Information about Bayesian

Probability is the likelihood that something is the case or will happen. Probability theory is used extensively in areas such as statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of
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Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
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Thomas Bayes

Thomas Bayes (The correct identification of this portrait has been [2] questioned.)
Born c.
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Bayes' theorem (also known as Bayes' rule or Bayes' law) is a result in probability theory, which relates the conditional and marginal probability distributions of random variables.
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In decision theory and estimation theory, a Bayes estimator is an estimator or decision rule that maximizes the posterior expected value of a utility function or minimizes the posterior expected value of a loss function. (See also prior probability.
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In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing^[1][2].

Given a model selection problem in which we have to choose between two models M₁ and M₂
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Bayesian spam filtering (pronounced "Bays-ee-en", IPA pronunciation: ['beɪz.i.ən], after Rev. Thomas Bayes), a form of e-mail filtering, is the process of using a Naive Bayes classifier to identify spam email.
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In game theory, a Bayesian game is one in which information about characteristics of the other players (i.e. payoffs) is incomplete. Following John C. Harsanyi's framework, a Bayesian game can be modelled by introducing Nature as a player in a game.
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Bayesian inference is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true. The name "Bayesian" comes from the frequent use of Bayes' theorem in the inference process.
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In statistics, the Bayesian information criterion (BIC) is a statistical criterion for model selection.
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In statistics, Bayesian linear regression is a Bayesian alternative to the more well-known ordinary least-squares linear regression.

Consider standard linear regression problem, where we specify the conditional density of y given x predictor variables:
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A common problem in statistical inference is to use data to decide between two or more competing models. Frequentist statistics uses hypothesis tests for this purpose. There are several Bayesian approaches. One approach is through Bayes factors.
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A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of variables and their probabilistic independencies. For example, a Bayesian network can be used to calculate the probability of a patient having a specific disease, given the
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Bayesian probability is an interpretation of the probability calculus which holds that the concept of probability can be defined as the degree to which a person (or community) believes that a proposition is true.
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In statistics, empirical Bayes methods are a class of methods which use empirical data to evaluate / approximate the conditional probability distributions that arise from Bayes' theorem. These methods allow one to estimate quantities (probabilities, averages, etc.
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A naive Bayes classifier is a simple probabilistic classifier based on applying Bayes' theorem with strong (naive) independence assumptions. A more descriptive term for the underlying probability model would be "independent feature model".
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