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IlyaShpitser comments on Rationality Quotes August 2013 - Less Wrong
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I do not see why any of Chapman's examples cannot be given appropriate distributions and modeled in a Bayesian analysis just like anything else:
Dynamical chaos? Very statistically modelable, in fact, you can't really deal with it at all without statistics, in areas like weather forecasting.
Inaccessibility? Very modelable; just a case of missing data & imputation. (I'm told that handling issues like censoring, truncation, rounding, or intervaling are considered one of the strengths of fully Bayesian methods and a good reason for using stuff like JAGS; in contrast, whenever I've tried to deal with one of those issues using regular maximum-likelihood approaches it has been... painful.)
Time-varying? Well, there's only a huge section of statistics devoted to the topic of time-series and forecasts...
Sensing/measurement error? Trivial, in fact, one of the best cases for statistical adjustment (see psychometrics) and arguably dealing with measurement error is the origin of modern statistics (the first instances of least-squared coming from Gauss and other astronomers dealing with errors in astronomical measurement, and of course Laplace applied Bayesian methods to astronomy as well).
Model/abstraction error? See everything under the heading of 'model checking' and things like model-averaging; local favorite Bayesian statistician Andrew Gelman is very active in this area, no doubt he would be quite surprised to learn that he is misapplying Bayesian methods in that area.
One’s own cognitive/computational limitations? Not just beautifully handled by Bayesian methods + decision theory, but the former is actually offering insight into the former, for example "Burn-in, bias, and the rationality of anchoring".
gwern, I am curious. You do a lot of practical data analysis. How often do you use non-Bayesian methods?
Pretty frequently (if you'll pardon the pun). Almost all papers are written using non-Bayesian methods, people expect results in non-Bayesian terms, etc.
Besides that: I decided years ago (~2009) that as appealing as Bayesian approaches were to me, I should study 'normal' statistics & data analysis first - so I understood them and why I didn't want to use them before I began studying Bayesian statistics. I didn't want to wind up in a situation where I was some sort of Bayesian fanatic who could tell you how to do a Bayesian analysis but couldn't explain what was wrong with the regular approach or why Bayesian approaches were better!
(I think I'm going to be switching gears relatively soon, though: I'm working with a track coach on modeling triple-jumping performance, and the smallness of the data suggests it'll be a natural fit for a multilevel model using informative priors, which I'll want to read Gelman's textbook on, and that should be a good jumping off point.)
Random question - if you were to recommend a textbook or two, from frequentist and Bayesian analysis both, to a random interested undergraduate...
(As you might guess, not a hypothetical, unfortunately.)