Oscillation of adaptative Metropolis-Hasting and simulated annealing algorithms around penalized least squares estimator

TL;DR

This paper investigates the oscillatory behavior of adaptive Metropolis-Hastings algorithms near penalized least squares solutions as temperature approaches zero, proposing new criteria for parameter selection and comparing with simulated annealing.

Contribution

It introduces new criteria for selecting proposal distributions and temperature in Metropolis-Hastings algorithms, enhancing understanding of their behavior around penalized least squares estimators.

Findings

Derived criteria for proposal distribution selection.

Analyzed oscillation behavior as temperature approaches zero.

Compared performance of Metropolis-Hastings and simulated annealing.

Abstract

In this work we study, as the temperature goes to zero, the oscillation of Metropolis-Hasting's algorithm around the Basis Pursuit De-noising solutions. We derive new criteria for choosing the proposal distribution and the temperature in Metropolis-Hasting's algorithm. Finally we apply these results to compare Metropolis-Hasting's and simulated annealing algorithms.