1. Price is another important figure in mathematics and philosopher, and have taken Bayes’ theorem and applied it to insurance and moral philosophy.↩︎

2. See the paper by John Aldrich on this.↩︎

4. 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).↩︎
5. 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.↩︎