Bayesian Computation via Auxiliary-Try Metropolis and Parallel Annealed Chains

Music City Center 

The Multiple-Try Metropolis (MTM) algorithm extends the traditional Metropolis-Hastings method by generating multiple candidate proposals per iteration, improving the exploration of the state space. However, MTM can struggle with navigating complex topographies, such as plateaus and local maxima, when relying solely on local proposals. In this work, we introduce the Auxiliary-Try Metropolis (ATM) algorithm, an extension of MTM that utilizes an auxiliary variable to guide the generation of candidate proposals. This auxiliary mechanism enables more effective traversal of challenging regions in the state space, enhancing the chain's ability to escape local optima and explore more broadly. We rigorously establish the validity of ATM as a Markov chain Monte Carlo method and demonstrate its superior performance compared to existing MTM approaches. Furthermore, we propose a novel Monte Carlo method that leverages the ATM algorithm as the foundation for constructing parallel annealed chains, offering a powerful tool for Bayesian computation in high-dimensional and complex models.

Markov chain Monte Carlo

Multiple-Try Metropolis

guided proposals

parallel Markov chains