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The pymc3 documentation says that the support of the mixture model $f(x|w, \theta) = \Sigma_{i=1}^{n}w_if_i(x|\theta_i)$ is $\cap_{i=1}support(f_i)$.

I was thinking that it should be the union of all the mixture models' functions support, i.e. $\cup_{i=1}support(f_i)$, rather than the intersection? Am I right or have I misunderstood something?

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You are correct, it's $\bigcup_i\,\mathrm{support}(f_i)$. Imagine a mixture of $\mathcal{U}(0, 1)$ and $\mathcal{U}(0.5, 1.5)$ with mixing proportions $\pi, 1-\pi$. From the definition, with probability $\pi$ you will see $0 < x < 0.5$, so obviously the support is the union of supports.

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