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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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conjugateblmBayesian linear regression model with conjugate prior for data likelihood
semiconjugateblmBayesian linear regression model with semiconjugate prior for data likelihood
diffuseblmBayesian linear regression model with diffuse conjugate prior for data likelihood
empiricalblmBayesian linear regression model with samples from prior or posterior distributions
customblmBayesian linear regression model with custom joint prior distribution
mixconjugateblmBayesian linear regression model with conjugate priors for stochastic search variable selection (SSVS)
mixsemiconjugateblmBayesian linear regression model with semiconjugate priors for stochastic search variable selection (SSVS)
lassoblmBayesian linear regression model with lasso regularization

Functions

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bayeslmCreate Bayesian linear regression model object
estimateEstimate posterior distribution of Bayesian linear regression model parameters
summarizeDistribution summary statistics of standard Bayesian linear regression model
plotVisualize prior and posterior densities of Bayesian linear regression model parameters
estimatePerform predictor variable selection for Bayesian linear regression models
summarizeDistribution summary statistics of Bayesian linear regression model for predictor variable selection
plotVisualize prior and posterior densities of Bayesian linear regression model parameters
simulateSimulate regression coefficients and disturbance variance of Bayesian linear regression model
sampleroptionsCreate Markov chain Monte Carlo (MCMC) sampler options
forecastForecast responses of Bayesian linear regression model

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