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Bayesian network
Evidence-based design
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Bayesian network
A Bayesian network is a form of probabilistic graphical model, also known as Bayesian belief network or just belief network.
A Bayesian network can be represented by a graph (as in graph theory) with probabilities attached. Thus, a Bayesian network represents a set of variables together with a joint probability distribution with explicit independence assumptions.
- 1 Definition
- 2 Example
If there are two reasons which could cause grass to be wet, either the sprinkler is on or it's raining, then the situation can be modelled with adjacent Bayesian network. Here, all variables have two possible states T (for true) and F (for false).
The joint probability function is
Pr(GRASSWET, SPRINKLER, RAIN) = Pr(GRASSWET | SPRINKLER, RAIN) Pr(SPRINKLER | RAIN) Pr(RAIN)
The model can answer questions like "What is the likelihood that it is raining, given the grass is wet?" by using the conditional probability formula and summing over all nuisance variables:
Substituting numerical values yields Pr(RAIN=T | GRASSWET=T) = 891/2491 ? 35.77%.
- 3 Causal Bayesian networks
- 4 Structure learning
- 5 Parameter learning
- 6 Inference
- 7 Applications
- 8 See also
- 9 Links and software
- 10 References
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