I've read quite a few posts comparing/contrasting bayesian and frequentist statistics. But there's one thing that I'm still struggling to understand. Based on the following premises (which I think are correct):
Premise 1: A 'sampling distribution' of a statistic (e.g., a sample mean) is a piece of knowledge that tells us what we should expect a statistic to be (given some null hypothesis)
Premise 2: A bayesian 'prior distribution' is a piece of knowledge that we use to describe our degree of belief in a particular parameter of some model/hypothesis (e.g., a particular mean of our data?).
Is it incorrect to assume that a frequentist sampling distribution is just a prior on the mean value (or any particular statistic) of the null model?
If this isn't correct, what makes the sampling distribution different from a bayesian prior distribution?
Thanks for reading
Premise 1: A 'sampling distribution' of a statistic (e.g., a sample mean) is a piece of knowledge that tells us what we should expect a statistic to be (given some null hypothesis)
Premise 2: A bayesian 'prior distribution' is a piece of knowledge that we use to describe our degree of belief in a particular parameter of some model/hypothesis (e.g., a particular mean of our data?).
Is it incorrect to assume that a frequentist sampling distribution is just a prior on the mean value (or any particular statistic) of the null model?
If this isn't correct, what makes the sampling distribution different from a bayesian prior distribution?
Thanks for reading