What is a Bayesian Statistic?

A Bayesian statistic is one that starts from what you already believe and updates that belief as new data arrives.

How does Bayesian statistics work?

You state a prior, the belief you hold before seeing the data. You collect evidence. Bayes' theorem combines the two into a posterior, your updated belief. Run it again with more data and today's posterior becomes tomorrow's prior. The output is a probability distribution over answers, not a single verdict.

Why does Bayesian thinking matter?

It answers the question founders actually ask. A frequentist test says whether a result this extreme would be rare if nothing were happening. A Bayesian test says there is an 85% chance B beats A, which is what you need to make the call. It also handles small samples honestly, which is most startup data.

Where did it come from?

Thomas Bayes described the theorem in a paper published in 1763, two years after his death, and Pierre-Simon Laplace developed it into a usable method. The approach fell out of fashion for most of the twentieth century and returned when cheap computing made the math practical.

How do you use it well?

Say your prior out loud, because you have one whether or not you write it down. Do not let a strong prior outvote a lot of evidence. Report the interval, not just the point estimate. In A/B testing, decide the stopping rule before you look, since Bayesian methods make it easy to peek and easier to fool yourself. And connect the output to a decision, or it is just analytics with better math.

Bottom line: Bayesian statistics gives you the probability that you are right, which is the number you actually wanted.

For more startup terminology, visit startupdefinitions.com.