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.
Learn about Bayesian analyses and how a Bayesian view of linear regression differs from a classical view.
Implement Bayesian Linear Regression
Combine standard Bayesian linear regression prior models and data to estimate posterior distribution features or to perform Bayesian predictor selection. Both workflows yield posterior models that are well suited for further analysis, such as forecasting.
Posterior Estimation and Simulation Diagnostics
Tune Markov Chain Monte Carlo sample for adequate mixing and perform a prior distribution sensitivity analysis.
Specify Gradient for HMC Sampler
Set up a Bayesian linear regression model for efficient posterior sampling using the Hamiltonian Monte Carlo sampler.
Tune Slice Sampler For Posterior Estimation
Improve a Markov Chain Monte Carlo sample for posterior estimation and inference of a Bayesian linear regression model.
Compare Robust Regression Techniques
Address influential outliers using regression models with ARIMA errors, bags of regression trees, and Bayesian linear regression.
Perform variable selection using Bayesian lasso regression.
Bayesian Stochastic Search Variable Selection
Implement stochastic search variable selection (SSVS), a Bayesian variable selection technique.
Replacing Removed Syntaxes of estimate
The estimate function of the Bayesian linear regression models conjugateblm, semiconjugateblm, diffuseblm, empiricalblm, and customblm returns only an estimated model and an estimation summary table.