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Posterior probability

A posterior probability is the updated chance of something being true after you have taken new evidence into account, starting from what you believed before.

By Fredrik FilipssonFounder and editor · Two decades in advisory, hospitality and mediaEditorial review by Morten Andersen · Last reviewed 13 September 2025

Last reviewed 13 September 2025 · Educational, not advice

Information, not advice. This page is general information, not financial, investment, legal, tax, or betting advice. Prediction markets carry a real risk of loss. You must be 18+ or the legal age in your region.
In plain terms

What the term means and how it is used.

The idea comes from Bayesian reasoning, a standard way of thinking about how beliefs should change as information arrives. You begin with a prior probability, your estimate before seeing the new evidence. You then observe something relevant. The posterior probability is your revised estimate afterwards, combining what you thought before with what the new evidence implies. In short, prior plus evidence gives posterior. It is simply the name for a belief after it has been updated.

The mechanism behind it is Bayes rule, which weighs how likely the new evidence would be if the claim were true against how likely it would be in general. Strong evidence that fits one explanation much better than the alternatives moves the posterior a lot. Weak or ambiguous evidence moves it only a little. This is why a single surprising data point can shift a careful forecaster's view sharply, while noise that could happen either way barely changes it at all.

Prediction market prices can be read as a kind of shared posterior. A contract price reflects the implied probability the market currently assigns to an outcome, and as fresh news arrives, participants update and the price moves to a new level. That new level is, loosely, the market's posterior after the news. Thinking this way is useful because it frames a price as a current belief that should respond to evidence, not as a fixed prediction or a guarantee about what will happen.

For anyone forming their own view, the posterior is a discipline rather than a formula to compute exactly. It reminds you to start from a sensible prior, to ask how much a new piece of information really tells you, and to update by a sensible amount rather than overreacting to every headline or ignoring evidence that should change your mind. Good forecasting is largely the habit of updating well, and the posterior is the name for where you land after each honest update.

A worked example

Suppose you think an outcome has a forty percent chance, your prior. A credible report arrives that would be far more likely to appear if the outcome were going to happen than if it were not. Applying that evidence, you revise upward to, say, sixty five percent. That sixty five percent is your posterior. If a later report is weak and could have appeared either way, it might nudge you only slightly, to sixty seven percent.

Illustrative only. Numbers are examples, not a quote or a prediction, and exclude fees.

A note on risk,

A probability, even a carefully updated one, is never a certainty, and markets can and do move against a well reasoned view. Prediction markets can lose you money. Stake only what you can afford to lose, never to chase a loss, and never on borrowed money. If it stops feeling like a free choice, step back. In the United States you can call or text the helpline on 1-800-GAMBLER or visit ncpgambling.org.

Common questions

Answered plainly.

What is a posterior probability?

It is your updated estimate of how likely something is after taking new evidence into account, starting from a prior belief you held beforehand.

How is it different from a prior?

The prior is what you believed before the new evidence. The posterior is what you believe after combining that prior with the evidence. Each new piece of information turns your current posterior into the prior for the next update.

How does this relate to market prices?

A contract price reflects the probability the market currently assigns to an outcome. As news arrives and participants update, the price moves, so a price can be read loosely as the market's posterior after the latest information.

Does a high posterior mean the outcome is certain?

No. A probability below one hundred percent always leaves room for the other result. Updating well improves your reasoning, but it never removes the genuine uncertainty in an event that has not yet happened.

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