Bayesian Updater

Drag a prior, feed in data, and watch the posterior emerge for the canonical conjugate pairs

Purpose

The central Bayesian idea – prior plus likelihood yields posterior – is abstract until a reader sees a prior distribution morph into a posterior as data accumulate. The Bayesian Updater shows exactly that for the canonical conjugate pairs (beta-binomial, normal-normal, gamma-Poisson), with a single slider for each prior parameter and a second slider for the amount of data observed.

User inputs

• Conjugate pair selector (beta-binomial, normal-normal with known variance, gamma-Poisson)
• Prior parameter sliders with sensible ranges
• Observed data: either numeric input (sum and count) or an interactive data-entry panel
• “Prior type” presets: flat, weakly informative, skeptical, enthusiastic

Outputs

• Overlay plot: prior (dashed), likelihood (light), posterior (solid), all on the same scale
• Summary table: prior mean/variance, posterior mean/variance, 95% credible interval
• Sequential-update animation: add one data point at a time and watch the posterior tighten
• Posterior predictive distribution for the next observation

Didactic value

The app makes four points that are hard to convey in prose: (1) a flat prior is not “objective”, it is informative on the opposite scale; (2) as data accumulate, the posterior concentrates on the MLE regardless of the prior; (3) a strong prior can pull inference far from the data when \(n\) is small; (4) the posterior predictive distribution is wider than the posterior for the mean, and this matters for honest forecasting.

Embedded in

• bayesian/conjugate-priors.md
• bayesian/prior-selection.md
• bayesian/posterior-summaries.md

Source code

Local: apps/10-bayesian-updater/

Run with:

shiny::runApp("apps/10-bayesian-updater")