File:part1-fig-05-dirichlet-simplex.png

Figure file · Categorical data and the Dirichlet distribution

Draws from three symmetric Dirichlet distributions. The uniform \operatorname{Dirichlet}(1,1,1) fills the triangle; increasing the common concentration to 5 pulls probability vectors toward (1/3,1/3,1/3); reducing it to 0.1 puts most draws near an edge or corner. Symmetry fixes the same centre in all three panels, so the visible change is concentration rather than location.

Draws from three symmetric Dirichlet distributions. The uniform \operatorname{Dirichlet}(1,1,1) fills the triangle; increasing the common concentration to 5 pulls probability vectors toward (1/3,1/3,1/3); reducing it to 0.1 puts most draws near an edge or corner. Symmetry fixes the same centre in all three panels, so the visible change is concentration rather than location.

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Summary

Description. Draws from three symmetric Dirichlet distributions. The uniform \operatorname{Dirichlet}(1,1,1) fills the triangle; increasing the common concentration to 5 pulls probability vectors toward (1/3,1/3,1/3); reducing it to 0.1 puts most draws near an edge or corner. Symmetry fixes the same centre in all three panels, so the visible change is concentration rather than location.

Appears in. Categorical data and the Dirichlet distribution

Made by. A figure from the course chapter.

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