Thomas Bayes (/beɪz/; c. 1701 – 1761) was an English statistician, philosopher, and

Presbyterian Presbyterianism is a part of the Reformed tradition within Protestantism that broke from the Roman Catholic Church in Scotland by John Knox, who was a priest at St. Giles Cathedral (Church of Scotland). Presbyterian churches derive their n ...

minister. Bayesian () refers either to a range of concepts and approaches that relate to statistical methods based on

Bayes' theorem In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For examp ...

, or a follower of these methods.BAYESIAN , Meaning & Definition for UK English , Lexico.com
/ref> A number of things have been named after Thomas Bayes, including:

Bayes

Bayes action In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the po ...

* Bayes Business School * Bayes classifier * Bayes discriminability index * Bayes error rate *

Bayes estimator In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the ...

* Bayes factor * Bayes Impact * Bayes linear statistics * Bayes prior * Bayes' theorem / Bayes-Price theorem -- sometimes called Bayes' rule or Bayesian updating. *

Empirical Bayes method Empirical Bayes methods are procedures for statistical inference in which the prior probability distribution is estimated from the data. This approach stands in contrast to standard Bayesian methods, for which the prior distribution is fixed b ...

* Evidence under Bayes theorem * Hierarchical Bayes model * Laplace–Bayes estimator *

Naive Bayes classifier In statistics, naive Bayes classifiers are a family of simple " probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features (see Bayes classifier). They are among the simplest Bay ...

* Random naive Bayes

Bayesian

* Approximate Bayesian computation * Bayesian average * Bayesian Analysis (journal) *

Bayesian approaches to brain function Bayesian approaches to brain function investigate the capacity of the nervous system to operate in situations of uncertainty in a fashion that is close to the optimal prescribed by Bayesian statistics. This term is used in behavioural sciences and ...

* Bayesian bootstrap *

Bayesian control rule Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that addresses the exploration-exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward w ...

* Bayesian cognitive science *

Bayesian econometrics Bayesian econometrics is a branch of econometrics which applies Bayesian principles to economic modelling. Bayesianism is based on a degree-of-belief interpretation of probability, as opposed to a relative-frequency interpretation. The Bayesian ...

Bayesian efficiency Bayesian efficiency is an analog of Pareto efficiency for situations in which there is incomplete information.Palfrey, Thomas R.; Srivastava, Sanjay; Postlewaite, A. (1993) Bayesian Implementation.' Pg. 13-14. Under Pareto efficiency, an allocati ...

Bayesian epistemology Bayesian epistemology is a formal approach to various topics in epistemology that has its roots in Thomas Bayes' work in the field of probability theory. One advantage of its formal method in contrast to traditional epistemology is that its conc ...

* Bayesian expected loss *

Bayesian experimental design Bayesian experimental design provides a general probability-theoretical framework from which other theories on experimental design can be derived. It is based on Bayesian inference to interpret the observations/data acquired during the experiment. T ...

Bayesian game In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the soluti ...

* Bayesian hierarchical modeling * Bayesian History Matching *

Bayesian inference Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and ...

* Bayesian inference in phylogeny *

Bayesian information criterion In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; models with lower BIC are generally preferred. It is based, in part, o ...

(BIC) and * Widely applicable Bayesian information criterion (WBIC) * Bayesian Kepler periodogram * Bayesian Knowledge Tracing * Bayesian learning mechanisms * Bayesian linear regression * Bayesian model of computational anatomy * Bayesian model averaging (BMA) * Bayesian model combination (BMC) *

Bayesian model reduction Bayesian model reduction is a method for computing the evidence and posterior over the parameters of Bayesian models that differ in their priors. A full model is fitted to data using standard approaches. Hypotheses are then tested by defining one ...

Bayesian model selection The Bayes factor is a ratio of two competing statistical models represented by their marginal likelihood, and is used to quantify the support for one model over the other. The models in questions can have a common set of parameters, such as a nul ...

* Bayesian multivariate linear regression *

Bayesian Nash equilibrium In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the soluti ...

Bayesian network 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). Ba ...

* Bayesian neural network * Bayesian operational modal analysis (BAYOMA) *

Bayesian-optimal mechanism A Bayesian-optimal mechanism (BOM) is a mechanism in which the designer does not know the valuations of the agents for whom the mechanism is designed, but the designer knows that they are random variables and knows the probability distribution of th ...

Bayesian-optimal pricing Bayesian-optimal pricing (BO pricing) is a kind of algorithmic pricing in which a seller determines the sell-prices based on probabilistic assumptions on the valuations of the buyers. It is a simple kind of a Bayesian-optimal mechanism, in which t ...

* Bayesian optimization *

Bayesian poisoning Bayesian poisoning is a technique used by e-mail spammers to attempt to degrade the effectiveness of spam filters that rely on Bayesian spam filtering. Bayesian filtering relies on Bayesian probability to determine whether an incoming mail is spam ...

Bayesian probability Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification ...

* Bayesian procedures *

Bayesian programming Bayesian programming is a formalism and a methodology for having a technique to specify probabilistic models and solve problems when less than the necessary information is available. Edwin T. Jaynes proposed that probability could be considere ...

* Bayesian program synthesis * Bayesian quadrature *

Bayesian regret In stochastic game theory, Bayesian regret is the expected difference ("regret") between the utility of a Bayesian strategy and that of the optimal strategy (the one with the highest expected payoff). The term ''Bayesian'' refers to Thomas Bayes ...

Bayesian search theory Bayesian search theory is the application of Bayesian statistics to the search for lost objects. It has been used several times to find lost sea vessels, for example USS ''Scorpion'', and has played a key role in the recovery of the flight recorde ...

Bayesian spam filtering Naive Bayes classifiers are a popular statistical technique of e-mail filtering. They typically use bag-of-words features to identify email spam, an approach commonly used in text classification. Naive Bayes classifiers work by correlating the u ...

Bayesian statistics Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...

* Bayesian structural time series * Bayesian support-vector machine * Bayesian survival analysis * Bayesian template estimation * Bayesian tool for methylation analysis * Bayesian vector autoregression * Dynamic Bayesian network * International Society for Bayesian Analysis *

Perfect Bayesian equilibrium In game theory, a Perfect Bayesian Equilibrium (PBE) is an equilibrium concept relevant for dynamic games with incomplete information (sequential Bayesian games). It is a refinement of Bayesian Nash equilibrium (BNE). A perfect Bayesian equilibriu ...

(PBE) * Quantum Bayesianism * Recursive Bayesian estimation * Robust Bayesian analysis * Variable-order Bayesian network * Variational Bayesian methods

References

External links

* {{cite journal , last = Fienberg , first = Stephen , date = 2006 , title = When did Bayesian inference become "Bayesian"? , journal = Bayesian Analysis , pages = 1–41 , citeseerx = 10.1.1.124.8632 Bayes, Thomas

Bayes

Bayesian

See also

References

External links