Merrill Liechty (Drexel University): Multivariate Sufficient Statistics Using Kronecker Products

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, and 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.

Keywords Multivariate Summary Statistic · Multivariate Normal Distribution · Inverse-Wishart Distribution · Computationally Efficient Sufficient Statistic · Bayesian Regression

Joint work with Tibbits, Matt (U.S. Department of Defense)