Bayes Updater
Start with a prior probability. Add evidence one item at a time. Watch your belief update at every step.
ADVANCED (WORTH LEARNING)
How to change your mind correctly when new info arrives
What is this?
Bayesian updating = updating your beliefs as new evidence comes in, mathematically. Most people either ignore new info (too stubborn) or overreact to it (panic). Bayes tells you exactly how much to shift your position.
You start with a prior belief (what you thought before). New evidence arrives. You update to a posterior belief (what you should think now). This tool runs that math so you don't over- or under-react to breaking news.
Real-World Example
→ News Breaks
You believed "Fed cuts in March" was 40% likely. Then a surprise inflation print comes in hot (bad for cuts). Historically, hot CPI cuts the probability of a near-term rate cut by about 35%.
Bayes Updater outputs: your new probability should be roughly 26%, not 40. The market is still at 38¢. That's now a NO bet, and you have the math to back it up.
✅Action: When news breaks, don't just react — calculate. Enter your prior, the new info, and get your updated probability instantly.
Bottom line: This is how CIA analysts think. Separate from emotion. Update systematically. Win more.
Full guide →Worked Example
Interactive Calculator
Your starting probability before adding evidence
Probability Chain
Related Tools
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.
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