Imperial College London
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ProfessorDanCrisan

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8489d.crisan Website

 
 
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Location

 

670Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Crisan:2017:10.1017/apr.2017.38,
author = {Crisan, DO and Miguez, J},
doi = {10.1017/apr.2017.38},
journal = {Advances in Applied Probability},
pages = {1170--1200},
title = {Uniform convergence over time of a nested particle filtering scheme forrecursive parameter estimation in state–space Markov models},
url = {http://dx.doi.org/10.1017/apr.2017.38},
volume = {49},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We analyse the performance of a recursive Monte Carlo method forthe Bayesian estimation of the staticparameters of a discrete–time state–space Markov model. The algorithm employs two layers of particlefilters to approximate the posterior probability distribution of the model parameters. In particular, thefirst layer yields an empirical distribution of samples on the parameter space, while the filters in the secondlayer are auxiliary devices to approximate the (analytically intractable) likelihood of the parameters. Thisapproach relates the novel algorithm to the recent sequential Monte Carlo square (SMC2) method, whichprovides anon-recursivesolution to the same problem. In this paper, we investigate the approximationof integrals of real bounded functions with respect to the posterior distribution of the system parameters.Under assumptions related to the compactness of the parametersupport and the stability and continuityof the sequence of posterior distributions for the state–space model, we prove that theLpnorms of theapproximation errors vanish asymptotically (as the number of Monte Carlo samples generated by thealgorithm increases) and uniformly over time.  We also prove that, under the same assumptions, theproposed scheme can asymptotically identify the parameter valuesfor a class of models. We conclude thepaper with a numerical example that illustrates the uniform convergence results by exploring the accuracyand stability of the proposed algorithm operating with long sequences of observations.
AU  - Crisan,DO
AU  - Miguez,J
DO  - 10.1017/apr.2017.38
EP  - 1200
PY  - 2017///
SN  - 1475-6064
SP  - 1170
TI  - Uniform convergence over time of a nested particle filtering scheme forrecursive parameter estimation in state–space Markov models
T2  - Advances in Applied Probability
UR  - http://dx.doi.org/10.1017/apr.2017.38
UR  - http://hdl.handle.net/10044/1/48945
VL  - 49
ER  -
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