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 on Bayesian linear regression, see Bayesian Linear Regression.
To start a Bayesian linear regression analysis, create a 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.
|Bayesian linear regression model with conjugate prior for data likelihood|
|Bayesian linear regression model with semiconjugate prior for data likelihood|
|Bayesian linear regression model with diffuse conjugate prior for data likelihood|
|Bayesian linear regression model with samples from prior or posterior distributions|
|Bayesian linear regression model with custom joint prior distribution|
Learn about Bayesian analyses and how a Bayesian view of linear regression differs from a classical view.
Use the Bayesian multiple linear regression framework to estimate posterior distribution features and forecast observations using the posterior predictive distribution.
Tune Markov Chain Monte Carlo sample for adequate mixing and perform a prior distribution sensitivity analysis.
Set up a Bayesian linear regression model for efficient posterior sampling using the Hamiltonian Monte Carlo sampler.
Improve a Markov Chain Monte Carlo sample for posterior estimation and inference of a Bayesian linear regression model.
Address influential outliers using regression models with ARIMA errors, bags of regression trees, and Bayesian linear regression.
Perform variable selection using Bayesian lasso regression.
Implement stochastic search variable selection (SSVS), a Bayesian variable selection technique, and compare the performance of several supported MCMC samplers.