Skip to main content

On the use of local optimizations within Metropolis–Hastings updates

Buy Article:

$51.00 plus tax (Refund Policy)

Abstract:

Summary. 

We propose new Metropolis–Hastings algorithms for sampling from multimodal dis- tributions on ℜn. Tjelmeland and Hegstad have obtained direct mode jumping proposals by optimization within Metropolis–Hastings updates and different proposals for ‘forward’ and ‘backward’ steps. We generalize their scheme by allowing the probability distribution for forward and backward kernels to depend on the current state. We use the new setting to combine mode jumping proposals and proposals from a prior approximation. We obtain that the frequency of proposals from the different proposal kernels is automatically adjusted to their quality. Mode jumping proposals include local optimizations. When combining this with a prior approximation it is tempting to use local optimization results not only for mode jumping proposals but also to improve the prior approximation. We show how this idea can be implemented. The resulting algorithm is adaptive but has a Markov structure. We evaluate the effectiveness of the proposed algorithms in two simulation examples.

Keywords: Adaptation; Markov chain Monte Carlo methods; Metropolis; Mode jumping proposals; Multimodal distribution; Optimization; Prior approximation; –Hastings updating

Document Type: Research Article

DOI: https://doi.org/10.1046/j.1369-7412.2003.05329.x

Publication date: 2004-04-01

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more