Particle filtering for partially observed Gaussian state space models

Solving Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models. A large number of algorithms based on particle filtering methods, also known as sequential Monte Carlo algorithms, have recently been pro...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2002-10, Vol.64 (4), p.827-836
Main Authors: Andrieu, Christophe, Doucet, Arnaud
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Bayesian estimation
Bayesian method
Dynamic modeling
Estimation
Estimation methods
Evaluation
Exact sciences and technology
Filtering
Filtration
Gaussian distributions
Generalized linear time series
Importance sampling
Kalman filters
Marginalization
Mathematical foundations
Mathematics
Probability and statistics
Sampling
Sciences and techniques of general use
Sequential methods
Sequential Monte Carlo sampling
Space based observatories
State estimation
State space model
Statistical methods
Statistical models
Statistics
Time series
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Summary:Solving Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models. A large number of algorithms based on particle filtering methods, also known as sequential Monte Carlo algorithms, have recently been proposed to solve these problems. We propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions of partially observed Gaussian state space models. This algorithm is based on a marginalization idea for improving efficiency and can lead to substantial gains over standard algorithms. It differs from previous algorithms which were only applicable to conditionally linear Gaussian state space models. Computer simulations are carried out to evaluate the performance of the proposed algorithm for dynamic tobit and probit models.
ISSN:1369-7412
1467-9868
DOI:10.1111/1467-9868.00363