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In statistics, Bayesian linear regression is an approach to linear regression in which the statistical analysis is undertaken within the context of Bayesian inference. When the regression model has errors that have a normal distribution, and if a particular form of prior distribution is assumed, explicit results are available for the posterior probability distributions of the model's parameters. ==Model setup== Consider a standard linear regression problem, in which for we specify the conditional distribution of '''' given a '''' predictor vector '''': : where '''' is a '''' vector, and the are independent and identical normally distributed random variables: : This corresponds to the following likelihood function: : The ordinary least squares solution is to estimate the coefficient vector using the Moore-Penrose pseudoinverse: : where is the '''' design matrix, each row of which is a predictor vector ; and is the column -vector . This is a frequentist approach, and it assumes that there are enough measurements to say something meaningful about . In the Bayesian approach, the data are supplemented with additional information in the form of a prior probability distribution. The prior belief about the parameters is combined with the data's likelihood function according to Bayes theorem to yield the posterior belief about the parameters and . The prior can take different functional forms depending on the domain and the information that is available a priori. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Bayesian linear regression」の詳細全文を読む スポンサード リンク
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