Subregion Adaptive Integration of
Functions Having a Dominant Peak
Alan Genz and Robert E. Kass
Many statistical multiple integration problems involve
integrands that have a dominant peak. In applying numerical methods to
solve these problems, statisticians have paid relatively little
attention to existing quadrature
methods and available software developed in the
numerical analysis literature. One reason these methods have been
largely overlooked, even though they are known to be more efficient
than Monte Carlo for well-behaved problems of modest dimensionality,
may be that
when applied naively they are
poorly suited for peaked-integrand problems.
In this paper
we use transformations based on ``split-t'' distributions
to allow the integrals to be efficiently
computed using a subregion-adaptive numerical integration algorithm.
Our split-t distributions are modifications of those suggested by
and may also be used to define Monte Carlo
importance functions. We then compare our approach to Monte Carlo.
In the several examples we examine here, we find
to be substantially more efficient than importance sampling.
Key Words: Importance sampling,
Monte Carlo, multiple integrals, numerical quadrature,
Bayesian computation, split-t distributions.
Here is the full postscript text for this
technical report. It is 465264 bytes long.