Thomas Bayes Thomas Bayes ( ; 1701 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for formulating a specific case of the theorem that bears his name: Bayes' theorem. Bayes never published what would become h ...

(/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 na ...

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 exa ...

, 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 pos ...

Bayes Business School Bayes Business School, formerly known as Cass Business School, is the business school of City, University of London, located in St Luke's, just to the north of the City of London. It was established in 1966, and it is consistently ranked as one ...

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 In statistical classification, Bayes error rate is the lowest possible error rate for any classifier of a random outcome (into, for example, one of two categories) and is analogous to the irreducible error.K. Tumer, K. (1996) "Estimating the Bayes ...

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 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 nu ...

Bayes Impact Bayes Impact is a non-profit organization, founded by Paul Duan, Eric Liu, and Pascal Corpet. Initially launched in the US in 2014, Bayes Impact started several projects throughout the world and especially in Europe. Bayes Impact's mission is t ...

* 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 into ...

* 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 ...

* Evidence under Bayes theorem *

Hierarchical Bayes model Multilevel models (also known as hierarchical linear models, linear mixed-effect model, mixed models, nested data models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parame ...

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 ...

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 Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that operates by constructing a multitude of decision trees at training time. For classification tasks, the output of t ...

Bayesian

Approximate Bayesian computation Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics that can be used to estimate the posterior distributions of model parameters. In all model-based statistical inference, the lik ...

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 probability, Bayesian interpretation. Th ...

Bayesian Analysis (journal) ''Bayesian Analysis'' is an open-access peer-reviewed scientific journal covering theoretical and applied aspects of Bayesian methods. It is published by the International Society for Bayesian Analysis and is hosted at the Project Euclid web site. ...

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 problem. It consists of choosing the action that maximizes the expected reward ...

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 "computationa ...

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 In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants ...

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. ...

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 solut ...

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 in phylogeny Bayesian inference of phylogeny combines the information in the prior and in the data likelihood to create the so-called posterior probability of trees, which is the probability that the tree is correct given the data, the prior and the likelihood ...

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, ...

(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 ...

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 learning mechanisms are probabilistic causal models used in computer science to research the fundamental underpinnings of machine learning, and in cognitive neuroscience, to model conceptual development. Bayesian learning mechanisms have ...

Bayesian linear regression 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 wel ...

Bayesian model of computational anatomy Computational anatomy (CA) is a discipline within medical imaging focusing on the study of anatomical shape and form at the visible or gross anatomical scale of morphology. The field is broadly defined and includes foundations in anatomy, ...

Bayesian model averaging In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. Unlike a statistical ensemble in statist ...

(BMA) * Bayesian model combination (BMC) * Bayesian model reduction *

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 nu ...

* 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 solut ...

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 ...

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 ...

* 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 t ...

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 ...

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 o ...

* 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 quadrature is a method for approximating intractable integration problems. It falls within the class of probabilistic numerical methods. Bayesian quadrature views numerical integration as a Bayesian inference task, where function eva ...

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 Bay ...

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 ...

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 structural time series (BSTS) model is a statistical technique used for feature selection, time series forecasting, nowcasting, inferring causal impact and other applications. The model is designed to work with time series data. The mod ...

* Bayesian support-vector machine *

Bayesian survival analysis Survival analysis is normally carried out using parametric models, semi-parametric models, non-parametric models to estimate the survival rate in clinical research. However recently Bayesian models are also used to estimate the survival rate Sur ...

* Bayesian template estimation *

Bayesian tool for methylation analysis Bayesian tool for methylation analysis, also known as BATMAN, is a statistical tool for analysing methylated DNA immunoprecipitation (MeDIP) profiles. It can be applied to large datasets generated using either oligonucleotide arrays (MeDIP-chip) o ...

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 The International Society for Bayesian Analysis (ISBA) is a society with the goal of promoting Bayesian analysis for solving problems in the sciences and government. It was formally incorporated as a not for profit corporation by economist Arnold ...

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 equilib ...

(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 ...

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 in ...

Robust Bayesian analysis In statistics, robust Bayesian analysis, also called Bayesian sensitivity analysis, is a type of sensitivity analysis applied to the outcome from Bayesian inference or Bayesian optimal decisions. Sensitivity analysis Robust Bayesian analysis, a ...

Variable-order Bayesian network Variable-order Bayesian network (VOBN) models provide an important extension of both the Bayesian network models and the variable-order Markov models. VOBN models are used in machine learning in general and have shown great potential in bioinformat ...

Variational Bayesian methods Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning. They are typically used in complex statistical models consisting of observed variables (usually ...

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