# Learning probabilities: Beta Distribution

This applet shows how the parameter in a beta distribution changes as data is received. Each piece of data is either "positive" or "negative".

The x-axis shows the probability of *positive*, that is each *x*
value represents *P*(*positive*)=*x*. The leftmost point is
*P*(*positive*)=0, the rightmost point is
*P*(*positive*)=1. For any value x in the range [0,1] the y-axis
shows *P*(*P*(*positive*)=*x*|*observations*) which
is proportional to
*P*(*observations*|*P*(*positive*)=*x*), assuming a
uniform prior. This can either be intepreted as a probability density
function, where the area under the curve has value 1. In this case the value
of the top line after a reset is 1.0. Alternatively, it can be seen as a
probability distribution when there are (about) 500 points on the x-axis, and
the y-value is the probability of that point. In this case the value of the
top line after a reset has value 1/500.

When there are only two states (here "positive" and "negative") it is
called the **Beta distribution**. When there are more states it is called
the **Dirichlet distribution**.

Remember copies the top graph onto the "Remembered" graph at the bottom. This is so you can compare a pair of beta distributions.

You can get the source code.

Copyright © David Poole, 2008. This web page and applet are released under a Creative Commons Attribution-Noncommercial-Share Alike license.