This chapter provides a survey of the main methods in nonuniform random variate
generation, and highlights recent research on the subject. Classical paradigms such as …

Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of
probability distributions commonly encountered in modern applications. For MCMC …

Heuristically, a discrete-time stochastic process has the Markov property if the past and
future are independent given the present. In this introductory chapter, we give the formal …

Statisticians are increasingly posed with thought-provoking and even paradoxical questions,
challenging our qualifications for entering the statistical paradises created by Big Data. By …

It is desirable that nonlinear dynamic analyses for structural fragility assessment are
performed using unscaled ground motions. The widespread use of a simple dynamic …

Abstract Restricted Boltzmann machines (RBMs) are probabilistic graphical models that can
be interpreted as stochastic neural networks. They have attracted much attention as building …

General state-space Markov chain theory has evolved to make it both more accessible and
more powerful. Markov Chain Monte Carlo in Practice introduces MCMC methods and their …

Identifying the boundary beyond which quantum machines provide a computational
advantage over their classical counterparts is a crucial step in charting their usefulness …

Hidden Markov models—most often abbreviated to the acronym “HMMs”—are one of the
most successful statistical modelling ideas that have came up in the last forty years: the use …

In this article, we present an overview of methods for sequential simulation from posterior
distributions. These methods are of particular interest in Bayesian filtering for discrete time …