Multivariate sufficient statistics using Kronecker products

Authors:
Merrill W. Liechty;Matthew Tibbits
Affiliations:
Department of Decision Sciences, LeBow College of Business, Drexel University, Philadelphia, USA 19104;Department of Statistics, Pennsylvania State University, University Park, USA 16803
Venue:
Statistics and Computing
Year:
2010

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The ubiquitous Kronecker product

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra

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Abstract

We present a multivariate sufficient statistic using Kronecker products that dramatically increases computational efficiency in evaluating likelihood functions and/or posterior distributions. In particular, we examine the example of multivariate regression in a Bayesian setting. We compare the computation time for using the Gibbs sampler both with and without the sufficient statistic. We show that the difference in computation time grows quadratically with the number of covariates and products and linearly with the number of individuals. In the simulation study, speedup factors ranging from at least 20 times to almost 300 times were observed when using the Kronecker sufficient statistic.