In my understanding, Bayesians view probability as a measure of subjective belief, based on prior beliefs and then use Bayes update rule. Incorporating these elements, they calculate posterior probabilities, which represent the updated beliefs after considering the data. For example, if I want to calculate the p of getting heart disease, I will start with some prior knowledge about the usual p of the population getting heart disease – say, 1 in 5 people do. Then, suppose I get diagnosed with heart palpitations, which would then update my prior belief.
Frequentists, on the other hand, view probability as objective parameters, where observed frequencies are related to the behavior of past events in repeated experiments.
My question is, isn't the Frequentist view just the prior , but without the update in the Bayesian approach? So in the example above, the frequentist way to calculate the chances of getting heart disease would just use the observed p of the population getting heart disease, so 1 in 5 people, without incorporating the new information from the diagnoses. In other words, isn't the way that Bayesians start with the initial priors, exactly the frequentist approach? If I am wrong, please provide a more clear counter example. Thanks for the help!