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
* 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
* 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
*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
* Bayesian average
* Bayesian Analysis (journal)
* Bayesian approaches to brain function
* 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 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
* Bayesian hierarchical modeling
* Bayesian History Matching
* Bayesian inference
* 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, ...
(BIC) and
* Widely applicable Bayesian information criterion (WBIC)
* Bayesian Kepler periodogram
* Bayesian Knowledge Tracing
*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
*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 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 program synthesis
* Bayesian quadrature
* Bayesian regret
*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
* 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 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
*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 ...
See also
*Banburismus
Banburismus was a cryptanalytic process developed by Alan Turing at Bletchley Park in Britain during the Second World War. It was used by Bletchley Park's Hut 8 to help break German ''Kriegsmarine'' (naval) messages enciphered on Enigma machine ...
, a cryptanalytic process
* Bayesian approaches to brain function
* Bayesian inference in marketing
*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 ...
* Bayesian tool for methylation analysis (BATMAN)
*Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occu ...
*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 ...
* Evidence under Bayes' theorem
*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
Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing Westphalian sovereignty, sovereign states.
In early times, the meaning was restricted to information about states, pa ...
*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 ...
*Inverse resolution Inverse resolution is an inductive reasoning
Inductive reasoning is a method of reasoning in which a general principle is derived from a body of observations. It consists of making broad generalizations based on specific observations. Inductive ...
*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