Econometrics Toolbox includes a self-contained framework that allow you to implement Bayesian linear regression. The framework contains two groups of prior models for the regression coefficient β and the disturbance variance σ2: -Standard Bayesian linear regression prior models - The five prior model objects in this group range from the simple conjugate normal-inverse-gamma prior model through flexible prior models specified by draws from the prior distributions or a custom function. Although standard prior models can serve several purposes, they are best suited for posterior estimation, simulation (from the joint or, for most models, conditional posterior), and forecasting from the posterior predictive distribution.-Bayesian prior models for predictor variable selection - The models in this group can perform Bayesian lasso regression or stochastic search variable selection (SSVS). They are best suited for posterior estimation, during which the predictor selection algorithm occurs. The resulting posterior model is represented by draws from the Gibbs sampler (an empirical model object), and the estimation summary contains the results from the predictor selection algorithm. The estimation procedure does not remove insignificant or redundant variables for you, but the coefficient of a well tuned model are close to zero. Therefore, like standard models, you can simulated raws from the posterior distribution or forecast from the posterior predictive distribution without having to remove any variables.The more important topics in this book are the next: -"Bayesian Linear Regression" -"Bayesian Linear Regression Workflow -"Specify Gradient for HMC Sampler" -"Posterior Estimation and Simulation Diagnostics" -"Tune Slice Sampler For Posterior Estimation" -"Compare Robust Regression Techniques" -"Bayesian Lasso Regression" -"Bayesian Stochastic Search Variable Selection" -"Replacing Discouraged Syntaxes of estimate"-"Discrete-Time Markov Chains" -"Markov Chain Modeling" -"Create and Modify Markov Chain Model Objects" -"Visualize Markov Chain Structure and Evolution" -"Determine Asymptotic Behavior of Markov Chain" -"Identify Classes in Markov Chain" -"Compare Markov Chain Mixing Times" -"Simulate Random Walks Through Markov Chain" -"Compute State Distribution of Markov Chain at Each Time Step"