Re: bayesian update hyperparameters

erehwon wrote:

If I'm determining a posterior (multinomial) distribution based on
observed data, and if the chosen prior distribution is just the uniform
distribution, then there aren't any hyperparameters right?

Prior for which parameters? Obviously not the probabilities (unless m=2), as they are constrained to add up to 1.

(I have seen that when the prior distribution is Dirichlet, then there is a
single hyperparameter, but I believe this is different scenario...but I'm
not entirely sure.)

No, the Dirichlet has as many parameters as there are classes.

The Dirichlet is the conjugate prior for the multinomial, and setting alpha=1 for all classes is equivalent to using a uniform distribution.


Bob O'Hara
Department of Mathematics and Statistics
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FIN-00014 University of Helsinki

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