Probability as Degrees of Belief
- According to this view, probabilities measure degrees of belief. These can be beliefs about the occurrence of an event, the truth of a hypothesis, or the truth of any random fact. In other words, probabilities represent how certain you are about the truth of statements. These statements can refer to the past, the present, or the future.
- A probability of 1 represents the certain belief that something is true and a probability of 0 represents the certain belief that something is false. Anything in between implies some uncertainty about the truth of the event/hypothesis.
- Probabilities should reflect your knowledge and experience. The principle of indifference is also used here to assign probabilities to events when you know nothing about them or when you have no reason to believe any event is more likely than the others.
Relation to Other Probability Definitions
- Just like with the propensity definition, you can still talk about probabilities of single events. However degree of belief extends beyond physical properties allowing you to attach probabilities to virtually any statement.
- Unlike the long-term frequency definition, there is no requirement for repeatability of the events
- Both propensity definition and long-term frequency definition do not update probabilities with Bayes’ theorem
Updating probabilities
Probabilities are updated using Bayes’ theorem, where your initial belief is your prior probability for an event, which can be updated into a posterior probability with new information.