# Bayesian Belief Network

A Bayesian belief network (also known as a

BayesianNetwork, a

BeliefNetwork or a

BayesNet) is a representation of dependence (and so also independence) of random variables. It is named after

ThomasBayes.

A belief network can be described in terms of

- structure: a directed acyclic graph where the nodes are random variables and a domain for each random variable
- function: how each variable depends on its parents, such as using a table, a decision tree, a "noisy or", or some parametrized form
- number: the actual numbers needed to specify a conditional probability of each variable given its parents

# History

# Algorithms for Inference in Belief networks

## Exact Algorithms

The main exact algorithms are

- VariableElimination
^{?} which exploits the sparseness of the graph to answer single queries
- CliqueTreePropagation
^{?} which creates a secondary structure to give the posterior on each variable and allow for the incorporation of new evidence.
- RecursiveConditioning
^{?} that allows for the tradeoff between time and space

## Approximate Algorithms

- StochasticSimulation
^{?}
- VariationalMethods
^{?}
- Search-basedAlgorithms
^{?}

# Learning Belief networks

# Causality

# Alternative Related Representations

- A DecisionNetwork
^{?} adds decision varibles and utility variables for making sequential decisions
- A CausalNetwork makes predictions of interventions

# Industrial Applications