Probability

Whether we want to determine the likelihood of a stock market crash or if people with a given gene have a higher risk of a disease, we need to understand the details of how to calculate and assess probabilities. But first, what exactly are probabilities and where do they come from? There are two primary views. The frequentist view says that probabilities relate to the proportion of occurrences in a series of events. For example, the probability of a coin coming up heads being 1/2 means that with a large number of coin flips, half should be heads and half tails. The probability then corresponds to how often something will occur. However, we also discuss the probability of events that may only happen once. We may want to know the probability that a recession will end if a policy is enacted, or the chances of a federal interest rate change on a particular date. In the frequentist case, we can get close to inferring the true probability by doing a large number of tests, but when an event may only occur once, we must instead rely on background knowledge and belief. There is another interpretation of probability, referred to as the Bayesian or subjectivist view. Here the probabilities correspond to degrees of belief in the outcome occurring. In this case, one must have what is called a prior, on which the belief is based.