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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 nam ...
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

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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 ...
* Bayes Business School *
Bayes classifier In statistical classification, the Bayes classifier minimizes the probability of misclassification. Definition Suppose a pair (X,Y) takes values in \mathbb^d \times \, where Y is the class label of X. Assume that the conditional distribution of ' ...
* 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 po ...
* Bayes factor * Bayes Impact * Bayes linear statistics *
Bayes prior In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken int ...
* 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 be ...
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Evidence under Bayes theorem The use of evidence under Bayes' theorem relates to the probability of finding evidence in relation to the accused, where Bayes' theorem concerns the probability of an event and its inverse. Specifically, it compares the probability of finding p ...
* Hierarchical Bayes model *
Laplace–Bayes estimator In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. The formula is still used, particularly to estimate underlying probabilities when t ...
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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 Baye ...
* Random naive Bayes


Bayesian

* Approximate Bayesian computation *
Bayesian average A Bayesian average is a method of estimating the mean of a population using outside information, especially a pre-existing belief, which is factored into the calculation. This is a central feature of Bayesian interpretation. This is useful when the ...
* 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 n ...
* 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 In probability theory and machine learning, the multi-armed bandit problem (som ...
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Bayesian cognitive science Bayesian cognitive science, also known as computational cognitive science, is an approach to cognitive science concerned with the rational analysis of cognition through the use of Bayesian inference and cognitive modeling. The term "computation ...
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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 ...
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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 ...
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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 concep ...
* 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. ...
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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 ...
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Bayesian hierarchical modeling Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method.Allenby, Rossi, McCulloch (January 2005)"Hierarchical Bayes ...
* 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, a ...
* 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, on ...
(BIC) and * Widely applicable Bayesian information criterion (WBIC) *
Bayesian Kepler periodogram Doppler spectroscopy (also known as the radial-velocity method, or colloquially, the wobble method) is an indirect method for finding extrasolar planets and brown dwarfs from radial-velocity measurements via observation of Doppler shifts in th ...
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Bayesian Knowledge Tracing Bayesian knowledge tracing is an algorithm used in many intelligent tutoring systems to model each learner's mastery of the knowledge being tutored. It models student knowledge in a hidden Markov model as a latent variable, updated by observing the ...
* 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 *
Bayesian multivariate linear regression In statistics, Bayesian multivariate linear regression is a Bayesian approach to multivariate linear regression, i.e. linear regression where the predicted outcome is a vector of correlated random variables rather than a single scalar random varia ...
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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 ...
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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). Bay ...
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Bayesian neural network Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected units ...
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Bayesian operational modal analysis Bayesian operational modal analysis (BAYOMA) adopts a Bayesian inference, Bayesian system identification approach for operational modal analysis (OMA). Operational modal analysis aims at identifying the modal properties (natural frequency, natural ...
(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 ...
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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 the ...
* 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 ...
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Bayesian probability Bayesian probability is an Probability interpretations, interpretation of the concept of probability, in which, instead of frequentist probability, frequency or propensity probability, propensity of some phenomenon, probability is interpreted as re ...
* 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 ...
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Bayesian program synthesis In programming languages and machine learning, Bayesian program synthesis (BPS) is a program synthesis technique where Bayesian probabilistic programs automatically construct new Bayesian probabilistic programs. This approach stands in contrast to r ...
* 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 Baye ...
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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 (SSN-589), USS ''Scorpion'', and has played a key role in the recover ...
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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 th ...
* Bayesian statistics * Bayesian structural time series * Bayesian support-vector machine *
Bayesian survival analysis Survival analysis is normally carried out using parametric models, semi-parametric models, non-parametric model Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions ( ...
* Bayesian template estimation * Bayesian tool for methylation analysis *
Bayesian vector autoregression In statistics and econometrics, Bayesian vector autoregression (BVAR) uses Bayesian methods to estimate a vector autoregression (VAR) model. BVAR differs with standard VAR models in that the model parameters are treated as random variables, with ...
* 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 equilibr ...
(PBE) *
Quantum Bayesianism In physics and the philosophy of physics, quantum Bayesianism is a collection of related approaches to the interpretation of quantum mechanics, of which the most prominent is QBism (pronounced "cubism"). QBism is an interpretation that takes an a ...
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Recursive Bayesian estimation In probability theory, statistics, and machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function ( PDF) recursively over time using inc ...
* Robust Bayesian analysis * Variable-order Bayesian network * Variational Bayesian methods


See also

* Banburismus, a cryptanalytic process *
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 n ...
*
Bayesian inference in marketing In marketing, Bayesian inference allows for decision making and market research evaluation under uncertainty and with limited data. Introduction Bayes’ theorem is fundamental to Bayesian inference. It is a subset of statistics, providing a mat ...
*
Bayesian inference in motor learning Bayesian inference is a statistical tool that can be applied to motor learning, specifically to adaptation. Adaptation is a short-term learning process involving gradual improvement in performance in response to a change in sensory information. Ba ...
* Bayesian inference using Gibbs sampling (BUGS) *
Bayesian interpretation of kernel regularization Within bayesian statistics for machine learning, kernel methods arise from the assumption of an inner product space or similarity structure on inputs. For some such methods, such as support vector machines (SVMs), the original formulation and its r ...
* Bayesian tool for methylation analysis (BATMAN) * Conditional Probability *
Credibility theory Credibility theory is a form of statistical inference used to forecast an uncertain future event developed by Thomas Bayes. It is employed to combine multiple estimates into a summary estimate that takes into account information on the accuracy o ...
*
Evidence under Bayes' theorem The use of evidence under Bayes' theorem relates to the probability of finding evidence in relation to the accused, where Bayes' theorem concerns the probability of an event and its inverse. Specifically, it compares the probability of finding pa ...
*
Dempster–Shafer theory The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and i ...
, a generalization of Bayes' theorem. * History of Bayesian statistics *
Inverse probability In probability theory, inverse probability is an obsolete term for the probability distribution of an unobserved variable. Today, the problem of determining an unobserved variable (by whatever method) is called inferential statistics, the method o ...
* Inverse resolution *
Polytree In mathematics, and more specifically in graph theory, a polytree (also called directed tree, oriented tree; . or singly connected network.) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, if we replace its ...


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