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Bayesian inference (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available.
For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and learning in Bayesian networks.
One of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of observations given a model configuration (i.e., the likelihood function) to obtain the probability of the model configuration given the observations (i.e., the posterior probability).
In his founding book Probability Theory: The Logic of Science [1] he developed this theory and proposed what he called “the robot,” which was not a physical device, but an inference engine to automate probabilistic reasoning—a kind of Prolog for probability instead of logic.
Bayesian probability (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation [2] representing a state of knowledge [3] or as quantification of a personal belief.
Example of a naive Bayes classifier depicted as a Bayesian Network. In statistics, naive Bayes classifiers are a family of "probabilistic classifiers" which assumes that the features are conditionally independent, given the target class. The strength (naivety) of this assumption is what gives the classifier its name.
Variable elimination (VE) is a simple and general exact inference algorithm in probabilistic graphical models, such as Bayesian networks and Markov random fields. [1] It can be used for inference of maximum a posteriori (MAP) state or estimation of conditional or marginal distributions over a subset of variables.
Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst. Cornerstones in this field are computational learning theory , granular computing , bioinformatics , and, long ago, structural probability ( Fraser 1966 ).