Bayesian theory: Methods and applications

Bayesian law expresses the relationship between dependent variables. The Bayesian relation uses a numerical estimate of the probabilistic knowledge of the hypothesis before the observations occur, and provides a numerical estimate of the probabilistic knowledge of the hypothesis after the observations. This law for classifying phenomena is based on the probability of occurrence or nonoccurrence of a phenomenon and is important and widely used in probability theory. If we can choose such a separation for a given sample space that knowing which of the separated events occurred would reduce an important part of the uncertainty. This is useful because it can be used to calculate the probability of an event being conditional on the occurrence or nonoccurrence of another event. In many cases, it is difficult to calculate the probability of an incident directly. Using this theorem and conditioning one event on another, the probability can be calculated. Bayesian theory has three methods: Bayes Optimal Classifier, Naive Bayes classifier, and Bayesian network. In hydrological issues, the Bayesian network has been used more. These networks are graphical networks that represent a set of possible variables and their conditional dependencies by a directional noncyclic graph (DAG). Bayesian network nodes represent variables that can be visible values, hidden variables, or unknown parameters. The edges of this network indicate dependencies. Each node has a probability function that includes the initial probability (for parentless nodes) or conditional probabilities related to the combination of different states of the parent nodes.