Stochastic newton sampler: the R package sns

The r package sns implements the stochastic newton sampler (sns),a metropolis- hastings 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 newton- raphson 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. © 2016,american statistical association. all rights reserved.