Abstract:
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Estimation of normalizing constants is a key problem in statistics. Strategies for estimating normalizing constants often rely on our ability to obtain samples from the target distribution. However, many sampling methods do not work well when the target distribution is multi-modal. Some are specifically designed to sample from multi-modal distributions, such as parallel tempering, but the most efficient way to calculate the normalizing constant with the samples obtained is unclear, and tuning such algorithms is time-consuming. In this paper, we propose an adaptive MCMC method to sample from a multi-modal density and simultaneously perform much of the computation needed for a complementary estimation strategy. Our methods develop from the Warp-U bridge sampling estimation strategy proposed by Wang, Jones, and Meng (2016). We establish the ergodicity of our sampling algorithm. For the final estimation step, we introduce a stochastic bridge sampling approach that not only has a smaller asymptotic variance than classical bridge sampling but also lower computational cost. We demonstrate the advantages of our approach through a simulation study and an application to exoplanet detection.
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