Probabilistic Logics and Probabilistic Networks, Rolf Haenni; Jan-Willem Romeijn; Gregory Wheeler;

Автор: Koller Daphne, Friedman Nir
Название: Probabilistic Graphical Models: Principles and Techniques
ISBN: 0262013193 ISBN-13(EAN): 9780262013192
Издательство: MIT Press
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Описание:

A general framework for constructing and using probabilistic models of complex systems that would enable a computer to use available information for making decisions.

Most tasks require a person or an automated system to reason -- to reach conclusions based on available information. The framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality.

Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

Автор: Bass
Название: Probabilistic Techniques in Analysis
ISBN: 0387943870 ISBN-13(EAN): 9780387943879
Издательство: Springer
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Описание: Exploring the use of techniques drawn from probability research to tackle problems in mathematical analysis, this study includes discussion of the construction of the Martin boundary, Dahlberg`s Theorem, probabilistic proofs of the boundary Harnack principle, and much more.

Автор: Pardoux
Название: Probabilistic Models of Population Evolution
ISBN: 3319303260 ISBN-13(EAN): 9783319303260
Издательство: Springer
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Описание: This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the population is bound to go extinct in finite time. It is explained when the interaction is strong enough so that the extinction time remains finite, when the ancestral population at time 0 goes to infinity. The material could be used for teaching stochastic processes, together with their applications.