Bayesian Analysis of Stochastic Process Models

Preface

To the best of our knowledge, this is the first book focusing on Bayesian analysis of stochastic process models at large. We believe that recent developments in the field and the growing interest in this topic deserve a book-length treatment.

The advent of cheap computing power and the developments in Markov chain Monte Carlo simulation produced a revolution within the field of Bayesian statistics around the beginning of the 1990s, allowing a true ‘model liberation’ that permitted treating models that previously we could only dream of dealing with. This has challenged analysts in trying to deal with more complex problems. Given this great advance in computing power, it is no surprise that several researchers have attempted to deal with stochastic processes in a Bayesian fashion, moving away from the usual assumptions of independent and identically distributed (IID) data. In 1998, this led us to organize the first Workshop on Bayesian Analysis of Stochastic Processes in Madrid. The seventh edition of this conference was held in 2011, which is an illustration of the great current interest in this subject area. Given the numerous papers written, we felt, therefore, that the time was right to provide a systematic account of developments in Bayesian analysis of stochastic processes. In doing this, it is interesting to note that most books in stochastic processes have referred mainly to probabilistic aspects and there are many fewer texts that treat them from a (classical) statistical ...