Mixture

Mixture(w, comp_dists, *args, **kwargs)	Mixture log-likelihood
NormalMixture(w, mu, *args, **kwargs)	Normal mixture log-likelihood

class pymc3.distributions.mixture.Mixture(w, comp_dists, *args, **kwargs)

Mixture log-likelihood

Often used to model subpopulation heterogeneity

\[f(x \mid w, \theta) = \sum_{i = 1}^n w_i f_i(x \mid \theta_i)\]

Support	\(\cap_{i = 1}^n \textrm{support}(f_i)\)
Mean	\(\sum_{i = 1}^n w_i \mu_i\)

Parameters:

• w (array of floats) – w >= 0 and w <= 1 the mixture weights
• comp_dists (multidimensional PyMC3 distribution or iterable of one-dimensional PyMC3 distributions) – the component distributions \(f_1, \ldots, f_n\)

class pymc3.distributions.mixture.NormalMixture(w, mu, *args, **kwargs)

Normal mixture log-likelihood

\[f(x \mid w, \mu, \sigma^2) = \sum_{i = 1}^n w_i N(x \mid \mu_i, \sigma^2_i)\]

Support	\(x \in \mathbb{R}\)
Mean	\(\sum_{i = 1}^n w_i \mu_i\)
Variance	\(\sum_{i = 1}^n w_i^2 \sigma^2_i\)

Parameters:

• w (array of floats) – w >= 0 and w <= 1 the mixture weights
• mu (array of floats) – the component means
• sd (array of floats) – the component standard deviations
• tau (array of floats) – the component precisions

pymc3.distributions.mixture.all_discrete(comp_dists)

Determine if all distributions in comp_dists are discrete