Rigorous Reasoning
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Probabilistic Reasoning · Free

Bayesian Update Tool

Enter a prior probability and the two likelihoods — P(E given H) and P(E given not-H) — and the tool computes the posterior using Bayes' rule. The result panel shows the Bayes factor with a plain-English strength band, the full worked calculation, and (when applicable) a focused callout for the base-rate-neglect / mammography-paradox case where intuition reliably misjudges the answer.

Used in: Bayesian Probability. The full unit covers what likelihood ratios mean, how to estimate them from real evidence, and why the same Bayes factor yields very different posteriors at different priors.

Where to go next

Fallacy DiagnosticWhen you spot a fallacy of base-rate neglect or weak induction in an argument, run the actual numbers here to see how much the evidence really moves the conclusion.Open tool →Relevance & Sufficiency CheckerEvaluate whether the premises support the conclusion. Bayes is the quantitative complement: relevance is whether evidence bears on the conclusion at all; the Bayes factor is by how much.Open tool →Induction Strength CheckerEvaluate inductive arguments structurally before reaching for the numbers. Often the right move when you don't have well-calibrated likelihoods to plug in here.Open tool →Argument to the Best ExplanationCompare candidate explanations across multiple criteria.Open tool →Causal Reasoning AnalyzerApply Mill's methods to identify candidate causes from a case set.Open tool →