0

I've been learning statistics for a long time but I still struggle to understand the "philosophical" differences between frequentist and bayesian statistics. One of my questions is the following:

Are confidence intervals and hypothesis tests purely frequentist devices? (Since their motivation is to bound our search for the "true" population parameters).

P.S.: This question was associated with a different one before, but the other question does not answer my question.

Paca
  • 121
  • 1
    Bayesians have (null) hypothesis tests as well - Bayesians can even evaluate the posterior probability of a hypothesis, so they are arguably more directly interpretable. Confidence intervals do not bound our search for the "true" population parameters, but Bayesian credible intervals do. https://stats.stackexchange.com/questions/26450/why-does-a-95-confidence-interval-ci-not-imply-a-95-chance-of-containing-the/26457#26457 AFAICS there is no reason why a Bayesian cannot construct a Bayesian confidence interval, it is just a different question. – Dikran Marsupial Jul 21 '22 at 17:49
  • Does this mean that bayesians also try to infer values about an "unknown probability distribution with defined parameters"? I struggle to understand the concept of credible intervals without a reference to a "true" population distribution. – Paca Jul 24 '22 at 09:34
  • Yes, A Bayesian may attempt to infer e.g. the mean and variance of a Gaussian from a sample of data from that distribution. The credible interval for the mean would be an interval that contains the true mean with probability $p$, so it is directly linked to the "true" population. Note a frequentist confidence interval does not contain the true value with probability $p$, it is a statement of what would happen if you resampled the data and repeated the experiment, so it IMHO is less directly related to the population distribution. – Dikran Marsupial Jul 24 '22 at 11:38

0 Answers0