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Parameter Estimation for Hidden Markov Models with Intractable Likelihoods
Author(s) -
Dean Thomas A.,
Singh Sumeetpal S.,
Jasra Ajay,
Peters Gareth W.
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12077
Subject(s) - mathematics , approximate bayesian computation , likelihood function , estimator , consistency (knowledge bases) , marginal likelihood , asymptotic distribution , estimation theory , markov chain monte carlo , statistics , monte carlo method , bayesian probability , mathematical optimization , algorithm , computer science , inference , artificial intelligence , geometry
Approximate Bayesian computation (ABC) is a popular technique for analysing data for complex models where the likelihood function is intractable. It involves using simulation from the model to approximate the likelihood, with this approximate likelihood then being used to construct an approximate posterior. In this paper, we consider methods that estimate the parameters by maximizing the approximate likelihood used in ABC. We give a theoretical analysis of the asymptotic properties of the resulting estimator. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how sequential Monte Carlo methods provide a natural method for implementing our likelihood‐based ABC procedures.