The name of Richard the Lionheart is familiar to us all. Curiously, this legendary figure is more often associated with Aquitaine and the Holy Land than with Normandy. A worthy descendant of William the Conqueror, Richard I maintained Normandy within the Plantagenet Empire, by countering the... číst celé
This is an introduction to Bayesian statistics and decision theory, including advanced topics such as Monte Carlo methods. This new edition contains several revised chapters and a new chapter on model choice.
Markov chain Monte Carlo methods were developed to provide the experimenter with realistic models. Written by two leading researchers, this up-to-date reference covers an important area of statistic which has many applications to engineering, aeronautics, biology, networks, and astronomy.
This monograph explores convergence monitoring for MCMC algorithms, focusing on discrete Markov chains. It begins with an overview of MCMC methods, including recent advancements like perfect simulation and Langevin Metropolis-Hastings algorithms, as well as current convergence diagnostics. The contributors establish a theoretical framework for studying MCMC convergence through discrete Markov chains, emphasizing its broad applicability, from latent variable models such as mixtures to chains with renewal properties and general Markov chains. They connect these concepts with practical convergence diagnostics, which include graphical plots (allocation maps, divergence graphs, variance stabilizing plots, normality plots), stopping rules (normality, stationarity, stability tests), and confidence bounds (divergence, asymptotic variance, normality). Many quantitative tools leverage manageable versions of the Central Limit Theorem (CLT). The proposed methods are evaluated using benchmark examples and three realistic applications: hidden Markov modeling of DNA sequences with perfect simulation, latent stage modeling of HIV infection dynamics, and modeling hospitalization duration through exponential mixtures. This work stems from a monthly research seminar at CREST, Paris, initiated in 1995, led by Christian P. Robert, a prominent figure in the field.