BinomialRevision
This applet illustrates Bayesian anaysis for binomial distributions. The applet begins with a prior uniform distribution for the unknown probability p. Clicking on the "Next Trial" button randomly samples an observation that may be either a Success or Failure. With each new observation, the posterior distribution (a beta distribution with parameters alpha and beta) is revised. To speed the process, click on the "50 Trials" button. The applet stops at 1000 trials. To clear the graph and begin again, click the "Reset" button.
In the example above, the true probability is 0.4. Use the reset button to observe again how quickly the posterior distribution converges around the estimate of 0.4.
Applet with Controls
This version of the applet allows the user to specify the values of the true probability p and the parameters (alpha and beta) of the beta prior distribution. After changing values in the text boxes, press the Return key to update the graph.
Credible Interval
This version, which may be displayed with or without the text boxes to change the parameters, also displays the 95% credible interval for the estimated probability p.