&gt; You have one variable which stands for p (distributed according to some prior, like a Beta distribution perhaps)<p>This prior sounds like the A_p distribution.<p>The point is it&#x27;s a distribution, not a number. You can&#x27;t just say &quot;I think the probability of seeing heads is <i>p</i>&quot;. But if you say &quot;I think the probability of seeing heads is distributed like this, which has a mean of <i>p</i>&quot;, then that captures everything you need to know about the coin to update your expectations when you see the results.<p>(In case it was unclear, A_p isn&#x27;t a specific shape of distribution, or class of shapes of distributions, like beta or gaussian. It&#x27;s a distribution over hypothesis-space, where the hypotheses are probabilities, and can have any valid distribution shape.)