Bayesian Inference for Probabilistic Risk Assessment

Recent years have seen significant advances in the use of risk analysis in many government agencies and private corporations. These advances are reflected both in the state of practice of risk analysis, and in the status of governmental requirements and industry standards. Because current risk and reliability models are often used to regulatory decisions, it is critical that inference methods used in these models be robust and technically sound.The goal of Bayesian Inference for Probabilistic Risk Assessment is to provide a Bayesian foundation for framing probabilistic problems and performing inference on these problems. It is aimed at scientists and engineers who perform or review risk analyses and it provides an analytical structure for combining data and information from various sources to generate estimates of the parameters of uncertainty distributions used in risk and reliability models.Inference in the book employs a modern computational approach known as Markov chain Monte Carlo (MCMC). MCMC methods were described in the early 1950s in research into Monte Carlo sampling at Los Alamos. Recently, with the advance of computing power and improved analysis algorithms, MCMC is increasingly being used for a wide range of Bayesian inference problems in a variety of disciplines. MCMC is effectively (although not literally) numerical (Monte Carlo) integration by way of Markov chains. Inference is performed by sampling from a target distribution (i.e., a specially constructed Markov chain, based upon the inference problem) until convergence (to the posterior distribution) is achieved. The MCMC approach may be implemented using custom-written routines or existing general purpose commercial or open-source software. This book uses an open-source program called OpenBUGS (commonly referred to as WinBUGS) to solve the inference problems that are described. A powerful feature of OpenBUGS is its automatic selection of an appropriate MCMC sampling scheme for a given problem. The approach that is taken in this book is to provide analysis "building blocks" that can be modified, combined, or used as-is to solve a variety of challenging problems.The MCMC approach used is implemented via textual scripts similar to a macro-type programming language. Accompanying each script is a graphical Bayesian network illustrating the elements of the script and the overall inference problem being solved. The book also covers the important topic of MCMC convergence.