Parameter Estimation for Hidden Markov Models with Intractable Likelihoods
研究了当似然函数难以计算时，如何通过最大化近似贝叶斯计算中的近似似然来估计隐马尔可夫模型的参数，并证明了该估计量的一致性和渐近正态性。
ABSTRACT 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.