Beta–Bernoulli Point-Null Bayes Factor
Compare a point null with a continuous alternative using integrated evidence and model odds.
Free theory articleCompare a point null with a continuous alternative using integrated evidence and model odds.
Concept & interpretation
In Bayesian inference, a Bayes factor compares the predictive success of two models. Here we compare a point null hypothesis (H0: p = 0.5) against a continuous alternative hypothesis (H1: p ~ Beta(a, b)) for Bernoulli sequence data.
Experiment
Open the Beta–Bernoulli Point-Null Bayes Factor module to explore this interactively.
- Set Trials to 4 and Successes to 2.
- Set Beta alpha and Beta beta to 1 (Uniform prior).
- Observe the Bayes factor alternative over null of approximately 0.5333.
- Set Successes to 4. Notice the Bayes factor increases to 3.2, favoring the alternative, and the posterior probability of H1 increases to 0.7619...
- Change the Prior alternative to 0 and observe the posterior alternative probability immediately drop to 0, regardless of the Bayes Factor.