THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

计量经济分析 = Econometric analysis

Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

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Sequential Monte Carlo methods in practice

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Current Gibbs sampling schemes in mixture of Dirichlet process (MDP) models are restricted to using “conjugate” base measures that allow analytic evaluation of the transition probabilities when resampling configurations, or alternatively need to rely on approximate numeric evaluations of some transition probabilities. Implementation of Gibbs sampling in more general MDP models is an open and important problem because most applications call for the use of nonconjugate base measures. In this article we propose a conceptual framework for computational strategies. This framework provides a perspective on current methods, facilitates comparisons between them, and leads to several new methods that expand the scope of MDP models to nonconjugate situations. We discuss one in detail. The basic strategy is based on expanding the parameter vector, and is applicable for MDP models with arbitrary base measure and likelihood. Strategies are also presented for the important class of normal-normal MDP models and...

https://stat.duke.edu/~scs/Courses/Stat376/Papers/DirichletProc/MacEachernMullerDirichletJCGS1998.pdf

Estimating mixture of dirichlet process models

The problem of estimating many normal means is approached by means of an hierarchical model. The hierarchical model is the standard conjugate model with one exception: the normal distribution at the middle stage is replaced by a Dirichlet process with a normal shape. Estimation for this model is accomplished through the implementation of the Gibbs sampler (see Escobar and West,1991)Thisarticle describes a new Gibbs sampler algorithm that is implemented on a collapsed state space Results that apply to a general setting are obtained, suggesting that a collapse of the state space willimprove the rate of convergence of the Gibbs sampler. An example shows that the proposed collapse of the state space may result in a dramatically improved algorithm

Estimating normal means with a conjugate style dirichlet process prior

We consider dependent nonparametric models for related random probability distributions. For example, the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations. We propose a model that describes dependence across random distributions in an analysis of variance (ANOVA)-type fashion. We define a probability model in such a way that marginally each random measure follows a Dirichlet process (DP) and use the dependent Dirichlet process to define the desired dependence across the related random measures. The resulting probability model can alternatively be described as a mixture of ANOVA models with a DP prior on the unknown mixing measure. The main features of the proposed approach are ease of interpretation and computational simplicity. Because the model follows the standard ANOVAstructure, interpretation and inference parallels conventions for ANOVA mode...

An ANOVA model for dependent random measures

SUMMARY A model is proposed for a Bayesian semiparametric analysis of randomised block experiments. The model is a hierarchical model in which a Dirichlet process is inserted at the middle stage for the distribution of the block effects. This model allows an arbitrary distribution of block effects, and it results in effective estimates of treatment contrasts, block effects and the distribution of block effects. An effective computational strategy is presented for describing the posterior distribution.

A semiparametric Bayesian model for randomised block designs

There are two generations of Gibbs sampling methods for semiparametric models involving the Dirichlet process. The first generation suffered from a severe drawback: the locations of the clusters, or groups of parameters, could essentially become fixed, moving only rarely. Two strategies that have been proposed to create the second generation of Gibbs samplers are integration and appending a second stage to the Gibbs sampler wherein the cluster locations are moved. We show that these same strategies are easily implemented for the sequential importance sampler, and that the first strategy dramatically improves results. As in the case of Gibbs sampling, these strategies are applicable to a much wider class of models. They are shown to provide more uniform importance sampling weights and lead to additional Rao-Blackwellization of estimators.



Deux generations d'echantillonneurs de Gibbs ont ete popularisees pour les modeles semi-parametriques ou intervient le processus de Dirichlet. La premiere generation etait lourdement handicapee du fait que la localisation des grappes, ou groupes de parametres, pouvait devenir quasi-stationnaire. La deuxieme generation d'echantillonneurs a comble cette lacune en incorporant deux strategies: I'integration et I'ajout d'une eeape de relocalisation des grappes. Les auteurs montrent ici que ces strategies sont egalement applicables a la methode d'echantillonnage sequentiel pondere et que I'integration est particulierement efficace dans ce contexte. Comme dans le cas de l'echantillonnage de Gibbs, les deux strategies s'appliquent en fait a une classe beaucoup plus grande de modeles. Comme les auteurs le font valoir, elles produisent des poids d'echantillonnage plus uniformes et permettent une Rao-Blackwellisation additionnelle des estimateurs.

Steven N. MacEachern

Papers

Estimating mixture of dirichlet process models

Estimating normal means with a conjugate style dirichlet process prior

An ANOVA model for dependent random measures

A semiparametric Bayesian model for randomised block designs

Sequential importance sampling for nonparametric Bayes models: The next generation