Shiny App Pitch: Introduction to Bayesian Inference

J. Mark Shoun
30 November 2016

Bayesian Inference App

Application Screenshot

  • My application allows the user to experiment with Bayesian inference
  • Presents simple but useful problem: one- and two-sample inference from binomial data
  • Solves two problems with most intro statistics courses
  • Source code for the application is hosted here

Problem #1: Frequentist Binomial Inference is Hard

Problem:

  • Exact one-sample confidence intervals are on discrete distribution
  • Using normal approximation requires continuity correction
  • Normal approximation doesn't work for small or extreme data
  • Exact inference for two-sample data is complex.

Solution:

  • Bayesian intervals are from continuous distributions
    • No approximation or discretization needed!
  • Two-sample inference isn't much harder than one-sample

Problem #2: Bayes' Theorem Is Given Short Shrift

Problem:

  • Bayes' Theorem is a part of the standard curriculum, but…
  • Only discrete examples are discussed (no continuous estimands)
  • Choices of prior aren't discussed in detail
  • Math for continuous Bayesian inference is considered intimidating

Solution:

  • Show a simple but practical problem where the math is tractable
  • Visualize the prior and posterior distributions to foster intuition
  • Automatically take care of technical details

Mathematical Details: How It Works

  • The beta distribution is a conjugate prior for binomial/Bernoulli data
  • If your prior distribution is beta, so is your posterior
  • The beta distribution is included in R
  • Easy example of how it works:
    • Find a 90% uncertainty interval
    • For 10 observed successes and 5 observed failures
    • Assuming a uniform prior on the probability scale
interval.quantiles <- c(.05, .95)
successes <- 10
failures <- 5
qbeta(interval.quantiles, successes + 1, failures + 1)

[1] 0.4516529 0.8222341