# Bayesian Linear Regression

Bayesian Linear Regression

Regression analysis
Models
• Generalized linear model
• Discrete choice
• Logistic regression
• Multinomial logit
• Mixed logit
• Probit
• Multinomial probit
• Ordered logit
• Ordered probit
• Poisson
• Multilevel model
• Fixed effects
• Random effects
• Mixed model
• Nonlinear regression
• Nonparametric
• Semiparametric
• Robust
• Quantile
• Isotonic
• Principal components
• Least angle
• Local
• Segmented
• Errors-in-variables
Estimation
• Least squares
• Ordinary least squares
• Linear (math)
• Partial
• Total
• Generalized
• Weighted
• Non-linear
• Iteratively reweighted
• Ridge regression
• LASSO
• Least absolute deviations
• Bayesian
• Bayesian multivariate
Background
• Regression model validation
• Mean and predicted response
• Errors and residuals
• Goodness of fit
• Studentized residual
• Gauss–Markov theorem

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.