Bayesian Decision Theory

Basic Concepts

The Bayesian decision theory method is a basic method in statistical model decision making. Its basic idea is:

• Known class conditional probability density parameter expression and prior probability
• Convert to posterior probability using Bayesian formula
• Decision classification based on posterior probability

Related formulas

Let D1, D2, ..., Dn be a partition of the sample space S. If P(Di) represents the probability of event Di occurring, and P(Di)>0(i=1, 2, ..., n), for any event x, P(x)>0, we have

in conclusion

For any given problem, the likelihood test decision rule can be used to obtain the minimum error probability, which is called the Bayesian error rate and is the best result that can be obtained among all classifiers.

The decision rule that minimizes the probability of error is the one that maximizes the posterior probability criterion.