Bayes Updater

What is Bayesian Updating?

Bayesian updating is the mathematically correct way to revise a probability when new evidence arrives. You start with a prior — your best estimate before seeing any evidence — and update it each time you learn something new. The result is a posterior probability that accounts for both what you believed before and how strongly the new evidence should shift that belief.

In prediction markets, this is how sharp traders think. The market prices a Fed rate cut at 45%. New jobs data comes in stronger than expected. How much should that shift your estimate? It depends on two things: how likely was that jobs report if the Fed is going to cut, and how likely was it if they're not? The Bayes formula takes both answers and gives you the right posterior.

Likelihood Ratios

The two inputs for each piece of evidence are its likelihoods: how probable was this evidence given that the hypothesis is true, versus given that it's false? If strong jobs data is just as likely whether the Fed cuts or not, it shouldn't move your estimate much. But if strong jobs data is far more likely when the Fed holds rates, it should push your estimate down significantly. The ratio of those two likelihoods is what drives the update.

Chaining updates

The power of this tool is chaining multiple evidence items. Each update feeds into the next — the posterior from step 1 becomes the prior for step 2. This is exactly how information should accumulate over time, and it's why prediction markets tend to be more efficient as more evidence arrives and traders update their beliefs in sequence.