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, and they apply to all statistical
models for discrete data that admit a parametrization by real analytic
functions.