The Valencia International Meetings on Bayesian Statistics, held every four years, provide the forum for researchers to come together and discuss frontier developments in the field. The resulting Proceedings provide a definitive, up-to-date overview encompassing a wide range of theoretical and applied research. This fifth Proceedings is no exception. In particular, it reflects a growing emphasis on computational issues, concerned with making Bayesian methods routinely available to applied practitioners, both statisticians and speciailists in other subject-matter, whose work depends on careful quantification of uncertainties. This book contains several invited papers by leading authorities.