Problem Set 1 Solutions 1. Discuss the difference between Bayesian and frequentist ideas of probability. Frequentists define the probability of an event as the relative frequency of the event as the number of trials in which the event could occur goes to infinity. Bayesians treat probability as a subjective phenomena, a belief about the likelihood of an event which varies from individual to individual based on their background knowledge.
Frequentist definitions are comfortably objective sounding, but are in practice unrealizable.
Many events to which people would like to assign probabilities are in principle not repeatable, which is a problem for the frequentist definition. Bayesian definitions mean that it is impossible to ever fix the probability of an event by some means external to the observer. Personally, I see some value in each stance. I think Bayesians are correct in that all observations can do is update our beliefs, and that that the idea of an objective probability is probably indefensible. On the other hand, I think it is important that we devise some standardized method by which we can all agree on the significance of a set of measurements, which is impossible if prior probabilities can be anything anyone wants them to be.