Frequentist vs. Bayesian Probability

Contrasting the 2 most common schools of thought about probability

Did you know that statisticians and mathematicians have 2 major schools of thought about how to interpret probability? They are called frequentist and Bayesian probability; let's explore the definitions, then illustrate them with a simple example about coin flipping.

Frequentist probability assumes that probability is the long-run frequency of an event. To determine the probability of an event of interest, you need to observe a random process many times, count how often the event occurs, and calculate the proportion.

Bayesian probability assumes that probability derives from background knowledge about the random process - whether it is the underlying scientific mechanism or your subjective belief.

Suppose that you are flipping a coin, and you want to determine the probability of getting heads.

• The frequentist flips the coin 10,000 times, counts the number of heads, and calculates the proportion. She does NOT use any underlying knowledge about the coin to determine the probability of getting heads; instead, she focuses solely on what she observes from flipping the coin many times.

• The Bayesian studies the shape of the coin and finds that it is constructed symmetrically on both sides. Thus, he concludes that the coin is fair, and believes that the probability of getting heads is 0.50.

This post focuses on how frequentists and Bayesians interpret probability. How do they actually determine the true probability of random processes in real life, and how do their approaches differ? Those questions fall under the domain of statistical inference, and I will address that in a future article.