Bayesian MAP Estimates and Regression Assumptions

hlsmith

Omega Contributor
#1
I am new to Bayesian regression models. I am trying to learn how to assess regression model assumptions while within the Bayesian context. Much of the literature is about implementing Bayesian models, but little to no information on model assumptions.

I am planning to get maximum a posteriori (MAP) estimates by using the parameter estimate modes from the posterior distribution. Then scoring the dataset using these values and doing residual checks for the model. However, I just came across my first hiccup, in that my posterior data set has no mode within the 10,000 observations (posterior dist is normally distributed, but all values are unique). I am just planning on rounding the estimates up and using the mode from those values. Does anyone have any suggestions or resources that may help me better understand checking model assumptions from Bayesian linear regression models.

Thanks!
 
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Dason

Ambassador to the humans
#2
Are you using R? Nobody typically takes the actual "mode" from the MCMC output. You build a pdf based on that using kernel density or something like that and take the 'mode' of that distribution. There are good packages in R that do this for you.
 

hlsmith

Omega Contributor
#4
Great @Dason ! I just missed your post before replying to myself. I am still playing around in SAS with learning this stuff, but plan to move over to R and use JAGS and WinBUGS after I figure out the basics.

SAS has two main ways to do Bayesian Reg. The first you just tell it to do BAYES with a simple line of code within the normal regression code. Super simple. If you don't state priors it uses default flats priors. The other option is using PROC MCMC, which I believe codes like WinBUGS. So I am figuring it out the simple way and progressing toward the other procedures and programs.

Yes, I would be interested if you could provide some R package names, functions, or links. Since I hope to learn that as well.
 

hlsmith

Omega Contributor
#5
@Dason :

Interestingly, I was also able to export the Kernel Values and Densities from the SAS model. So I will play around with those tomorrow if I have time.
 

hlsmith

Omega Contributor
#6
I was able to use the posterior parameter estimates in a kernel density function to get the kernel values and their respective densities. Am I now to assume the MAP estimate is just the kernel value with the largest density, given the distribution is unimodal?

P.S., I am feeling fairly confident that I can now run most fixed effects Bayesian regression models in SAS. I still need to branch outside of the safe bubble of SAS to ensure I can understand the concepts in other software.