scholarly journals Accelerating Metropolis-Hastings algorithms by Delayed Acceptance

2019 ◽  
Vol 1 (2) ◽  
pp. 103-128 ◽  
Author(s):  
Marco Banterle ◽  
◽  
Clara Grazian ◽  
Anthony Lee ◽  
Christian P. Robert ◽  
...  
Keyword(s):  
Metropolis Hastings Algorithms

A First Course in Statistical Programming with R

2021 ◽  
Author(s):  
W. John Braun ◽  
Duncan J. Murdoch
Keyword(s):  
Data Science ◽  
Worked Examples ◽  
Design Principles ◽  
Complex Projects ◽  
Statistical Programming ◽  
Programming Skills ◽  
Downloadable Code ◽  
Metropolis Hastings Algorithms

This third edition of Braun and Murdoch's bestselling textbook now includes discussion of the use and design principles of the tidyverse packages in R, including expanded coverage of ggplot2, and R Markdown. The expanded simulation chapter introduces the Box–Muller and Metropolis–Hastings algorithms. New examples and exercises have been added throughout. This is the only introduction you'll need to start programming in R, the computing standard for analyzing data. This book comes with real R code that teaches the standards of the language. Unlike other introductory books on the R system, this book emphasizes portable programming skills that apply to most computing languages and techniques used to develop more complex projects. Solutions, datasets, and any errata are available from www.statprogr.science. Worked examples - from real applications - hundreds of exercises, and downloadable code, datasets, and solutions make a complete package for anyone working in or learning practical data science.

Smoothed Langevin proposals in Metropolis-Hastings algorithms

2000 ◽  
Vol 49 (4) ◽  
pp. 345-354 ◽  
Author(s):  
Øivind Skare ◽  
Fred Espen Benth ◽  
Arnoldo Frigessi
Keyword(s):  
Metropolis Hastings Algorithms

scholarly journals On the geometric ergodicity of Metropolis-Hastings algorithms

Statistics ◽  
2007 ◽  
Vol 41 (1) ◽  
pp. 77-84 ◽  
Author(s):  
Yves F. Atchadé ◽  
François Perron
Keyword(s):  
Geometric Ergodicity ◽  
Metropolis Hastings Algorithms

A note on acceptance rate criteria for CLTS for Metropolis–Hastings algorithms

1999 ◽  
Vol 36 (04) ◽  
pp. 1210-1217 ◽  
Author(s):  
G. O. Roberts
Keyword(s):  
Markov Chains ◽  
Central Limit ◽  
Limit Theorems ◽  
Acceptance Rate ◽  
Ergodic Averages ◽  
Current State ◽  
Rejection Probability ◽  
Independence Sampler ◽  
Positive Recurrent ◽  
Metropolis Hastings Algorithms

This paper considers positive recurrent Markov chains where the probability of remaining in the current state is arbitrarily close to 1. Specifically, conditions are given which ensure the non-existence of central limit theorems for ergodic averages of functionals of the chain. The results are motivated by applications for Metropolis–Hastings algorithms which are constructed in terms of a rejection probability (where a rejection involves remaining at the current state). Two examples for commonly used algorithms are given, for the independence sampler and the Metropolis-adjusted Langevin algorithm. The examples are rather specialized, although, in both cases, the problems which arise are typical of problems commonly occurring for the particular algorithm being used.

scholarly journals Metropolis-Hastings Algorithm with Delayed Acceptance and Rejection

2019 ◽  
Vol 2 (2) ◽  
pp. 7
Author(s):  
Yulin Hu ◽  
Yayong Tang
Keyword(s):  
Computational Cost ◽  
Acceptance Rate ◽  
Acceptance Probability ◽  
Likelihood Functions ◽  
Second Stage ◽  
Mh Algorithm ◽  
Delayed Rejection ◽  
Complex Target ◽  
Metropolis Hastings Algorithms

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.

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