Prior Belief

Prior belief is the probability distribution representing your initial assumptions or existing knowledge about a parameter (such as conversion rate) before collecting new data from an experiment, serving as the starting point for Bayesian analysis.

Meaning & Context

In Bayesian A/B testing, prior beliefs formalize what you already know or assume about your metrics before the test begins, whether from historical data, domain expertise, or complete uncertainty. Priors can be informative (based on specific previous data) or uninformative (assuming little prior knowledge). As test data accumulates, the prior is combined with the likelihood of the observed data to produce the posterior distribution.

Why It Matters

Properly specified priors allow you to incorporate existing knowledge into your analysis, potentially reaching reliable conclusions faster than starting from scratch. They make the assumptions underlying your analysis explicit and transparent. Using informative priors based on historical performance can improve estimation accuracy, especially early in a test when data is limited, leading to more efficient experimentation.

Example

Before testing a new pricing page, you set a prior belief that the conversion rate will be around 3% with some uncertainty, based on six months of historical data showing the current page converts at 2.8-3.2%. This prior is then updated with data from the new test to calculate posterior probabilities.