When are Bayesian methods preferable to Frequentist?

When we apply Bayes’s Rule with a normal distribution as a prior, on the other hand, we obtain a very different kind of guidance. Instead of a multiplicative rule, we get an Average Rule:

The flip side of the flexibility of the Bayesian approach is that it can also be accused of having too many free parameters.

Bayesian updating refers to a mathematical process whereby an accepted theory or predictive model gets increasingly accurate through the iterative testing of competing variants of that theory.

Essentially, the frequentist approach toward statistics seeks to wash its hands of the reason that predictions most often go wrong: human error. It views uncertainty as something intrinsic to the experiment rather than something intrinsic to our ability to understand the real world. The frequentist method also implies that, as you collect more data

As an empirical matter, we all have beliefs and biases, forged from some combination of our experiences, our values, our knowledge, and perhaps our political or professional agenda. One of the nice characteristics of the Bayesian perspective is that, in explicitly acknowledging that we have prior beliefs that affect how we interpret new evidence, i

Bayes’ rule is a description of how to reason rationally under conditions of uncertainty.

If we had copious data, drawn from a perfectly representative sample, completely mistake-free, and representing exactly what we’re trying to evaluate, then using the most complex model available would indeed be the best approach.

Price, in framing Bayes’s essay, gives the example of a person who emerges into the world (perhaps he is Adam, or perhaps he came from Plato’s cave) and sees the sun rise for the first time. At first, he does not know whether this is typical or some sort of freak occurrence. However, each day that he survives and the sun rises again, his confidence