Statistics Seminar: John Ormerod -- Skew-Normal Variational Approximations

John Ormerod School of Mathematics and Statistics University of Sydney 

Location: Carslaw 173 

Time: 2pm Friday, September 17, 2010 

Title: Skew-Normal Variational Approximations 

Abstract: High-dimensional analytically intractable integrals are a pervasive problem in
Bayesian inference.  Monte Carlo methods can be used in the analysis of models where
such problems arise.  However, for large datasets or complex models such methods become
computationally burdensome and it may become desirable to seek alternatives.  

Popular deterministic alternatives include variational Bayes and Laplace's method.
However, variational Bayes only performs well under particular conjugacy and
independence assumptions and Laplace's method only works well when the posterior is
nearly normal in shape.  

In this talk I introduce the skew-normal variational approximation which minimises the
Kullback-Leibler distance between a posterior density and a multivariate skew-normal
density.  The resulting approximation often simplifies calculations to the maximisation
of a sum of univariate integrals which may be handled using a combination of standard
optimisation and quadrature techniques.  It is shown for a number of examples that the
approach is more accurate than variational Bayes and Laplace's method whilst remaining
faster than standard Monte Carlo methods.