Use of runif() in proposal function of MCMC

Algorithms
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1

Hi team,

Can anyone please help here with the explanation of the below code chunk in the proposal function of MCMC -

if (runif(1) < probab){ 
         chain[i+1,] = proposal 
}else{  
        chain[i+1,] = chain[I,] 
      }
  1. Why is the runif() function used here? Is there any theory to support this?
  2. Can we use any other function in place of runif() function?

I really appreciate any help you can provide.

Complete reference for the code : Metropolis-Hastings MCMC in R

2

This is part of the Metropolis algorithm, see Section 11.2 of Bayesian Data Analysis (page 282 in the online version here) for a more complete background

1 Like
3

Hi @andrjohns,

Going through the book only helped me know the advantages of Uniform Distribution but it did not seem to answer the question, why compare with a value less than 1 and greater than 0 generated by Uniform distribution and accept or reject the acceptance ratio for the candidate in the Metropolisā€“Hastings algorithm?

4

@Taranpreet_Kaur the intuitions behind the randomness in the metropolis proposal acceptance/rejection rule is in the core of a lot of MCMC samplers.

Try this book https://www.mcmchandbook.net/ it might help you.