﻿

# bayesian statistics

a somewhat controversial statistical methodology that, unlike conventional statistics, which treats population parameters as fixed (though unknown) values, treats parameters as random variables with a specified probability distribution, termed the prior (or a priori) distribution. Bayes theorem is then used to convert the probability distribution of an observable statistic (treated as a conditional probability for a given parameter value) to a conditional probability distribution of the parameter values for a given value of the observable statistic. This distribution is termed the posterior (or a posteriori) distribution because it assigns a probability to each parameter value that depends on the observed data. The controversial point is the prior distribution, which represents a subjective opinion of the experimenter as to the a priori credibility of the various parameter values; for example, in estimating the probability of the presence of a particular disease given a positive test result, the prior distribution represents the experimenter's judgment of the prevalence of the disease in the population under study.

Medical dictionary. 2011.

### Look at other dictionaries:

• Bayesian statistics — Statistical theory, based on Bayes&’ decision rule, that outlines a framework for producing decisions based on relative payoffs of different outcomes. Used in genetic counselling …   Dictionary of molecular biology

• Bayesian probability — Bayesian statistics Theory Bayesian probability Probability interpretations Bayes theorem Bayes rule · Bayes factor Bayesian inference Bayesian network Prior · Posterior · Likelihood …   Wikipedia

• Bayesian inference — is statistical inference in which evidence or observations are used to update or to newly infer the probability that a hypothesis may be true. The name Bayesian comes from the frequent use of Bayes theorem in the inference process. Bayes theorem… …   Wikipedia

• 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. This allows accounting for… …   Wikipedia

• 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 . The usual procedure is as follows:# Formulate a number of hypotheses about what… …   Wikipedia

• statistics — /steuh tis tiks/, n. 1. (used with a sing. v.) the science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and… …   Universalium

• 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 (DAG). For example …   Wikipedia

• Bayesian model comparison — A common problem in statistical inference is to use data to decide between two or more competing models. Frequentist statistics uses hypothesis tests for this purpose. There are several Bayesian approaches. One approach is through Bayes… …   Wikipedia

• Bayesian linear regression — In statistics, Bayesian linear regression is a Bayesian alternative to the more well known ordinary least squares linear regression.Consider standard linear regression problem, where we specify the conditional density of y, given x, predictor… …   Wikipedia

• Bayesian multivariate linear regression — Consider a collection of m linear regression problems for n observations, related through a set of common predictor variables {x {c}}, and a jointly normal errors {epsilon {c}} ::y {1} = eta {1} x {1} + epsilon {1},,:y {c} = eta {c} x {c} +… …   Wikipedia