Bayesian

Bayesian school

Subjectivism, epistemic, logical probability

Bayesian modeling means that you can condition an event. It sees the world as succession of random event.

Frequentist Unlike the approach that only calculates the probability of data given a hypothesis, Bayesian modeling considers the posterior probability that a hypothesis is true given the data from the perspective of belief.

Frequentist believes there are some parameter behind randomness, while Bayesian solely rely on data considering everything is random with uncertainty. Prior is assumption based on dataset which determines posterior probability.

It is interpreted as the reliability of probability and is based on that.

Relative probability

The likelihood of an event occurring compared to another event, often expressed as a ratio or fraction.

PAC-Bayesian

It presents probabilistic bounds that guarantee the model's performance and focuses on calculating the generalization error of how well a given learning algorithm will perform using

PAC

Bayesian Epistemology

We can think of belief as an all-or-nothing affair. For example, I believe that I am alive, and I don’t believe that I am a historian of the Mongol Empire. However, often we want to make distinctions between how strongly we believe or disbelieve something. I strongly believe that I am alive, am fairly confident that I will stay alive until my next conference presentation, less confident that the presentation will go well, and strongly disbelieve that its topic will concern the rise and fall of the Mongol Empire. The idea that beliefs can come in different strengths is a central idea behind Bayesian epistemology. Such strengths are called degrees of belief, or credences. Bayesian epistemologists study norms governing degrees of beliefs, including how one’s degrees of belief ought to change in response to a varying body of evidence. Bayesian epistemology has a long history. Some of its core ideas can be identified in Bayes’ (1763) seminal paper in statistics (Earman 1992: ch. 1), with applications that are now very influential in many areas of philosophy and of science.