Conditional probability and frequentism

Question

I'm brushing up on my basic statistics from undergrad engineering, and (being much older) I've found myself trying to understand the Frequentism vs. Bayesianism debate. Luckily there's plenty online for that.

Some questions that came to mind while researching this (and that I cannot find through extensive searching) are:

1. Is conditional probability a foundation for Bayesian probability (due to it being a part of the likelihood function) and strictly confined to the Bayesian concept of probability, given that it requires a prior?
2. Is there such a thing as a frequentist's conditional probability?

Thanks in advance

Answer 1

Conditional probability is

measures the probability of an event given that (by assumption, presumption, assertion or evidence) another event has occurred

using a definition taken from Wikipedia. It is a domain of probability theory, not statistics, while Bayesian and frequentionist are two approaches to statistics. Bayesian statistics heavily use probability theory, so you see conditional probability often in Bayesian literature, but statistics in general are founded on probability theory. So, no, conditional probability is not connected to any particular area of statistics but is rather more elementary concept.