The Beta Coin Experiment

]> The Beta Coin Experiment

Description

The random experiment is to toss a coin $n$ times, where the probability of heads is $p$ . The probability of heads is modeled with a prior beta distribution, having left parameter $a$ and right parameter $b$ . The prior probability density function and the true probability of heads are shown in blue in the graph on the right. On each update, the number of heads $X$ is recorded in the data table. On each update, the posterior beta probability density function, which has left parameter $a X$ and right parameter $b n X$ , is shown in red in graph on the right. Also, the Bayesian estimate of $p$ , $U a X a b n$ is recorded in the data table on each update. Finally, the second table gives the true bias and mean square error of $U$ , and on each update gives the empirical bias and mean square error, based on the all of the runs of the experiment. The parameters $n$ , $p$ , $a$ , and $b$ can be varied with scroll bars.