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Unformatted text preview: ew of these conjugate prior relationships to try to gain
additional insight. For Bernoulli-Beta, we saw that the prior hyperparame
ters can be interpreted as starting the tossing with a certain number of Heads
and Tails on the record. The posterior hyperparameters then simply add the
observed number of heads (mH ) to the prior hyperparameter for number of
Heads (α), and the observed number of tails (m − mH ) to the prior hyperpa
rameter for number of tails (β ).
For Binomial-Beta, we now have m Binomial experiments, each of which
consists of a certain number of coin tosses (mi ) and a certain number of
Heads (yi ). As before, the ﬁrst prior hyperparameter corresponds to number
of “hallucinated” Heads, and in the posterior we combine the prior hyperparameter α with the total number of observed Heads across all Binomial
trials. Similarly, for the second posterior hyperparameter, we compute the
total number of Tails observed across all Binomial trials and combine it with
the corresponding prior hyperpar...
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This note was uploaded on 03/24/2014 for the course MIT 15.097 taught by Professor Cynthiarudin during the Spring '12 term at MIT.
- Spring '12