Bayesianism vs frequentism: which one is better for science?

[Cinitiator]

Which interpretation of probability is better for testing scientific hypotheses, and for scientific modeling in general: Bayesianism or frequentism, and why?

 

[Stephen Tashi]

Which interpretation of probability is better for testing scientific hypotheses, and for scientific modeling in general: Bayesianism or frequentism, and why?

Discussion of relgious and political topics is forbidden in this section of the forum, but I suppose your question is permitted even though it deals with matters of fatih.

I'll be content with observing that this question could investigated statistically, but it seldom is. The arguments in favor of one way or another often claim undocumented empirical support - such as "I have used .. thus-and-such-a method and it has proven effective" or "Thus-and-such-a method is the standard practice in industry."

What is standard practice in industry or in a field of science isn't a direct proof of effectiveness. For example, if a drug company uses certain statistical methods to evaluate how promsing new compounds are for some purpose and the company's stock price holds up and it continues to bring new drugs to marker, you could cite this as "proof" that its statistical methods are effective. However, that type of recommendation mixes together the effects of all the companies business practices and research methods.

It's easy for a person to claim that he has used a certain method effectively, but often this only means that the person got reports published, didn't make any disasterous financial decision, etc. This kind of recommendation may show sufficiency of a given method. It doesn't show optimality.

In fairness to debaters on both sides, there is additional expense and labor in doing statistical testing. A statistical test of a statistical test would go something like this. You apply a given statistical test of a batch of similar situations. You reach a decision on each problem. Then you do follow-up investigation (such as taking further samples) to test how often your initial test made the right decision. I think that's the minimum that should be done to supply empirical evidence in favor of a test. It isn't a mathematical proof. There is a circularity about the logic since in the follow-up you might be trusting the result of a second test. However, most Bayesians and frequentists believe that if you take a huge number of samples, you can nail things down pretty well. The practical question is what is are the most effective methods to use when you haven't done that.

 

[ImaLooser]

Which interpretation of probability is better for testing scientific hypotheses, and for scientific modeling in general: Bayesianism or frequentism, and why?

Baysian is very useful if you have a solid prior. If not, then frequentism is your only resort.