Metropolis-Hastings Algorithm with Delayed Acceptance and Rejection

Authors

  • Yulin Hu College of Mathematics, Sichuan University
  • Yayong Tang College of Mathematics, Sichuan University

DOI:

https://doi.org/10.30564/ret.v2i2.682

Abstract

Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions. To solve this problem, one can use the delayed acceptance Metropolis-Hastings algorithm (MHDA) of Christen and Fox (2005). However, the acceptance rate of a proposed value will always be less than in the standard Metropolis-Hastings. We can fix this problem by using the Metropolis-Hastings algorithm with delayed rejection (MHDR) proposed by Tierney and Mira (1999). In this paper, we combine the ideas of MHDA and MHDR to propose a new MH algorithm, named the Metropolis-Hastings algorithm with delayed acceptance and rejection (MHDAR). The new algorithm reduces the computational cost by division of the prior or likelihood functions and increase the acceptance probability by delay rejection of the second stage. We illustrate those accelerating features by a realistic example.

Keywords:

Metropolis-Hastings algorithm; Delayed acceptance; Delayed rejection

References

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Issue

Vol. 2 , Iss. 2 (April 2019)

Article Type

Research Article

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