Bayesian vs Frequentist

In statistics, there are two main schools of thought for making inferences from data. Frequentist and the Bayesian approaches aim to answer the same questions, such as estimating parameters, testing hypotheses or predicting future outcomes, but they differ in how they interpret probability and uncertainty.
Flip a coin. Before you look at the result, pause and ask: What’s the probability the coin landed on heads?
Depending on your answer, you’re either a Frequentist or a Bayesian statistically speaking, at least.
According to a Frequentist statistical approach, there’s a single correct answer. If the coin is heads, the probability that the coin landed on heads is 100%. If it’s tails, the probability is 0%.
In Bayesian statistics, probabilities are interpreted subjectively. Using the coin toss as an example, a Bayesian would say that the probability of getting heads or tails reflects your personal belief. You might start by assuming there’s an equal 50% chance for each side, but your confidence in the coin’s fairness could shape that belief. After observing the outcome, you would then revise or update your belief in light of the new evidence.
The main difference between the two methodologies is how they handle uncertainty. Frequentists rely on long-term frequencies and assume that probabilities are objective and fixed. Bayesians embrace subjectivity and the idea that probabilities change based on new information.