During the last decades. the evolution of theoretical statistics has been marked by a considerable expansion of the number of mathematically and computationaly trac table models. Faced with this inflation. applied statisticians feel more and more un comfortable: they are often hesitant about their traditional (typically parametric) assumptions. such as normal and i. i. d . * ARMA forms for time-series. etc . * but are at the same time afraid of venturing into the jungle of less familiar models. The prob lem of the justification for taking up one model rather than another one is thus a crucial one. and can take different forms. (a) ~~~GBPifi~~~iQ~ : Do observations suggest the use of a different model from the one initially proposed (e. g. one which takes account of outliers). or do they render plau sible a choice from among different proposed models (e. g. fixing or not the value of a certai n parameter) ? (b) tlQ~~L~~l!rQ1!iIMHQ~ : How is it possible to compute a "distance" between a given model and a less (or more) sophisticated one. and what is the technical meaning of such a "distance" ? (c) BQe~~~~~~ : To what extent do the qualities of a procedure. well adapted to a "small" model. deteriorate when this model is replaced by a more general one? This question can be considered not only. as usual. in a parametric framework (contamina tion) or in the extension from parametriC to non parametric models but also.

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.

The Valencia International Meetings on Bayesian Statistics, held every four years, provide the forum for researchers to come together to present 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 fourth volume of 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 other specialists whose work depends on careful quantification of uncertainties. The growing interest in Bayesian methods is revealed by the ever-increasing participation in the Valencia meetings. This, in turn, is reflected in the high quality of this work, which contains 30 invited papers by leading authorities and 33 refereed contributed papers, selected from over 150 presented at the meeting.

The Valencia International Meetings on Bayesian Statistics, held every four years, provide the main forum for researchers in the area of Bayesian Statistics to come together to present and discuss frontier developments in the field. Covering a broad range of applications and models, including genetics, computer vision and computation, the resulting proceedings provide a definitive, up-to-date overview encompassing a wide range of theoretical and applied research. This eighth proceedings includes edited and refereed versions of 20 invited papers plus extensive and in-depth discussion along with 19 extended four page abstracts of the best presentations offering a wide perspective of the developments in Bayesian statistics over the last four years.