# Bayesian Linear Regression Models

Posterior estimation, simulation, and predictor variable selection using a variety of prior models for the regression coefficients and disturbance variance

Bayesian linear regression models treat regression coefficients and the disturbance variance as random variables, rather than fixed but unknown quantities. This assumption leads to a more flexible model and intuitive inferences. For more details, see Bayesian Linear Regression.

To start a Bayesian linear regression analysis, create a standard model object that best describes your prior assumptions on the joint distribution of the regression coefficients and disturbance variance. Then, using the model and data, you can estimate characteristics of the posterior distributions, simulate from the posterior distributions, or forecast responses using the predictive posterior distribution.

Alternatively, you can perform predictor variable selection by working with the model object for Bayesian variable selection.

## Objects

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 `conjugateblm` Bayesian linear regression model with conjugate prior for data likelihood `semiconjugateblm` Bayesian linear regression model with semiconjugate prior for data likelihood `diffuseblm` Bayesian linear regression model with diffuse conjugate prior for data likelihood `empiricalblm` Bayesian linear regression model with samples from prior or posterior distributions `customblm` Bayesian linear regression model with custom joint prior distribution
 `mixconjugateblm` Bayesian linear regression model with conjugate priors for stochastic search variable selection (SSVS) `mixsemiconjugateblm` Bayesian linear regression model with semiconjugate priors for stochastic search variable selection (SSVS) `lassoblm` Bayesian linear regression model with lasso regularization

## Functions

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 `bayeslm` Create Bayesian linear regression model object
 `estimate` Estimate posterior distribution of Bayesian linear regression model parameters `summarize` Distribution summary statistics of standard Bayesian linear regression model `plot` Visualize prior and posterior densities of Bayesian linear regression model parameters
 `estimate` Perform predictor variable selection for Bayesian linear regression models `summarize` Distribution summary statistics of Bayesian linear regression model for predictor variable selection `plot` Visualize prior and posterior densities of Bayesian linear regression model parameters
 `simulate` Simulate regression coefficients and disturbance variance of Bayesian linear regression model `sampleroptions` Create Markov chain Monte Carlo (MCMC) sampler options
 `forecast` Forecast responses of Bayesian linear regression model