MIT15_097S12_lec15

We choose a prior for that is a pareto distribution

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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.

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