCH process. In this sense we ex- tend to
the MS state space models the work of So [2006] on efficient MTM sampler for
continuous state space models. Finally, we suggest to further improve the
sampler efficiency by introducing the antithetic sampling of Craiu and Meng
[2005] and Craiu and Lemieux [2007] within the FFBS. Our simulation experiments
on MS-GARCH model show that our multi-point and multi-move strategies allow the
sampler to gain efficiency when compared with single-move Gibbs sampling.Comment: 38 pages, 7 figure
Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC)
We develop a novel advanced Particle Markov chain Monte Carlo algorithm that
is capable of sampling from the posterior distribution of non-linear state
space models for both the unobserved latent states and the unknown model
parameters. We apply this novel methodology to five population growth models,
including models with strong and weak Allee effects, and test if it can
efficiently sample from the complex likelihood surface that is often associated
with these models. Utilising real and also synthetically generated data sets we
examine the extent to which observation noise and process error may frustrate
efforts to choose between these models. Our novel algorithm involves an
Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm
(AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional
spaces efficiently, and is therefore superior to standard Gibbs or Metropolis
Hastings algorithms that are known to converge very slowly when applied to the
non-linear state space ecological models considered in this paper.
Additionally, we show how the AdPMCMC algorithm can be used to recursively
estimate the Bayesian Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive
expressions for these Cram\'er-Rao Bounds and estimate them for the models
considered. Our results demonstrate a number of important features of common
population growth models, most notably their multi-modal posterior surfaces and
dependence between the static and dynamic parameters. We conclude by sampling
from the posterior distribution of each of the models, and use Bayes factors to
highlight how observation noise significantly diminishes our ability to select
among some of the models, particularly those that are designed to reproduce an
Allee effect
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