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Abstract:
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We propose a new Monte Carlo method for sampling from multimodal distributions (Jumping Adaptive Multimodal Sampler). The idea of this technique is based on splitting the task into two: finding the modes of the target distribution and sampling, given the knowledge of the locations of the modes. The sampling algorithm is based on steps of two types: local ones, preserving the mode, and jumps to a region associated with a different mode. Besides, the method learns the optimal parameters while it runs, without requiring user intervention. Our technique should be considered as a flexible framework, in which the design of moves can follow various strategies known from the broad MCMC literature. In order to design an adaptive scheme that facilitates both local and jump moves, we introduce an auxiliary variable representing each mode and we define a new target distribution on an augmented state space. As the algorithm runs and updates its parameters, the target distribution also keeps being modified. This motivates a new class of algorithms, Auxiliary Variable Adaptive MCMC. We develop general ergodic theory for the whole class and apply it to the case of our algorithm. The performance o
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