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I think it would be useful if you could apply these principles to one of the examples in the article. Assume we have a woman who has a mammogram that indicates

by nkurz 7y ago

I think it would be useful if you could apply these principles to one of the examples in the article. Assume we have a woman who has a mammogram that indicates malignancy. The question that the patient would like answered is "What is the chance that I have breast cancer?" How does frequentist statistics answer this question? What's the null hypothesis that should be used here? Can this question be answered without assuming a prior on the likelihood that the individual had breast cancer before the test was performed?

BeetleB 7y ago
>How does frequentist statistics answer this question? By applying Bayes Theorem, just as the article did. By invoking Type I and Type II errors. This is a standard problem in stats textbooks - not breast cancer but the general problem of a diagnostic measure that is 99% accurate, for a disease that has less than 1% prevalence. Frequentists don't insist on using p-values to solve all problems. >Can this question be answered without assuming a prior on the likelihood that the individual had breast cancer before the test was performed? Why should one not assume a prior? There is a base rate for breast cancer. Why should a frequentist not use that information? I've never heard a statistician who does not describe himself as a Bayesian say one shouldn't. Every textbook suggests one should. Where are people getting the idea that frequentists don't use Bayesian methods. They always have used them. I'm finding this whole discussion orthogonal to Bayesian vs frequentist statistics. The main issue frequentists have with a lot of Bayesian approaches is that Bayesians often want to assign probabilities to one off events, whereas frequentists insist only on repeatable events. That is where the accusation of "subjective" comes from. Frequentists like to believe that any question of probability can be decided by taking N samples and seeing the outcome (even if only conceptually). For problems where there is a population, and one can do sampling (i.e. repeatability), there's never a problem with using Bayesian methods.
- FabHK 7y ago
  Good point. It would be illustrative to get some examples where a prototypical (but competent) Bayesian and a prototypical (but competent) frequentist would give different answers. It seems to me that when there really is a known base rate, the answers would coincide. And if there is no base rate, the Bayesian would guess (but explicitly) or refuse to answer, while the frequentist would give a plausible answer, which, however, very much hinges on the unknown base rate. In the light of the replication crisis, maybe the Bayesian approach is better.

by nkurz 7y ago

BeetleB 7y ago

>How does frequentist statistics answer this question? By applying Bayes Theorem, just as the article did. By invoking Type I and Type II errors. This is a standard problem in stats textbooks - not breast cancer but the general problem of a diagnostic measure that is 99% accurate, for a disease that has less than 1% prevalence. Frequentists don't insist on using p-values to solve all problems. >Can this question be answered without assuming a prior on the likelihood that the individual had breast cancer before the test was performed? Why should one not assume a prior? There is a base rate for breast cancer. Why should a frequentist not use that information? I've never heard a statistician who does not describe himself as a Bayesian say one shouldn't. Every textbook suggests one should. Where are people getting the idea that frequentists don't use Bayesian methods. They always have used them. I'm finding this whole discussion orthogonal to Bayesian vs frequentist statistics. The main issue frequentists have with a lot of Bayesian approaches is that Bayesians often want to assign probabilities to one off events, whereas frequentists insist only on repeatable events. That is where the accusation of "subjective" comes from. Frequentists like to believe that any question of probability can be decided by taking N samples and seeing the outcome (even if only conceptually). For problems where there is a population, and one can do sampling (i.e. repeatability), there's never a problem with using Bayesian methods.

FabHK 7y ago
Good point. It would be illustrative to get some examples where a prototypical (but competent) Bayesian and a prototypical (but competent) frequentist would give different answers. It seems to me that when there really is a known base rate, the answers would coincide. And if there is no base rate, the Bayesian would guess (but explicitly) or refuse to answer, while the frequentist would give a plausible answer, which, however, very much hinges on the unknown base rate. In the light of the replication crisis, maybe the Bayesian approach is better.