Questions about Bayesian Theory

[tom-hc-park]

Dear Professor Paul Gustafson,

I would like to ask you some questions regarding the chapter 5, hierarchical model from the Bayesian book on Wednesday. This is the list of questions I would like to bring.

The last chapter, ch 5.7 explains about weakly informative priors for hierarchical variance parameters, tau. It says we can pick some improper priors which can yield proper posterior density. An example of the case was uniform(0,A) as A goes infinity. But the book says when we pick the improper prior, uniform(0,A) but a very large A, then we would get positive miscalibration value. (This chapter also exmplains about the calibration, a Bayesian way of bias)

My question is as follows.

1. I would like to ask you more detail about the calibration.

2. I was trying to prove (not rigorously) that for Uniform(0,A) with large A value, we would get positive miscalibration but failed. I would like to ask your insight about this matter.

Thanks for your concern.

[paulgstf]

I actually don't know offhand what the authors mean by calibration, but I'll take a look before we talk tomorrow.

[tom-hc-park]

Thanks for your concern.

Here is a screenshot of the book that I've been stuck.

Best, Tom