1
$\begingroup$

For a Dirichlet process, there are two parameter $\alpha$ and $H$, and the Dirichlet process $X$ is defined as $$(X(B_1),\cdots,X(B_n))\sim Dir(\alpha H(B_1),\cdots,\alpha H(B_n))$$ where$\{B_i\}_{i=1}^n$is a partition of the measurable space.

While the Dirichlet distribution is like that $$f(x_1,x_2, \cdots ,x_{K - 1};\alpha _1,\alpha _2, \cdots ,\alpha _{K - 1},\alpha _K) = \frac{1}{B(\vec \alpha )}\prod\limits_{i = 1}^K x_i^{\alpha_i - 1} $$

My question is:

If I want to view the Dirichlet distribution as a special case of the Dirichlet process, then how should I set the parameters $\alpha$ and $H$ in the definition of Dirichlet process?

$\endgroup$

1 Answer 1

0
$\begingroup$

Here $\alpha$ is a number, and $H$ is a measure.

I believe that you should take a finite space, say, $\{1,...,K\}$. Then for any partition of $\{1,...,K\}$, your first formula will hold. $H$ measures the asymmetry of your Dirichlet process, as the parameters $\alpha_1,...,\alpha_K$ do in the second formula.

$\endgroup$
1
  • $\begingroup$ if I partition {1,...,K} into {1},{2}...,{K}, should $\alpha$ equals to $\sum _{i=1}^K \alpha_i$ and $H(i)$ equals to $\alpha_i/\alpha$ ? $\endgroup$ Sep 18, 2014 at 0:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.