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sci.Bayesian-update-beta-prior Calculator
Updates a Beta prior distribution with binomial observations to compute the posterior Beta(α+k, β+n−k) and posterior mean, mode, and credible interval. Beta-Binomial conjugacy gives a closed-form posterior — this is the canonical model for click-through rates, conversion rates, and clinical trial success probabilities.
Inputs
Alpha Prior
Reference formula or conversion factor shown for context.
Beta Prior
Reference formula or conversion factor shown for context.
Successes New
Reference formula or conversion factor shown for context.
Trials New
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 std deviation
Standard deviation -- the average spread of values around the mean. In a normal distribution: 68% within 1 SD, 95% within 2 SD.
posterior Alpha α₁
pH of the solution. Below 7: acidic. 7: neutral. Above 7: basic (alkaline).
posterior Beta β₁
Reference formula or conversion factor shown for context.