What is Bayesian updating?
Bayesian updating revises how likely each hypothesis is as evidence arrives. For every piece of evidence, you ask a narrow, answerable question: if this hypothesis were true, how likely would I be to see this? Bayes' theorem combines those answers with your starting estimates, called priors, to produce updated estimates, called posteriors. Each posterior becomes the prior for the next item. CIA analysts tested the method in the late 1960s and 1970s and published a handbook on it in 1975.
When to use it
Use Bayesian updating when you need to show how much each piece of evidence moved your judgment, not just where you ended up. It's especially useful when analysts disagree, because it shows whether the disagreement is about starting assumptions or about what a specific piece of evidence means. It pairs naturally with ACH: ACH finds the evidence that discriminates between hypotheses, and Bayesian updating measures how much it discriminates.
How to use this tool
- State the key question and list hypotheses that are mutually exclusive, or import them from your ACH matrix. Add a catch-all if the truth might be something you haven't listed.
- Set priors and explain them, using base rates, history or expert judgment, then confirm them to begin updating.
- Add evidence and estimate how likely each item is under each hypothesis.
- Link items that share a source. The tool warns you, because treating them as independent counts the same reporting twice.
- Read the results. You get final posteriors with ICD 203 estimative terms such as "likely," and a step-by-step trail of how each item moved them.
- Run the sensitivity check. It shows which items are pivotal, meaning that dropping them changes the leading hypothesis.
Common pitfalls
- Double-counting reports that trace back to one source.
- False precision. "53.85%" looks authoritative, but it's no better than your inputs.
- Overlapping hypotheses. If two can both be true, the probabilities stop meaning what they seem to.
Related
- Read the Bayesian Updating tutorial for a worked example.
- Run the same calculation in Python with
ProbabilityOfHypothesisGivenData. - Analysis of Competing Hypotheses supplies the hypotheses and evidence to start from.
- Indicators tracks the future evidence that would shift your posteriors.