Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Thomas A. Dean, Sumeetpal S. Singh, Ajay Jasra, Gareth W. Peters

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)970-987
Number of pages18
JournalScandinavian Journal of Statistics
Issue number4
Publication statusPublished - Dec 2014


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