Direct Elicitation in ND

import preliz as pz

pz.style.use("preliz-doc")

Dirichlet mode

dirichlet_mode returns a Dirichlet distribution where the marginals have the specified mode and mass and their masses lie within the range mode ± bound.

The mode of a Dirichlet is defined as:

\[x_i = \frac{\alpha_i - 1}{\alpha_0 - K}, \qquad \alpha_i > 1\]

where \(K\) is the number of categories (the length of the vector \(\alpha\)), and \(\alpha_0 = \sum_{i=1}^K\alpha_i\)

ax, dist = pz.dirichlet_mode([1/3, 1/3, 1/3], bound=0.2)

When the dimension of the Dirichlet is 3 we can also plot the joint pdf

dist.plot_pdf(marginals=False);

ax, dist = pz.dirichlet_mode([0.2, 0.3, 0.5], bound=0.1)

dist.plot_pdf(marginals=False);