Generalized Direct Sampling for Hierarchical Bayesian Models

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models involving large data sets. Samples are independent, so they can be collected in parallel, and we do not need to be concerned with issues like chain convergence and autocorrelation. Additionally, the method can be used to compute marginal likelihoods

On the Use of Surrogate Functions for Mixed Variable Optimization of Simulated Systems

This research considers the efficient numerical solution of linearly constrained mixed variable programming (MVP) problems, in which the objective function is a black-box stochastic simulation, function evaluations may be computationally expensive, and derivative information is typically not available. MVP problems are those with a mixture of continuous, integer, and categorical variables, the latter of which may take on values only from a predefined list and may even be non-numeric. Mixed Variable Generalized Pattern Search with Ranking and Selection (MGPS-RS) is the only existing, provably convergent algorithm that can be applied to this class of problems. Present in this algorithm is an optional framework for constructing and managing less expensive surrogate functions as a means to reduce the number of true function evaluations that are required to find approximate solutions. In this research, the NOMADm software package, an implementation of pattern search for deterministic MVP problems, is modified to incorporate a sequential selection with memory (SSM) ranking and selection procedure for handling stochastic problems. In doing so, the underlying algorithm is modified to make the application of surrogates more efficient. A second class of surrogates based on the Nadaraya-Watson kernel regression estimator is also added to the software. Preliminary computational testing of the modified software is performed to characterize the relative efficiency of selected surrogate functions for mixed variable optimization in simulated systems