Ideal-Theoretic Strategies for Asymptotic Approximation of Marginal Likelihood Integrals

  • Shaowei Lin

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.
Published
2017-02-08
How to Cite
LIN, Shaowei. Ideal-Theoretic Strategies for Asymptotic Approximation of Marginal Likelihood Integrals. Journal of Algebraic Statistics, [S.l.], v. 8, n. 1, feb. 2017. ISSN 1309-3452. Available at: <http://www.jalgstat.com/jalgstat/article/view/47>. Date accessed: 21 sep. 2017. doi: https://doi.org/10.18409/jas.v8i1.47.
Section
Articles - regular submission

Keywords

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