# Statistics: Sources for Statistics and Machine Learning ver. 1

Last Updated on November 25, 2021 by shibatau

## I. Frequentists vs. Bayesians

1.  Frequentist vs Bayesian- Which Approach Should You Use?, written by Anukrati Mehta

The author mentioned Fisher, Ramsey and Carnap and their definitions of probability.

i.Ronald Fisher – Probability as Long-Term Frequency

The probability of an event is equal to the long-term frequency of the event occurring when the same process is repeated multiple times. As per this definition, the probability of a coin toss resulting in heads is 0.5 because rolling the die many times over a long period results roughly in those odds.

ii.Frank Ramsey – Probability as Degree of Belief

The probability of an event is measured by the degree of belief. In other words, the likelihood of an event occurring depends on the beliefs about the occurrence of such event. or the truth of a hypothesis, or the truth of any random fact. That is, probabilities simply represent how certain you are about the truth of statements.

iii.Rudolf Carnap – Logical Probability

The probability of an event is measured by the degree of logical support there is for the event to occur. According to this definition, a probability is nothing but a generalization of classical logic.

The frequentist approach follows from the first definition of probability. The Bayesian approach, on the other hand, is rooted in the second and third definitions described above.

The author says:

Frequentists’ main objection to the Bayesian approach is the use of prior probabilities. Their criticism is that there is always a subjective element in assigning them. Paradoxically, Bayesians consider not using prior probabilities one of the biggest weaknesses of the frequentist approach.

3.Probability interpretations (Wikipedia)

To be continued.