Equation-solving estimator based on Metropolis-Hastings algorithm with delayed rejection

ABSTRACT

Numerous works have recently attempted to develop more efficient estimators for MCMC inference than classical ones. In this perspective and approximate nonstandard discrete distributions, Liang and Liu proposed the equation solving estimator as an alternative to the conventional frequency estimator. The specific MCMC method used is the Metropolis-Hastings (M-H) algorithm. In this work, we propose to adapt the equation-solving estimator to the context of simulation using the Metropolis-Hastings algorithm with delayed rejection (MHDR). Developed originally by Mira, this algorithm is considered an improved version of the standard M-H sampler which aims to reduce the variance of MCMC estimators. An application to a Bayesian hypothesis test problem shows the superiority of the equation-solving estimator, based on MHDR sampling, over the one introduced by Liang and Liu.

KEYWORDS:

• Bayesian inference
• Discrete probability distribution
• Equation-solving estimator
• Markov chain Monte Carlo
• Metropolis-Hastings algorithm with delayed rejection

MATHEMATICS SUBJECT CLASSIFICATION:

• 60J22
• 60C05