Ideal-Theoretic Strategies for Asymptotic Approximation of Marginal Likelihood Integrals computational algebra asymptotic approximation marginal likelihood learning coefficient real log canonical threshold 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. Lin, Shaowei 2017 2017-02-08 Article application/pdf islandora:1007801 http://hdl.handle.net/10560/islandora:1007801 MATH / Applied Mathematics Illinois Institute of Technology Journal of Algebraic Statistics en Open Access