Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Understand

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable.

• Although the use of ABC is widespread in many fields, there has been little investigation of the theoretical properties of the resulting estimators.
• In this paper we give a theoretical analysis of the asymptotic properties of ABC based maximum likelihood parameter estimation for hidden Markov models.
• In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation.