The Parallel C++ Statistical Library for Bayesian Inference: QUESO

Abstract

The Parallel C++ Statistical Library for the Quantification of Uncertainty for Estimation, Simulation and Optimization, Queso, is a collection of statistical algorithms and programming constructs supporting research into the quantification of uncertainty of models and their predictions. Queso is primarily focused on solving statistical inverse problems using Bayes's theorem, which expresses a distribution of possible values for a set of uncertain parameters (the posterior distribution) in terms of the existing knowledge of the system (the prior) and noisy observations of a physical process, represented by a likelihood distribution. The posterior distribution is not often known analytically, and so requires computational methods. It is typical to compute probabilities and moments from the posterior distribution, but this is often a high-dimensional object and standard Reimann-type methods for quadrature become prohibitively expensive. The approach Queso takes in this regard is to rely on Markov chain Monte Carlo (MCMC) methods which are well suited to evaluating quantities such as probabilities and moments of high-dimensional probability distributions. Queso's intended use is as tool to assist and facilitate coupling uncertainty quantification to a specific application called a forward problem. While many libraries presently exist that solve Bayesian inference problems, Queso is a specialized piece of software primarily designed to solve such problems by utilizing parallel environments demanded by large-scale forward problems. Queso is written in C++, uses MPI, and utilizes libraries already available to the scientific community.