Ideal-Theoretic Strategies for Asymptotic Approximation of Marginal Likelihood Integrals
arXiv:1003.5338 · doi:10.18409/jas.v8i1.47
Abstract
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.
arXiv comment34 pages. Moved technical parts of the computation for the statistics example to the appendix