For a particular Bayesian study I am going to apply Dirichlet distribution as my proposal random number generator. I am going to update the distribution parameter every trial based on a given calculated mean of distribution. So, I would like to calculate the parameter, alpha for a multivariate Dirichlet distribution given that I have the mean of marginal distributions. consider a three dimensional Dirichlet distribution with the following means: $mu = (mu_1, mu_2, mu_3)$ given that: $$\mu_i= \frac{a_i}{\sum{a_j}}$$

for a three dimensional distribution, I will have: $$\alpha_1(1-\mu_1)-\mu_1\alpha_2-\mu_1\alpha_3=0$$ $$\alpha_2(1-\mu_2)-\mu_2\alpha_1-\mu_2\alpha_3=0$$ $$\alpha_3(1-\mu_3)-\mu_3\alpha_1-\mu_3\alpha_2=0$$

$$\begin{pmatrix}\alpha_1 \\\ \alpha_2 \\\ \alpha_3\end{pmatrix} . \begin{pmatrix}\ 1-\mu_1 & -\mu_1 & -\mu_1 \\\ 1-\mu_2 & -\mu_2 & -\mu_2 \\\ 1-\mu_3 & -\mu_3 & -\mu_3 \end{pmatrix} = 0$$

Obviously, the coefficients matrix, here the matrix containing $\mu_i$, is singular. Any help to address this problem is highly appreciated.

Thanks Rezgar

  • 1
    $\begingroup$ you can achieve the mean-matching you're looking for by setting alpha proportional to mu. You are left with deciding the constant of proportionality, which plays a role similar to the variance parameter of a Gaussian proposal $\endgroup$ Commented Jul 13, 2022 at 16:40

1 Answer 1


As noticed by @JohnMadden in the comment, $\mu_i$ means would be proportional to $\alpha_i$ parameters, so you need to set the parameters appropriately. The parameters control also how anti-concentrated (lower that one), scattered (low) or concentrated (high) the values are, so your choice of scaling factor should reflect how you want them to behave.


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.