2013/08/03 by Alireza S. Mahani, Mahani, Alireza S., Mansour T. A. Sharabiani +1
Computer Science · Mathematics · #65C05 #65C60 #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.1308.0657
openalex publication_date 2013/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present MH-MGT, a multivariate technique for sampling from twice-differentiable, log-concave probability density functions. MH-MGT is Metropolis-Hastings sampling using asymmetric, multivariate Gaussian proposal functions constructed from Taylor-series expansion of the log-density function. The mean of the Gaussian proposal function represents the full Newton step, and thus MH-MGT is the stochastic counterpart to Newton optimization. Convergence analysis shows that MH-MGT is well suited for sampling from computationally-expensive log-densities with contributions from many independent observations. We apply the technique to Gibbs sampling analysis of a Hierarchical Bayesian marketing effectiveness model built for a large US foodservice distributor. Compared to univariate slice sampling, MH-MGT shows 6x improvement in sampling efficiency, measured in terms of `function evaluation equivalents per independent sample'. To facilitate wide applicability of MH-MGT to statistical models, we prove that log-concavity of a twice-differentiable distribution is invariant with respect to 'linear-projection' transformations including, but not restricted to, generalized linear models.