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Über dieses Buch

Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new sections, in addition to fully-updated examples, tables, figures, and a revised appendix. Intended primarily for practitioners, this book does not require sophisticated mathematical skills or deep understanding of the underlying theory and methods nor does it discuss alternative technologies for reasoning under uncertainty. The theory and methods presented are illustrated through more than 140 examples, and exercises are included for the reader to check his or her level of understanding. The techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined on the basis of numerous courses that the authors have held for practitioners worldwide.

Inhaltsverzeichnis

Frontmatter

Fundamentals

Frontmatter

Chapter 1. Introduction

Abstract
The desire to have computers perform intellectually challenging tasks has existed ever since the invention of the general-purpose computer that could be programmed to execute an arbitrary set of manipulations on numbers and symbols. Solving an intellectually challenging task can be characterized as a process of deriving conclusions (new pieces of knowledge) by manipulating a (large) body of knowledge, typically including definitions of entities (objects, concepts, events, phenomena, etc.), relations among them, and observations of states (values) of some of the entities.
Uffe B. Kjærulff, Anders L. Madsen

Chapter 2. Networks

Abstract
Probabilistic networks are graphical models of (causal) interactions among a set of variables, where the variables are represented as vertices (nodes) of a graph and the interactions (direct dependences) as directed edges (links or arcs) between the vertices. Any pair of unconnected vertices of such a graph indicates (conditional) independence between the variables represented by these vertices under particular circumstances that can easily be read from the graph. Hence, probabilistic networks capture a set of (conditional) dependence and independence properties associated with the variables represented in the network.
Uffe B. Kjærulff, Anders L. Madsen

Chapter 3. Probabilities

Abstract
The fact that the structure of a probabilistic network can be characterized as a DAG derives from basic axioms of probability calculus leading to recursive factorization of a joint probability distribution into a product of lower-dimensional conditional probability distributions. First, any joint probability distribution can be decomposed (or factorized) into a product of conditional distributions of different dimensionality, where the dimensionality of the largest distribution is identical to the dimensionality of the joint distribution. This gives rise to a densely connected DAG. Second, statements of local conditional independences manifest themselves as reductions of dimensionalities of some of the conditional probability distributions. Most often, these independence statements give rise to dramatic reductions of complexity of the DAG such that the resulting DAG appears to be quite sparse.
Uffe B. Kjærulff, Anders L. Madsen

Chapter 4. Probabilistic Networks

Abstract
Probabilistic networks are graphical models of (causal) interactions among a set of variables, where the variables are represented as vertices (nodes) of a graph and the interactions (direct dependences) as directed edges (links or arcs) between the vertices. Any pair of unconnected vertices of such a graph indicates (conditional) independence between the variables represented by these vertices under particular circumstances that can easily be read from the graph. Hence, probabilistic networks capture a set of (conditional) dependence and independence properties associated with the variables represented in the network.
Uffe B. Kjærulff, Anders L. Madsen

Chapter 5. Solving Probabilistic Networks

Abstract
An expert system consists of a knowledge base and an inference engine. The inference engine is used to solve queries against the knowledge base. In the case of probabilistic networks, we have a clear distinction between the knowledge base and the inference engine. The knowledge base is the Bayesian network or influence diagram, whereas the inference engine consists of a set of generic methods that applies the knowledge formulated in the knowledge base on task-specific data sets, known as evidence, to compute solutions to queries against the knowledge base. The knowledge base alone is of limited use if it cannot be applied to update our belief about the state of the world or to identify (optimal) decisions in the light of new knowledge.
Uffe B. Kjærulff, Anders L. Madsen

Model Construction

Frontmatter

Chapter 6. Eliciting the Model

Abstract
A probabilistic network consists of two components: structure and parameters [i.e., conditional probabilities and utilities (statements of preference)]. The structure of a probabilistic network is often referred to as the qualitative part of the network, whereas the parameters are often referred to as its quantitative part. As the parameters of a model are determined by its structure, the model elicitation process always proceeds in two consecutive stages: First, the variables and the causal, functional or informational relations among the variables are identified, providing the qualitative part of the model. Second, once the model structure has been determined through an iterative process involving testing of variables and conditional independences, and verification of the directionality of the links, the values of the parameters are elicited.
Uffe B. Kjærulff, Anders L. Madsen

Chapter 7. Modeling Techniques

Abstract
There are many reasons for considering the utilization of modeling techniques in the model development process. Modeling techniques may be applied in order, for instance, to simplify knowledge elicitation and model specification, capture certain properties of the problem domain that are not easily captured by an acyclic, directed graph, to reduce model complexity and improve efficiency of inference in the model, and so on.
Uffe B. Kjærulff, Anders L. Madsen

Chapter 8. Data-Driven Modeling

Abstract
In this book we consider the use of Bayesian networks to model the underlying process. The process of inducing a Bayesian network from a database of cases and expert knowledge consists of two main steps. The first step is to induce the structure of the model, that is, the DAG, while the second step is to estimate the parameters of the model as defined by the structure. In this chapter we consider only discrete Bayesian networks. Thus, the task of data-driven modeling is to construct a Bayesian network\(\mathcal{N} = (\mathcal{X},\mathcal{G},\mathcal{P})\) from the available information sources. In general, the problem of inducing the structure of a Bayesian network is NP-complete (Chickering 1996). Thus, heuristic methods are appropriate.
Uffe B. Kjærulff, Anders L. Madsen

Model Analysis

Frontmatter

Chapter 9. Conflict Analysis

Abstract
It is difficult or even impossible to construct models covering all aspects of (complex) problem domains of interest. A model is therefore most often an approximation of a problem domain that is designed to be applied according to the assumptions as determined by the background condition or context of the model. If a model is used under circumstances not consistent with the background condition, the results will in general be unreliable. The evidence need not be inconsistent with the model in order for the results to be unreliable. It may be that evidence is simply in conflict with the model. This implies that the model in relation to the evidence may be weak, and therefore the results may be unreliable.
Uffe B. Kjærulff, Anders L. Madsen

Chapter 10. Sensitivity Analysis

Abstract
We construct probabilistic networks to support and solve problems of belief update and decision making under uncertainty. In problems of belief update, the posterior probability of a single hypothesis variable is sometimes of interest. When the evidence set consists of a large number of findings or even when it consists of only a small number of findings, questions concerning the impact of subsets of the evidence on the hypothesis or a competing hypothesis emerge.
Uffe B. Kjærulff, Anders L. Madsen

Chapter 11. Value of Information Analysis

Abstract
Probabilistic networks are constructed to support belief update and decision making under uncertainty. A common solution to a belief update problem is the posterior probability distribution over a hypothesis variable given a set of evidence. Similarly, the solution to a decision-making problem is an optimal decision given a set of evidence. When faced with a belief update or decision-making problem, we may have the option to consult additional information sources for further information that may improve the solution. Value of information analysis is a tool for analyzing the potential usefulness of additional information before the information source is consulted.
Uffe B. Kjærulff, Anders L. Madsen

Backmatter

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