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This is an ok overview, but it's missing a key point. Classical statistics can be viewed as the statistic of interest being fixed but unknown. However, it's bet
by howlin 12y ago
This is an ok overview, but it's missing a key point. Classical statistics can be viewed as the statistic of interest being fixed but unknown. However, it's better thought of as the parameter is fixed but set in a way that will be most troublesome for your estimation algorithm. Statistical analysis (when done carefully) represents a conservative view on how likely you are to be mistaken.
Bayesian statistics abandons this worst-case approach, instead opting for an average case analysis. Here, we average over the all the possibilities, weighting their relative merit by the prior. The analysis is always a little bit conservative (thus the connection to regularization), but it is never "worst case" in the same way that classical statistics operates under.
Lots of the other talk in this article is not really about classic vs Bayesian statistics at all. Both methodologies are perfectly happy working with more complicated, hierarchal models. Both approaches have plenty of work dealing with regularization, and both methods will suffer if you mis-specify your model. The fact that Bayesian analysis is less likely to "crash" in a case of model mis-specification can be thought of as just as much of a drawback as it is a benefit.
- wfunction 12y agoCould you explain in what sense classical statistics is actually a worst-case view? i.e., can you link to a page or maybe explain yourself explicitly (i.e., using a min() operation) how classical statistics is a worst-case analysis? What scenarios is it actually worst-case with respect to? It's always seemed to me that the differences I see, such as in ML vs. MAP, are not due to a question of worst-case versus average-case analyses, but rather no-prior-knowledge versus yes-prior-knowledge analyses. I've never seen a proof that classical statistics gives a worst-case bound.
- howlin 12y agoMaximum likelihood is literally the simplest thing classic statistics will tell you. No serious statistician will regard this as meaningful without at least some indication of sample size, confidence interval or whatnot. The worst-case nature of classical/frequentist statistics is very well exposed in PAC (probably approximately correct) analysis: http://en.wikipedia.org/wiki/Probably_approximately_correct_learning http://en.wikipedia.org/wiki/Probably_approximately_correct_...