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A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). [1] While it is one of several forms of causal notation, causal networks are special cases of Bayesian ...
Both directed acyclic graphs and undirected graphs are special cases of chain graphs, which can therefore provide a way of unifying and generalizing Bayesian and Markov networks. [3] An ancestral graph is a further extension, having directed, bidirected and undirected edges. [4] Random field techniques
Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.
Considering messages between regions in a graph is one way of generalizing the belief propagation algorithm. [10] There are several ways of defining the set of regions in a graph that can exchange messages. One method uses ideas introduced by Kikuchi in the physics literature, [11] [12] [13] and is known as Kikuchi's cluster variation method. [14]
In the statistics literature, naive Bayes models are known under a variety of names, including simple Bayes and independence Bayes. [3] All these names reference the use of Bayes' theorem in the classifier's decision rule, but naive Bayes is not (necessarily) a Bayesian method.
Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often ...
In statistical classification, the Bayes classifier is the classifier having the smallest probability of misclassification of all classifiers using the same set of features. [ 1 ] Definition
Exploratory analysis of Bayesian models is an adaptation or extension of the exploratory data analysis approach to the needs and peculiarities of Bayesian modeling. In the words of Persi Diaconis: [17] Exploratory data analysis seeks to reveal structure, or simple descriptions in data. We look at numbers or graphs and try to find patterns.