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Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Poyiadjis, G and Doucet, A and Singh, SS (2009) Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation. Technical Report. Cambridge University Engineering Department.

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Abstract

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.

Item Type: Monograph (Technical Report)
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 12:27
Last Modified: 10 Mar 2014 18:04
DOI:

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