When are Bayesian methods preferable to Frequentist?

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

Fisher and his contemporaries had no problem with the formula called Bayes’s theorem per se, which is just a simple mathematical identity. Instead, they were worried about how it might be applied. In particular, they took issue with the notion of the Bayesian prior.46 It all seemed too subjective: we have to stipulate, in advance, how likely we thi

The core of Bayesian thinking (or Bayesian updating, as it can be called) is this: given that we have limited but useful information about the world, and are constantly encountering new information, we should probably take into account what we already know when we learn something new.

The transparency of Bayesian networks distinguishes them from most other approaches to machine learning, which tend to produce inscrutable “black boxes.” In a Bayesian network you can follow every step and understand how and why each piece of evidence changed the network’s beliefs.

In many walks of life, expressions of uncertainty are mistaken for admissions of weakness. When you first start to make these probability estimates, they may be quite poor. But there are two pieces of favorable news. First, these estimates are just a starting point: Bayes’s theorem will have you revise and improve them as you encounter new informat

Any Bayesian analysis begins with an initial belief, aka a prior. In our case, the prior was the initial guess we had about the location of the target ball. Then we encounter objective information, which in our case was whether the new ball landed to the left or the right of the target ball. When you combine the two it gives you the improved belief

This is perhaps the most important role of Bayes’s rule in statistics: we can estimate the conditional probability directly in one direction, for which our judgment is more reliable, and use mathematics to derive the conditional probability in the other direction, for which our judgment is rather hazy.