Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Propositional Logic
- 3 Probability Calculus
- 4 Bayesian Networks
- 5 Building Bayesian Networks
- 6 Inference by Variable Elimination
- 7 Inference by Factor Elimination
- 8 Inference by Conditioning
- 9 Models for Graph Decomposition
- 10 Most Likely Instantiations
- 11 The Complexity of Probabilistic Inference
- 12 Compiling Bayesian Networks
- 13 Inference with Local Structure
- 14 Approximate Inference by Belief Propagation
- 15 Approximate Inference by Stochastic Sampling
- 16 Sensitivity Analysis
- 17 Learning: The Maximum Likelihood Approach
- 18 Learning: The Bayesian Approach
- A Notation
- B Concepts from Information Theory
- C Fixed Point Iterative Methods
- D Constrained Optimization
- Bibliography
- Index
5 - Building Bayesian Networks
Published online by Cambridge University Press: 23 February 2011
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Propositional Logic
- 3 Probability Calculus
- 4 Bayesian Networks
- 5 Building Bayesian Networks
- 6 Inference by Variable Elimination
- 7 Inference by Factor Elimination
- 8 Inference by Conditioning
- 9 Models for Graph Decomposition
- 10 Most Likely Instantiations
- 11 The Complexity of Probabilistic Inference
- 12 Compiling Bayesian Networks
- 13 Inference with Local Structure
- 14 Approximate Inference by Belief Propagation
- 15 Approximate Inference by Stochastic Sampling
- 16 Sensitivity Analysis
- 17 Learning: The Maximum Likelihood Approach
- 18 Learning: The Bayesian Approach
- A Notation
- B Concepts from Information Theory
- C Fixed Point Iterative Methods
- D Constrained Optimization
- Bibliography
- Index
Summary
We address in this chapter a number of problems that arise in real-world applications, showing how each can be solved by modeling and reasoning with Bayesian networks.
Introduction
We consider a number of real-world applications in this chapter drawn from the domains of diagnosis, reliability, genetics, channel coding, and commonsense reasoning. For each one of these applications, we state a specific reasoning problem that can be addressed by posing a formal query with respect to a corresponding Bayesian network. We discuss the process of constructing the required network and then identify the specific queries that need to be applied.
There are at least four general types of queries that can be posed with respect to a Bayesian network. Which type of query to use in a specific situation is not always trivial and some of the queries are guaranteed to be equivalent under certain conditions. We define these query types formally in Section 5.2 and then discuss them and their relationships in more detail when we go over the various applications in Section 5.3.
The construction of a Bayesian network involves three major steps. First, we must decide on the set of relevant variables and their possible values. Next, we must build the network structure by connecting the variables into a DAG. Finally, we must define the CPT for each network variable. The last step is the quantitative part of this construction process and can be the most involved in certain situations.
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- Modeling and Reasoning with Bayesian Networks , pp. 76 - 125Publisher: Cambridge University PressPrint publication year: 2009