We had the pleasure of hosting a symposium in Brad’s honor in 2011. His presentation at CMU and our symposium sound like perfect compliments.

here is the link to his presentation:http://www.youtube.com/watch?v=FX6huSm2xU4&feature=youtu.be. It can be found via our news page http://www.s-3.com/news as well. Enjoy! ]]>

I’ve been thinking about this for a while, and it doesn’t make any sense from a (well, my) Bayesian point of view. As a pragmatic Bayesian, I don’t care about what I would have inferred in the case of data I didn’t actually observe. I only care about checking whether my inferences are robust to different reasonable ways I can translate the prior information into a prior distribution and model.

I’ve tried to think of models for which the frequentist standard error would be large but the posterior standard deviation would be small. This sort of situation would put sharpen the above point. So far, every scenario I’ve thought of has an obvious ancillary or near-ancillary statistic that makes (frequentist) conditional inference the best way to go. (And then the frequentist conditional standard error agrees more-or-less with the posterior standard deviation.)

]]>Entsophy: If you have not already you may wish to read Rubin’s The Bayesian Bootstrap. 1981.

(Footnote 1 raises questions about the justification of the bootstrap proceedure as it _implies_ the use of a horrendously wrong prior)

]]>Corey; even when the specification of the mean is wrong, the estimates are estimating *something* – typically a trend. So long as the independence assumption holds, in large samples, the robust standard errors can be turned into confidence intervals for this trend, and these can be useful.

For a more detailed critique of Freedman’s 2006 arguments, and some of his related concerns, this paper by Winston Lim is great.

]]>I agree. The violations of assumptions swamps the other concerns.

Larry

]]>“In the wild,” both i’s in “iid” are typically questionable, a much more fundamental issue than in the Bayesian/frequentist debate. That said, many of us still object to the injection of personal bias.

]]>Right. If someone uses a horrendously “wrong” prior like N(mean=0, sigma=weight of a M1 Main Battle Tank) for the weight of a human being, then the Bayesain estimates for my weight will be horrendously wrong as well. Oh wait; in this case the results will be identical (out to about 10 significant figures or something) as the elementary Frequentist text book estimates and Confidence Intervals.

It must be a never ending source of mystery to Frequentists why, with all their guarantees and objectivity, 95% CI’s in the wild don’t have anything like 95% coverage, and Bayesian intervals, with their subjective “impossible to interpret” priors consisting of nothing but hopes and wishful thinking, perform no worse and possible better. Could it be that those priors actually do encapsulate objectively true information, but that it’s being done in a way different from what Frequentists find palatable? If so, it would be important to understand what and how that happens so that you can judge Bayesian estimates using a meaningful criterion.

Results like Efron’s are almost always turn out to be important and useful, although usually for reasons different than those given initial. So by all means study the math in detail, but if you really endorse the claim that priors “wrong” according to Frequentist criterion lead to bad estimates, then you’re being lead down rabbit holes by your philosophy of statistics.

]]>Its also the situation of (almost) any anaylisis of non-randomised studies – much effort on getting standard errors of comparisons that have unknown biases.

]]>Tangentially and serendipitously, I read a paper* today by David Freedman making the same point in regards to the Huber sandwich estimator as a method for getting standard errors robust to model misspecification, i.e., if the model specification error causes bias, there’s little point in getting “robust” standard errors.

* On The So-Called “Huber Sandwich Estimator” and “Robust Standard Errors”. The American Statistician (2006) 60: 299-302. Reprinted in Statistical Models and Causal Inference: A Dialogue with the Social Sciences.

]]>Yes, Brad pointed that out in the question period after his talk.

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