[bblais]

"There is no mention of the CLT, MLE, method of moments estimation, biasedness of estimators, convergence in probability, how sampling distributions arise, or any of the theory of distributions that underpin all of the inferential procedures detailed in the book."

Lot's of good criticisms in this thread, which I'll have to look at. This one, however, is not. :) how many intro stats book, of the traditional kind, mention MLE, method of moments, biased vs unbiased estimators, etc...? None that I've seen. So, you're right, it becomes more "cookbooky" as a result, however, I would argue that all Bayes analysis follows the same recipe, whereas frequentist analysis typically follows many recipes - not obviously connected. It is that part that I criticize, not the fact that there is a recipe for doing things.

[daniel-levin]

>> how many intro stats book, of the traditional kind, mention MLE, method of moments, biased vs unbiased estimators, etc...? None that I've seen

Oh - there are quite a few. Here's a small sample (no pun intended):

- Probability and Statistical Inference by Hogg & Tanis (we used this in my stats course)

- Modern Mathematical Statistics with Applications by Devore & Berk

- Probability and Statistics by DeGroot & Schervish

[bblais]

Ah, yes. I concede the point. What I find interesting in all this is that the term "Introduction" is used is so many ways. When looking, for instance, for an intro bayes book you get things like Lee and Bolstad which, for some is intro. However, if you tried to teach med students or business students from that it would be a disaster.

Personally, MLE I see as just an approximation of MAP - which is superior. Biased vs unbiased also doesn't play into probability theory as logic, except as a consequence of those parameters that maximize the posterior.