Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.

Bayesian inference begins with a statistical model: M(x)={(x;θ) θ∈Θ} x∈R  for θ∈Θ⊂R    where (x;θ) is the distribution of the sample X:=(1  ) R is the sample space and Θ the parameter space. Bayesian inference modifies the frequentist inferential set up in two crucial respects: (A) It views the unknown parameter(s) θ as random variables with their own distribution, known as the prior distribution: (): Θ→ [0 1]

The range of Bayesian inference algorithms and their different applications has been greatly expanded since the first implementation of a Kalman filter by Stanley F. Schmidt for the Apollo program. Extended Kalman filters or particle filters are just some examples of these algorithms that have been extensively applied to logistics, medical services, search and rescue operations, or automotive safety, among others. This book takes a look at both theoretical foundations of Bayesian inference and practical implementations in different fields. It is intended as an introductory guide for the application of Bayesian inference in the fields of life sciences, engineering, and economics, as well as a source document of fundamentals for intermediate Bayesian readers. (Javier Prieto Tejedor)

In this essay, we will try to provide a formal analysis of practical inference, attentive to the various phases in which it is articulated, and being so capable of explaining both the logical conclusiveness of the inference and the probabilistic nature of its conclusion. An innovative purpose of this article is to show how the final deliberation leading to actionthe ultimate practical judgment-takes place according to a logic consistent with the use of Bayes' theorem. This is why we refer to Bayesian practical inference in the title of this essay.

In this paper, we present a brief review of research work attempting to tackle the issue of tractability in Bayesian inference, including an analysis of the applicability and trade-offs of each proposed solution. In recent years, the Bayesian approach has become increasingly popular, endowing autonomous systems with the ability to deal with uncertainty and incompleteness. However, these systems are also expected to be efficient, while Bayesian inference in general is known to be an NP-hard problem, making it paramount to develop approaches dealing with this complexity in order to allow the implementation of usable Bayesian solutions. Novel computational paradigms and also major developments in massively parallel computation technologies, such as multi-core processors, GPUs and FPGAs, provide us with an inkling of the roadmap in Bayesian computation for upcoming years.