Prior Probability

In Bayesian statistics, the prior probability expresses what is known or believed about an event before specific evidence is examined. It is typically grounded in a relevant Base Rate such as historical data on how often comparable events occur. For example, a forecaster estimating the probability of a central bank rate cut next quarter might start with the historical frequency of cuts during similar economic conditions. In a Prediction Market, the initial Contract Price often encodes the market's collective prior. From this starting point, new evidence such as economic data releases or central bank statements is incorporated to produce an updated Posterior Probability. Choosing a well-calibrated prior is critical to achieving good overall Calibration.

Priors range from highly informative to deliberately flat. An informative prior encodes specific background knowledge, while an uninformative or weakly informative prior starts closer to 50% to let data drive the conclusion. In prediction markets on Kalshi or Polymarket, early prices represent a rough consensus prior before substantial trading volume reveals the crowd's refined view. A key risk in forecasting is selecting a prior that is too extreme, making rational updating toward the truth slower and harder. The Wisdom of the Crowd effect suggests that aggregating many independent priors through Forecast Aggregation often outperforms any single forecaster's choice of starting probability, even when individual priors are biased.