Sampling from the posterior distribution and computing posterior quanti- ties of interest using Markov chain Monte Carlo (MCMC) samples are two major challenges involved in advanced Bayesian computation. This book examines each of these issues in detail and focuses heavily on comput- ing various posterior quantities of interest from a given MCMC sample. Several topics are addressed, including techniques for MCMC sampling, Monte Carlo (MC) methods for estimation of posterior summaries, improv- ing simulation accuracy, marginal posterior density estimation, estimation of normalizing constants,...
Sampling from the posterior distribution and computing posterior quanti- ties of interest using Markov chain Monte Carlo (MCMC) samples are two major ...
Prediction of a random field based on observations of the random field at some set of locations arises in mining, hydrology, atmospheric sciences, and geography. Kriging, a prediction scheme defined as any prediction scheme that minimizes mean squared prediction error among some class of predictors under a particular model for the field, is commonly used in all these areas of prediction. This book summarizes past work and describes new approaches to thinking about kriging.
Prediction of a random field based on observations of the random field at some set of locations arises in mining, hydrology, atmospheric sciences, and...
Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. This book sets out to lay some of the foundations for subsampling methodology and related methods.
Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resamp...
1.1 The DevelopmentofARCH Models Time series models have been initially introduced either for descriptive purposes like prediction and seasonal correction or for dynamic control. In the 1970s, the researchfocusedonaspecificclassoftimeseriesmodels, theso-calledautoregres- sive moving average processes (ARMA), which were very easy to implement. In thesemodels, thecurrentvalueoftheseriesofinterestiswrittenasalinearfunction ofits own laggedvalues andcurrentandpastvaluesofsomenoiseprocess, which can be interpreted as innovations to the system. However, this approach has two major drawbacks: 1) it...
1.1 The DevelopmentofARCH Models Time series models have been initially introduced either for descriptive purposes like prediction and seasonal correc...
Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach...
Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents ...
This book explores both non parametric and general statistical ideas by developing non parametric procedures in simple situations. The major goal is to give the reader a thorough intuitive understanding of the concepts underlying nonparametric procedures and a full appreciation of the properties and operating characteristics of those procedures covered. This book differs from most statistics books by including considerable philosophical and methodological discussion. Special attention is given to discussion of the strengths and weaknesses of various statistical methods and approaches....
This book explores both non parametric and general statistical ideas by developing non parametric procedures in simple situations. The major goal is t...
Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.
Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem ...
This book describes the development of statistics, which for more than a century was called "the calculus of observations." The approach will help readers gain a clearer understanding of the historical development as well as the essential nature of some of the commonly used statistical estimation procedures. Detailed descriptions of the fitting of linear relationships by the method of least squares and the closely related least absolute deviations and minimax absolute deviations procedures are presented, along with some of the important work by Laplace, Gauss, and Adrain.
This book describes the development of statistics, which for more than a century was called "the calculus of observations." The approach will help rea...
Graphs are used to understand the relationship between a regression model and the data to which it is fitted. The authors develop new, highly informative graphs for the analysis of regression data and for the detection of model inadequacies. As well as illustrating new procedures, the authors develop the theory of the models used, particularly for generalized linear models. The book provides statisticians and scientists with a new set of tools for data analysis. Software to produce the plots is available on the authors website.
Graphs are used to understand the relationship between a regression model and the data to which it is fitted. The authors develop new, highly informat...
Orthogonal arrays have played a vital role in improving the quality of products manufactured throughout the world. This first book on the subject since its introduction more than fifty years ago serves as a key resource to this area of designing experiments. Most of the arrays obtained by the methods in this book are available electronically. Anyone running experiments - whether in a chemistry lab or a manufacturing plant, or in agricultural or medical research - will find this book useful.
Orthogonal arrays have played a vital role in improving the quality of products manufactured throughout the world. This first book on the subject sinc...
