Probabilistic Conditional Independence Structures provides the mathematical description of probabilistic conditional independence structures; the author uses non-graphical methods of their description, and takes an algebraic approach. The monograph presents the methods of structural imsets and supermodular functions, and deals with independence implication and equivalence of structural imsets. Motivation, mathematical foundations and areas of application are included, and a rough overview of graphical methods is also given. In particular, the author has been careful to use suitable terminology, and presents the work so that it will be understood by both statisticians, and by researchers in artificial intelligence. The necessary elementary mathematical notions are recalled in an appendix.
Tychomancy—meaning “the divination of chances”—presents a set of rules for inferring the physical probabilities of outcomes from the causal or dynamic properties of the systems that produce them. Probabilities revealed by the rules are wide-ranging: they include the probability of getting a 5 on a die roll, the probability distributions found in statistical physics, and the probabilities that underlie many prima facie judgments about fitness in evolutionary biology. Michael Strevens makes three claims about the rules. First, they are reliable. Second, they are known, though not fully consciously, to all human beings: they constitute a key part of the physical intuition that allows us to navigate around the world safely in the absence of formal scientific knowledge. Third, they have played a crucial but unrecognized role in several major scientific innovations. A large part of Tychomancy is devoted to this historical role for probability inference rules. Strevens first analyzes James Clerk Maxwell’s extraordinary, apparently a priori, deduction of the molecular velocity distribution in gases, which launched statistical physics. Maxwell did not derive his distribution from logic alone, Strevens proposes, but rather from probabilistic knowledge common to all human beings, even infants as young as six months old. Strevens then turns to Darwin’s theory of natural selection, the statistics of measurement, and the creation of models of complex systems, contending in each case that these elements of science could not have emerged when or how they did without the ability to “eyeball” the values of physical probabilities.
Explains the material step-by-step starting from meaningful examples Steps detailed with R code in the spirit of reproducible research Real world data analyses from a Science paper reproduced and explained in detail Examples span a variety of fields across social and life sciences Overview of available software in and outside R
Written by some major contributors to the development of this class of graphical models, Chain Event Graphs introduces a viable and straightforward new tool for statistical inference, model selection and learning techniques. The book extends established technologies used in the study of discrete Bayesian Networks so that they apply in a much more general setting As the first book on Chain Event Graphs, this monograph is expected to become a landmark work on the use of event trees and coloured probability trees in statistics, and to lead to the increased use of such tree models to describe hypotheses about how events might unfold. Features: introduces a new and exciting discrete graphical model based on an event tree focusses on illustrating inferential techniques, making its methodology accessible to a very broad audience and, most importantly, to practitioners illustrated by a wide range of examples, encompassing important present and future applications includes exercises to test comprehension and can easily be used as a course book introduces relevant software packages Rodrigo A. Collazo is a methodological and computational statistician based at the Naval Systems Analysis Centre (CASNAV) in Rio de Janeiro, Brazil. Christiane Görgen is a mathematical statistician at the Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany. Jim Q. Smith is a professor of statistics at the University of Warwick, UK. He has published widely in the field of statistics, AI, and decision analysis and has written two other books, most recently Bayesian Decision Analysis: Principles and Practice (Cambridge University Press 2010).
The International Conference on Information Processing and Management of - certainty in Knowledge-Based Systems, IPMU, is organized every two years with the aim of bringing together scientists working on methods for the management of uncertainty and aggregation of information in intelligent systems. Since 1986, this conference has been providing a forum for the exchange of ideas between th theoreticians and practitioners working in these areas and related ?elds. The 13 IPMU conference took place in Dortmund, Germany, June 28–July 2, 2010. This volume contains 79 papers selected through a rigorous reviewing process. The contributions re?ect the richness of research on topics within the scope of the conference and represent several important developments, speci?cally focused on theoretical foundations and methods for information processing and management of uncertainty in knowledge-based systems. We were delighted that Melanie Mitchell (Portland State University, USA), Nihkil R. Pal (Indian Statistical Institute), Bernhard Sch ̈ olkopf (Max Planck I- titute for Biological Cybernetics, Tubing ̈ en, Germany) and Wolfgang Wahlster (German Research Center for Arti?cial Intelligence, Saarbruc ̈ ken) accepted our invitations to present keynote lectures. Jim Bezdek received the Kamp ́ede F ́ eriet Award, granted every two years on the occasion of the IPMU conference, in view of his eminent research contributions to the handling of uncertainty in clustering, data analysis and pattern recognition.
A decade after the publication of Contemporary Mathematics Vol. 287, the present volume demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models. --
CAUSAL INFERENCE IN STATISTICS A Primer Causality is central to the understanding and use of data. Without an understanding of cause–effect relationships, we cannot use data to answer questions as basic as "Does this treatment harm or help patients?" But though hundreds of introductory texts are available on statistical methods of data analysis, until now, no beginner-level book has been written about the exploding arsenal of methods that can tease causal information from data. Causal Inference in Statistics fills that gap. Using simple examples and plain language, the book lays out how to define causal parameters; the assumptions necessary to estimate causal parameters in a variety of situations; how to express those assumptions mathematically; whether those assumptions have testable implications; how to predict the effects of interventions; and how to reason counterfactually. These are the foundational tools that any student of statistics needs to acquire in order to use statistical methods to answer causal questions of interest. This book is accessible to anyone with an interest in interpreting data, from undergraduates, professors, researchers, or to the interested layperson. Examples are drawn from a wide variety of fields, including medicine, public policy, and law; a brief introduction to probability and statistics is provided for the uninitiated; and each chapter comes with study questions to reinforce the readers understanding.
The Minimum Message Length (MML) Principle is an information-theoretic approach to induction, hypothesis testing, model selection, and statistical inference. MML, which provides a formal specification for the implementation of Occam's Razor, asserts that the ‘best’ explanation of observed data is the shortest. Further, an explanation is acceptable (i.e. the induction is justified) only if the explanation is shorter than the original data. This book gives a sound introduction to the Minimum Message Length Principle and its applications, provides the theoretical arguments for the adoption of the principle, and shows the development of certain approximations that assist its practical application. MML appears also to provide both a normative and a descriptive basis for inductive reasoning generally, and scientific induction in particular. The book describes this basis and aims to show its relevance to the Philosophy of Science. Statistical and Inductive Inference by Minimum Message Length will be of special interest to graduate students and researchers in Machine Learning and Data Mining, scientists and analysts in various disciplines wishing to make use of computer techniques for hypothesis discovery, statisticians and econometricians interested in the underlying theory of their discipline, and persons interested in the Philosophy of Science. The book could also be used in a graduate-level course in Machine Learning and Estimation and Model-selection, Econometrics and Data Mining. C.S. Wallace was appointed Foundation Chair of Computer Science at Monash University in 1968, at the age of 35, where he worked until his death in 2004. He received an ACM Fellowship in 1995, and was appointed Professor Emeritus in 1996. Professor Wallace made numerous significant contributions to diverse areas of Computer Science, such as Computer Architecture, Simulation and Machine Learning. His final research focused primarily on the Minimum Message Length Principle.
