Bayesian vs. Frequentist Statistical Theory

The Frequentist view of probability is that a coin with a 50% probability of heads will turn up heads 50% of the time.

The Bayesian view of probability is that a coin with a 50% probabilit of heads is one on which a knowledgeable risk-neutral observer would put a bet at even odds.

The Bayesian view is better.

When it comes to statistics, the essence of the Frequentist view is to ask whether the number of heads that shows up in one or more trials is probable given the null hypothesis that the true odds in any one toss are 50%.

When it comes to statistics, the essence of the Bayesian view is to estimate, given the number of number of heads that shows up in one or more trials and the observer’s prior belief about the odds, the probability that the odds are 50% versus the odds being some alternative number.

I like the frequentist view better. It’s neater not to have a prior involved.