Gaussian Process Regression

Abstract

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. We presenting some important issues about Bayesian statistics, multivariate normal distribution and linear model. Then the posterior and posterior predictive distribution for linear regression model is derived. Some visual examples about the Bayesian linear model are also presented. Finally, the connection between standard Bayesian treatment of linear models and Gaussian process regression is discussed.

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. We presenting some important issues about Bayesian statistics, multivariate normal distribution and linear model. Then the posterior and posterior predictive distribution for linear regression model is derived. Some visual examples about the Bayesian linear model are also presented. Finally, the connection between standard Bayesian treatment of linear models and Gaussian process regression is discussed.