Ideal-Theoretic Strategies for Asymptotic Approximation of Marginal Likelihood Integrals

Shaowei Lin


The accurate asymptotic evaluation of marginal likelihood integrals is a fundamental problem in Bayesian statistics. Following the approach introduced by Watanabe, we translate this into a problem of computational algebraic geometry, namely, to determine the real log canonical threshold of a polynomial ideal, and we present effective methods for solving this problem. Our results are based on resolution of singularities. They apply to parametric models where the Kullback-Leibler distance is upper and lower bounded by scalar multiples of some sum of squared real analytic functions. Such models include finite state discrete models.


computational algebra; asymptotic approximation; marginal likelihood; learning coefficient; real log canonical threshold

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