Stochastic Newton Sampler: The R Package sns

Abstract

The R package sns implements the stochastic Newton sampler (SNS), a MetropolisHastings Markov chain Monte Carlo (MCMC) algorithm where the proposal density function is a multivariate Gaussian based on a local, second-order Taylor-series expansion of log-density. The mean of the proposal function is the full Newton step in the NewtonRaphson optimization algorithm. Taking advantage of the local, multivariate geometry captured in log-density Hessian allows SNS to be more efficient than univariate samplers, approaching independent sampling as the density function increasingly resembles a multivariate Gaussian. SNS requires the log-density Hessian to be negative-definite everywhere in order to construct a valid proposal function. This property holds, or can be easily checked, for many GLM-like models. When the initial point is far from density peak, running SNS in non-stochastic mode by taking the Newton step - augmented with line search - allows the MCMC chain to converge to high-density areas faster. For high-dimensional problems, partitioning the state space into lower-dimensional subsets, and applying SNS to the subsets within a Gibbs sampling framework can significantly improve the mixing of SNS chains. In addition to the above strategies for improving convergence and mixing, sns offers utilities for diagnostics and visualization, sample-based calculation of Bayesian predictive posterior distributions, numerical differentiation, and log-density validation.