How to compute a posterior probability distribution given a toin coss?
By Emma Valentine •
While debating with a friend we came up with the following question:
given a coin we have three hypotheses for the probability of head: $A=0.5$, $B=0.4$ and $C=0.6$. After a single flip it is straightforward to use Bayes' theorem to update the probabilities of these hypotheses given we start with equal probabilities for all three of them.
Now, lets say we do not want to start with a finite set of distinct hypotheses (A,B,C) but assume a distribution D of probabilities for each hypothesis in $[0,1]$. For example $D(0.5)$ would be the probability that hypothesis $P(Head)=0.5$ is correct.
Is there a way to compute a new distribution $D^H$ after observing one head? What kind of distribution would be a good choice to start with?
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