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Price is another important figure in mathematics and philosopher, and have taken Bayes’ theorem and applied it to insurance and moral philosophy.↩︎
See http://plato.stanford.edu/entries/probability-interpret/ for more information↩︎
In a purely subjectivist view of probability, assigning a probability \(P\) to an event does not require any justifications, as long as it follows the axioms of probability. For example, I can say that the probability of me winning the lottery and thus becoming the richest person on earth tomorrow is 95%, which by definition would make the probability of me not winning the lottery 5%. Most Bayesian scholars, however, do not endorse this version of subjectivist probability, and require justifications of one’s beliefs (that has some correspondence to the world).↩︎
The likelihood function in classical/frequentist statistics is usually written as \(P(y; \theta)\). You will notice that here I write the likelihood for classical/frequentist statistics to be different than the one used in Bayesian statistics. This is intentional: In frequentist conceptualization, \(\theta\) is fixed and it does not make sense to talk about probability of \(\theta\). This implies that we cannot condition on \(\theta\), because conditional probability is defined only when \(P(\theta)\) is defined.↩︎