This book is about using graphs to understand the relationship between a regression model and the data to which it is fitted. Because of the way in which models are fitted, for example, by least squares, we can lose infor mation about the effect of individual observations on inferences about the form and parameters of the model. The methods developed in this book reveal how the fitted regression model depends on individual observations and on groups of observations. Robust procedures can sometimes reveal this structure, but downweight or discard some observations. The novelty in our book is...

Graphic modelling is a form of multivariate analysis that uses graphs to represent models. These graphs display the structure of dependencies, both associational and causal, between the variables in the model. This textbook provides an introduction to graphical modelling with emphasis on applications and practicalities rather than on a formal development. It is based on the popular software package for graphical modelling, MIM, a freeware version of which can be downloaded from the Internet. Following an introductory chapter which sets the scene and describes some of the basic ideas of...

In the period since the first edition was published, I have appreciated the corre- spondence from all parts of the world expressing thanks for the presentation of statistics from a user's perspective. It has been particularIy pleasing to have been invited to contribute to course restructuring and development based on the ap- proach to learning and applying statistics that underlies this book. In addition, I have taken account of suggestions and criticisms, and I hope that this new edition will address all major concerns. The range of readily accessible statistical methods has greatly expanded...

This is an introduction to Bayesian statistics and decision theory, including advanced topics such as Monte Carlo methods. This new edition contains several revised chapters and a new chapter on model choice.

This is the second edition of Linear Models for Multivariate, Time Series and Spatial Data. It has a new title to indicate that it contains much new material. The primary changes are the addition of two new chapters: one on nonparametric regression and one on response surface maximization. As before, the presentations focus on the linear model aspects of the subject. For example, in the nonparametric regression chapter there is very little about kernal regression estimation but quite a bit about series approxi mations, splines, and regression trees, all of which can be viewed as linear...

Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of...

I have endeavored to provide a comprehensive introduction to a wide - riety of statistical methods for the analysis of repeated measurements. I envision this book primarily as a textbook, because the notes on which it is based have been used in a semester-length graduate course I have taught since1991.Thiscourseisprimarilytakenbygraduatestudentsinbiostat- tics and statistics, although students and faculty from other departments have audited the course. I also anticipate that the book will be a useful r- erence for practicing statisticians. This assessment is based on the positive responses I...

This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are usefulin statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each...

Networks of queues arise frequently as models for a wide variety of congestion phenomena. Discrete event simulation is often the only available means for studying the behavior of complex networks and many such simulations are non Markovian in the sense that the underlying stochastic process cannot be repre sented as a continuous time Markov chain with countable state space. Based on representation of the underlying stochastic process of the simulation as a gen eralized semi-Markov process, this book develops probabilistic and statistical methods for discrete event simulation of networks of...

Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch. Most of this can be read by a student with a basic knowledge of complex analysis. The next part treats complex multiplication, including a discussion of Deuring's theory of l-adic and p-adic representations, and elliptic curves with singular invariants. Part three covers curves...