Imperial College London
Alternate

Dr Nikolas Kantas

Faculty of Natural Sciences, Department of Mathematics

Reader in Statistics
 
 
 
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Contact

 

+44 (0)20 7594 2772n.kantas Website

 
 
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Location

 

538Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Ehrlich:2013:10.1007/s11009-013-9357-4,
author = {Ehrlich, E and Jasra, A and Kantas, N},
doi = {10.1007/s11009-013-9357-4},
journal = {Methodology and Computing in Applied Probability},
pages = {315--349},
title = {Gradient free parameter estimation for hidden Markov models with intractable likelihoods},
url = {http://dx.doi.org/10.1007/s11009-013-9357-4},
volume = {17},
year = {2013}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In this article we focus on Maximum Likelihood estimation (MLE) for the static model parameters of hidden Markov models (HMMs). We will consider the case where one cannot or does not want to compute the conditional likelihooddensity of the observation given the hidden state because of increased computationalcomplexity or analytical intractability. Instead we will assume that one may obtainsamples from this conditional likelihood and hence use approximate Bayesiancomputation (ABC) approximations of the original HMM. Although these ABCapproximations will induce a bias, this can be controlled to arbitrary precision viaa positive parameter , so that the bias decreases with decreasing . We first establishthat when using an ABC approximation of the HMM for a fixed batch of data,then the bias of the resulting log- marginal likelihood and its gradient is no worsethan O(n), where n is the total number of data-points. Therefore, when usinggradient methods to perform MLE for the ABC approximation of the HMM, onemay expect parameter estimates of reasonable accuracy. To compute an estimate ofthe unknown and fixed model parameters, we propose a gradient approach based onsimultaneous perturbation stochastic approximation (SPSA) and Sequential MonteCarlo (SMC) for the ABC approximation of the HMM. The performance of thismethod is illustrated using two numerical examples.
AU  - Ehrlich,E
AU  - Jasra,A
AU  - Kantas,N
DO  - 10.1007/s11009-013-9357-4
EP  - 349
PY  - 2013///
SN  - 1573-7713
SP  - 315
TI  - Gradient free parameter estimation for hidden Markov models with intractable likelihoods
T2  - Methodology and Computing in Applied Probability
UR  - http://dx.doi.org/10.1007/s11009-013-9357-4
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000354094300003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/40827
VL  - 17
ER  -
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