Bayesian - AbsoluteAstronomy.com

Bayesian refers to methods in probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

and statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

named after the Reverend Thomas Bayes

Thomas Bayes

Thomas Bayes was an English mathematician and Presbyterian minister, known for having formulated a specific case of the theorem that bears his name: Bayes' theorem...

(ca. 1702–1761), in particular methods related to statistical inference

Statistical inference

In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...

the Bayesian probability
Bayesian probability
Bayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions, whose truth or falsity is...

or degree-of-belief interpretation of probability, as opposed to frequency
Frequency probability
Frequency probability is the interpretation of probability that defines an event's probability as the limit of its relative frequency in a large number of trials. The development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the...

or proportion or propensity
Propensity probability
The propensity theory of probability is one interpretation of the concept of probability. Theorists who adopt this interpretation think of probability as a physical propensity, or disposition, or tendency of a given type of physical situation to yield an outcome of a certain kind, or to yield a...

interpretations: see probability interpretation
Bayes' theorem
Bayes' theorem
In probability theory and applications, Bayes' theorem relates the conditional probabilities P and P. It is commonly used in science and engineering. The theorem is named for Thomas Bayes ....

on conditional probability
Bayesian inference
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...

These methods include:

Bayes estimator
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 . Equivalently, it maximizes the posterior expectation of a utility function...
Bayes factor
Bayes factor
In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing. Bayesian model comparison is a method of model selection based on Bayes factors.-Definition:...
Bayesian average
Bayesian average
A Bayesian average is a method of estimating the mean of a population consistent with Bayesian interpretation, where instead of estimating the mean strictly from the available data set, other existing information related to that data set may also be incorporated into the calculation in order to...
Bayesian spam filtering
Bayesian spam filtering
Bayesian spam filtering is a statistical technique of e-mail filtering. It makes use of a naive Bayes classifier to identify spam e-mail.Bayesian classifiers work by correlating the use of tokens , with spam and non spam e-mails and then using Bayesian inference to calculate a probability that an...
Bayesian game
Bayesian game
In game theory, a Bayesian game is one in which information about characteristics of the other players is incomplete. Following John C. Harsanyi's framework, a Bayesian game can be modelled by introducing Nature as a player in a game...
Bayesian inference
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...
Bayesian information criterion
Bayesian multivariate linear regression
- Bayesian linear regression
  Bayesian linear regression
  In statistics, Bayesian linear regression is an approach to linear regression in which the statistical analysis is undertaken within the context of Bayesian inference...
  
  , a special case
Bayesian network
Bayesian network
A Bayesian network, Bayes network, belief network or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph . For example, a Bayesian network could represent the probabilistic...
Empirical Bayes method
Empirical Bayes method
Empirical Bayes methods are procedures for statistical inference in which the prior distribution is estimated from the data. This approach stands in contrast to standardBayesian methods, for which the prior distribution is fixed before any data are observed...
Naive Bayes classifier
Naive Bayes classifier
A naive Bayes classifier is a simple probabilistic classifier based on applying Bayes' theorem with strong independence assumptions...
Bayesian additive regression kernels
Bayesian additive regression kernels
Bayesian additive regression kernels is a non-parametric statistical model for regression and statistical classification.The unknown mean function is represented as a weighted sum of kernel functions, which is constructed by a prior using...
Bayesian econometrics
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....
Bayesian experimental design
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 inference in phylogeny
Bayesian inference in phylogeny
Bayesian inference in phylogeny generates a posterior distribution for a parameter, composed of a phylogenetic tree and a model of evolution, based on the prior for that parameter and the likelihood of the data, generated by a multiple alignment. The Bayesian approach has become more popular due...
Bayesian search theory
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 the USS Scorpion.-Procedure:The usual procedure is as follows:...
Bayesian VAR
Bayesian VAR
Bayesian Vector Autoregression is a term which indicates that Bayesian methods are used to estimate a vector autoregression . In that respect, the difference with standard VAR models lies on the fact that the model parameters are treated as random variables, and prior probabilities are assigned to...

— Bayesian vector autoregression

Bayesian also refers to the application of this probability theory to the functioning of the brain

Bayesian brain
Bayesian brain
Bayesian brain is a term that is used to refer to the ability 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 neuroscience and studies associated with this term...

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