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Bayesian Linear Regression Models

Posterior estimation and simulation using conjugate, semiconjugate, diffuse priors, or more flexible empirical or custom priors

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.

Using Objects

 `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

Functions

 `bayeslm` Create Bayesian linear regression model object
 `estimate` Fit parameters of Bayesian linear regression model to data `summarize` Distribution summary statistics of Bayesian linear regression model `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

Topics

Bayesian Linear Regression

Learn about Bayesian analyses and how a Bayesian view of linear regression differs from a classical view.

Bayesian Linear Regression Workflow

Use the Bayesian multiple linear regression framework to estimate posterior distribution features and forecast observations using the posterior predictive distribution.

Posterior Estimation and Simulation Diagnostics

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.

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.

Implement Bayesian Variable Selection

Implement stochastic search variable selection (SSVS), a Bayesian variable selection technique, and compare the performance of several supported MCMC samplers.