  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.
