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Abstract:
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The sequential Monte Carlo (SMC) methodologies are powerful tools in solving very high-dimensional and complex problems often encountered in applications. The key to a successful SMC implementation is efficiency, which is related directly to the design of the key components of SMC. Many problems in applications share a common feature: The target distribution is constrained highly. That is, the target distribution is a truncated distribution on an ill-shaped subspace of a high-dimensional space. The constraints, without careful treatments, are a main source of obstacles in successful implementations of SMC. In this talk, we develop a set of algorithms categorized as Constrained Sequential Monte Carlo (CSMC) for solving such problems, including strategies in designing the intermediate distributions, the trial distributions, the resampling steps, and Markov moves with CSMC.
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