Monte Carlo Methods in Statistics

Monte Carlo methods are now an essential part of the statistician's toolbox, to the point of being more familiar to graduate students than the measure theoretic notions upon which they are based! We recall in this note some of the advances made in the design of Monte Carlo techniques towards their use in Statistics, referring to Robert and Casella (2004,2010) for an in-depth coverage.Comment: Entry submitted to the International Handbook of Statistical Method

Discussion of "Is Bayes Posterior just Quick and Dirty Confidence?" by D. A. S. Fraser

Discussion of "Is Bayes Posterior just Quick and Dirty Confidence?" by D. A. S. Fraser [arXiv:1112.5582].Comment: Published in at http://dx.doi.org/10.1214/11-STS352A the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Simulation in Statistics

Simulation has become a standard tool in statistics because it may be the only tool available for analysing some classes of probabilistic models. We review in this paper simulation tools that have been specifically derived to address statistical challenges and, in particular, recent advances in the areas of adaptive Markov chain Monte Carlo (MCMC) algorithms, and approximate Bayesian calculation (ABC) algorithms.Comment: Draft of an advanced tutorial paper for the Proceedings of the 2011 Winter Simulation Conferenc

Inference for the limiting cluster size distribution of extreme values

Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The underlying Poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes. In the present paper we introduce estimators of the limiting cluster size probabilities, which are constructed through a recursive algorithm. We derive estimators of the extremal index which plays a key role in determining the intensity of cluster positions. We study the asymptotic properties of the estimators and investigate their finite sample behavior on simulated data.Comment: Published in at http://dx.doi.org/10.1214/07-AOS551 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Search for Certainty: a critical assessment

The Search for Certainty was published in 2009 by Krzysztof Burdzy. It examines the "philosophical duopoly" of von Mises and de Finetti at the foundation of probability and statistics and find this duopoly missing. This review exposes the weakness of the arguments presented in the book, it questions the relevance of introducing a new set of probability axioms from a methodological perspective, and it concludes at the lack of impact of this book on statistical foundations and practice.Comment: This is a revision of a book review of K. Burdzy's "The Search for Certainty", revision that is submitted to Bayesian Analysi