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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Standard Models

`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

Models for Bayesian Variable Selection

`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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Create Prior Model

bayeslm Create Bayesian linear regression model object

Estimate Posterior

`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

Perform Predictor Variable Selection

`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

Sample From Posterior

`simulate`	Simulate regression coefficients and disturbance variance of Bayesian linear regression model
`sampleroptions`	Create Markov chain Monte Carlo (MCMC) sampler options

Generate Minimum Mean Square Error Forecasts

forecast Forecast responses of Bayesian linear regression model

Topics

Bayesian Linear Regression
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.
Bayesian Lasso 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.