I've been working my way through Kruschke's Doing Bayesian Data Analysis, and have been able to successfully run a Bayesian multivariable regression using R code provided with the book. Kruschke's code is set up to produce posterior distributions around the regression Betas.
However, I would like to view a distribution of the predicted (Y) variable. That is, to construct a forecast with a frequentist approach, I would simply take the regression betas, multiply them by the new X values, and have a Y estimate. What is the Bayesian equivalent to doing this?
Kruschke's code can be found in a link in item 5 here: https://sites.google.com/site/doingbayesiandataanalysis/software-installation.
My code is based on "Jags-Ymet-XmetMulti-Mrobust-Example.R".
I'm new to Bayesian analysis, so any advice or pointers are greatly appreciated!
Update: This blog post by Kruschke provides the solution to my problem for the univariate regression case. Still working on the multivariate case. [Link removed because I don't have enough reputation for two links; the post below links to the blog post covering the single variable case].
Update 2: Professor Kruschke is a saint; in response to my, and other, emails, he wrote a blog post with the code and explanation for estimating the posterior predictive distribution for a Bayesian multiple linear regression: http://doingbayesiandataanalysis.blogspot.com/2016/10/posterior-predictive-distribution-for.html