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sci.bayesian-posterior-beta Calculator
Updates Beta(α, β) prior with binomial data (k successes in n trials) to compute posterior Beta(α+k, β+n−k) and credible intervals. The Beta distribution is the conjugate prior for binomial probability — posterior mean = (α+k)/(α+β+n) shrinks toward prior with small samples and toward data with large samples.
Inputs
Alpha Prior
Reference formula or conversion factor shown for context.
Beta Prior
Reference formula or conversion factor shown for context.
Successes
Reference formula or conversion factor shown for context.
Trials
Reference formula or conversion factor shown for context.
Results
posterior mean p̂
Arithmetic average — sum divided by count. Simple and familiar, but pulled by outliers. If your data contains extreme values, the median may be more representative.
posterior mode (MAP estimate)
The most frequently occurring value.
posterior variance
Standard deviation squared — average squared deviation from the mean. Essential for ANOVA, regression, and many statistical tests, though the squared units make it less intuitive directly.
posterior α, β
Reference formula or conversion factor shown for context.
Beta(α,β) posterior
Reference formula or conversion factor shown for context.