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Abstract:
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This talk presents a novel method of high-dimensional stochastic integration for calculating marginal likelihoods when a posterior MCMC sample is available. The accuracy and efficiency of importance sampling depends strongly on the importance function having approximately the same shape as the target function. In high dimensions, such importance functions can be extremely hard to build. However, in the Bayesian context, the target is proportional to the posterior, so a posterior MCMC sample can be used to guide the choice of importance function. We do this by centering multivariate student distributions around some of the MCMC points and then adapting their parameters to minimize the variance in the importance weights. Our work is done in the context of exoplanet detection, first in determining how many planets are present, and second in scheduling telescope time.
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