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What is a “prior” in the context of hypothesis testing? That seems to me to be a concept used in parameter estimation, with Bayes rule. But hypothesis testing i

• travisjungroth 3y ago
  As the linked post points out, you can regularize a p-value based on prior experiments. IMO, null hypothesis testing is way overused. We should be quantifying the comparison of the null versus alternative hypotheses. People already compare them. Might as well bring some math into it.
• mitthrowaway2 3y ago
  How is hypothesis testing different from parameter estimation? They seem conceptually the same to me, with one a special case of the other.
• PheonixPharts 3y ago
  In Bayesian terms there is no distinction between hypothesis testing and parameter estimation. If your hypothesis is that A is greater than B, then you're test boils down to "The probability that A is greater than B", which is arrived at through parameter estimation via Bayes' Theorem. You can consider the distribution of estimates for a parameter to represent a space of possible hypothesis for the true value of that parameter and their absolutely or relative likelihood based on the information available. The also has the pleasant consequence that hypothesis testing using Bayesian methods nearly always is closer to the actual question someone wants to answer rather than replying with confusing statements such as "the probability of rejecting the null hypothesis", which contains an implicit double negative.
  • mjfl 3y ago
    > If your hypothesis is that A is greater than B, then you're test boils down to "The probability that A is greater than B", which is arrived at through parameter estimation via Bayes' Theorem. but even in this situation you would need a threshold for decision making, i.e. a p-value.
    • uoaei 3y ago
      "p-value" as a term already has a definition -- one that imposes a frequentist perspective -- so you'd have to come up with a new term to define a Bayesian analogue of that concept.
      • mjfl 3y ago
        I fail to understand why the terminology matters. If you need to make a decision then there will be a threshold in the probability that will determine it. It doesn’t matter if you call it p values or anything else.
        • uoaei 3y ago
          I'm not understanding your confusion. Different concepts require different words to distinguish them in conversation. p-value is a name, not merely a descriptor, of one possible way to define a threshold. Other ways of defining thresholds get different names so that everyone knows what's being discussed. Bob bob bob'bob bob bob bob bob, bob bob bob bob bob "Bob".
        • PheonixPharts 3y ago
          I'm curious how much professional statistical experience you have? In my experience probabilities alone are very rarely used and distributions of beliefs are combined with distributions of value so you can choose optimal risk/reward scenarios. Bayesian decision making typically involves combining a cost function with your posterior distribution. It's worth pointing out that this is typically not possible in most frequentist frameworks since they work in double negative style assertions and arbitrary threshold rather than modeling the problem itself. While you can map Bayesian approaches to frequentists tests, this is usually a misunderstanding of Bayesian methods coming from a purely frequentist background. Bayesian analysis is fundamentally more flexible since it just the application of the sum and product rules (you don't even need Bayes' theorem since it can be trivially derived from these) as well as corresponding cost/value functions.
    • PheonixPharts 3y ago
      I know this reply is a bit late, but, at least in my professional experience, Bayesian decision making typically does not involve just a probability of an event (in which thresholds are more or less arbitrary, including p-values) but involves mapping the probably to a cost/value in which the threshold isn't determined by arbitrary probability threshold but died to business value. In the most common situations this typically means the expected value well exceeds the expected cost and you're comfortable with the risk if you're wrong.
• stale2002 3y ago
  > What is a “prior” in the context of hypothesis testing? A prior could be any previous knowledge that you have on the subject, or anything about the world. Let me give you a silly example. Imagine I do an experiment, on if person A can see the future, and predict coin flips. Now, imagine that I do this experiment, and lo and behold it passes the 5% threshold P value! Remember what a P value is. It is simply the percent chance that the results that you got were by chance. So, if I do that experiment, and it actually gets at the "P value" of 5%, which means that there is a 5% chance of it happening by chance, do you know believe that Person A can see the future? I wouldn't. I would need a much lower P value to start believing that. Thats all a prior is. It is using the fact that "Person A can see the future!" is an extraordinary claim. And for that, we require extraordinary evidence. Much better evidence than a mere "5% that it happened by chance". P