An informative prior

We might also have entered the experiment with a belief (for whatever reason) that participants will perform around chance.

Before uncollapsing this box, think about what a prior that reflects this belief might look like.

Now, we observe the first trial, a success.

Think again about how you expect the posterior to look before uncollapsing this next box.

Did the posterior (dark blue) move as far from the prior (light blue) as you expected?

Now let’s watch data from the first ten trials come in.

How does this differ from the situation before, where we began with a uniform prior?