> Frequentism and the propensity view have better philosophical justifications, though.
Not really if the knowledge we care about is related to a concrete situation (rather than the frequency of something under hypothethical replications defined in some ad-hoc way). As you said, whether that's okay or not depends on the task.
If we care about whether there was life on Mars or whether Aduhlem is an effective treatment for Alzheimer's I don't think that frequentist inference has good philosophical support. Frequentist epistemology is not directly applicable.
Of course if you consider the frequentist methods themselves as genuine stochastic processes with corresponding objective probabilities (which also requires a valid model, by the way) you have good philosophical support to say things about those methods and their long-term frequency properties.
But this knowledge about the statistical methods used doesn't translate into knowledge about the existence of life on Mars or the efficacy of Aduhlem unless you are ready to make additional assumptions - 'philosophically unjustified' as they may be.
You're involuntarily confirming my negative criticism of Bayesianism by suggesting Bayesian methods could tell us whether there is life on Mars. Sometimes you really need to gather more information and/or develop an analytic model. It seems that a lot of Bayesianism consists of wishful thinking and trying to take shortcuts (e.g. trying to avoid randomized controlled trials for new drugs).
> suggesting Bayesian methods could tell us whether there is life on Mars.
What I suggest is that Bayesian methods provide a framework to reason about the plausability of some statement about the world in a systematic way (unlike Frequentist methods, whatever the limitations in Bayesian methods).
> Sometimes you really need to gather more information and/or develop an analytic model.
Bayesian methods are definitely not a way to escape the need for an analytic model (including all the prior knowledge) and data gathering. What they provide is a mechanism to integrate the data using the model and calculate the impact of incremental information on our knowledge / uncertainty.
I’m not saying that it’s easy to have a good model and useful data for complex questions. But with Frequentist methods in addition to the model and the data you’d be missing the mechanism to use them in a meaningful way.
I wonder why do you say that Bayesians try to avoid randomized controlled trials for new drugs, by the way. Bayesian methods are increasingly used in randomized clinical trials.
Not really if the knowledge we care about is related to a concrete situation (rather than the frequency of something under hypothethical replications defined in some ad-hoc way). As you said, whether that's okay or not depends on the task.
If we care about whether there was life on Mars or whether Aduhlem is an effective treatment for Alzheimer's I don't think that frequentist inference has good philosophical support. Frequentist epistemology is not directly applicable.
Of course if you consider the frequentist methods themselves as genuine stochastic processes with corresponding objective probabilities (which also requires a valid model, by the way) you have good philosophical support to say things about those methods and their long-term frequency properties.
But this knowledge about the statistical methods used doesn't translate into knowledge about the existence of life on Mars or the efficacy of Aduhlem unless you are ready to make additional assumptions - 'philosophically unjustified' as they may be.