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

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