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Fundamentals of Mathematical Statistics
Fundamentals of Mathematical Statistics is meant for a standard one-semester advanced undergraduate or graduate-level course in Mathematical Statistics. It covers all the key topics—statistical models, linear normal models, exponential families, estimation, asymptotics of maximum likelihood, significance testing, and models for tables of counts. It assumes a good background in mathematical analysis, linear algebra, and probability but includes an appendix with basic results from these areas. Throughout the text, there are numerous examples and graduated exercises that illustrate the topics covered, rendering the book suitable for teaching or self-study. Features A concise yet rigorous introduction to a one-semester course in Mathematical Statistics Covers all the key topics Assumes a solid background in Mathematics and Probability Numerous examples illustrate the topics Many exercises enhance understanding of the material and enable course use This textbook will be a perfect fit for an advanced course in Mathematical Statistics or Statistical Theory. The concise and lucid approach means it could also serve as a good alternative, or supplement, to existing texts.
Graphical Models
The idea of modelling systems using graph theory has its origin in several scientific areas: in statistical physics (the study of large particle systems), in genetics (studying inheritable properties of natural species), and in interactions in contingency tables. The use of graphical models in statistics has increased considerably over recent years and the theory has been greatly developed and extended. This book provides the first comprehensive and authoritative account of the theory of graphical models and is written by a leading expert in the field. It contains the fundamental graph theory required and a thorough study of Markov properties associated with various type of graphs. The stati...
Handbook of Defeasible Reasoning and Uncertainty Management Systems
Reasoning under uncertainty is always based on a specified language or for malism, including its particular syntax and semantics, but also on its associated inference mechanism. In the present volume of the handbook the last aspect, the algorithmic aspects of uncertainty calculi are presented. Theory has suffi ciently advanced to unfold some generally applicable fundamental structures and methods. On the other hand, particular features of specific formalisms and ap proaches to uncertainty of course still influence strongly the computational meth ods to be used. Both general as well as specific methods are included in this volume. Broadly speaking, symbolic or logical approaches to uncertaint...
Introduction to Graphical Modelling
A useful introduction to this topic for both students and researchers, with an emphasis on applications and practicalities rather than on a formal development. It is based on the popular software package for graphical modelling, MIM, freely available for downloading from the Internet. Following a description of some of the basic ideas of graphical modelling, subsequent chapters describe particular families of models, including log-linear models, Gaussian models, and models for mixed discrete and continuous variables. Further chapters cover hypothesis testing and model selection. Chapters 7 and 8 are new to this second edition and describe the use of directed, chain, and other graphs, complete with a summary of recent work on causal inference.
Bayesian Networks and Decision Graphs
This is a brand new edition of an essential work on Bayesian networks and decision graphs. It is an introduction to probabilistic graphical models including Bayesian networks and influence diagrams. The reader is guided through the two types of frameworks with examples and exercises, which also give instruction on how to build these models. Structured in two parts, the first section focuses on probabilistic graphical models, while the second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision process and partially ordered decision problems.
Probabilistic Networks and Expert Systems
Probabilistic expert systems are graphical networks which support the modeling of uncertainty and decisions in large complex domains, while retaining ease of calculation. Building on original research by the authors, this book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures, and algorithms. The book will be of interest to researchers in both artificial intelligence and statistics, who desire an introduction to this fascinating and rapidly developing field. The book, winner of the DeGroot Prize 2002, the only book prize in the field of statistics, is new in paperback.
Generalized Linear Mixed Models
Generalized Linear Mixed Models: Modern Concepts, Methods, and Applications (2nd edition) presents an updated introduction to linear modeling using the generalized linear mixed model (GLMM) as the overarching conceptual framework. For students new to statistical modeling, this book helps them see the big picture – linear modeling as broadly understood and its intimate connection with statistical design and mathematical statistics. For readers experienced in statistical practice, but new to GLMMs, the book provides a comprehensive introduction to GLMM methodology and its underlying theory. Unlike textbooks that focus on classical linear models or generalized linear models or mixed models, t...
The Nurse: Inside Denmark's Most Sensational Criminal Trial
The award-winning true-crime account of a Danish nurse accused of killing her patients—now a Netflix miniseries starring Josephine Park. In the early hours of March 2015, the police receive a call from a nurse at a provincial Danish hospital. She suspects her colleague is deliberately killing patients and fears that it has just happened again. Soon, several witnesses reveal that they too suspect the same nurse of poisoning patients; some have been harbouring their suspicion for years... so why has no one done anything about it before? And now that those patients’ bodies have long been cremated, where is the evidence? To this day, the nurse, Christina Aistrup Hansen, maintains her innocen...
Algorithmic Learning in a Random World
Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.
Highly Structured Stochastic Systems
Highly Structured Stochastic Systems (HSSS) is a modern strategy for building statistical models for challenging real-world problems, for computing with them, and for interpreting the resulting inferences. Complexity is handled by working up from simple local assumptions in a coherent way, and that is the key to modelling, computation, inference and interpretation; the unifying framework is that of Bayesian hierarchical models. The aim of this book is to make recent developments in HSSS accessible to a general statistical audience. Graphical modelling and Markov chain Monte Carlo (MCMC) methodology are central to the field, and in this text they are covered in depth. The chapters on graphica...
