pymc.Wishart

class pymc.Wishart(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)

Wishart distribution.

The Wishart distribution is the probability distribution of the maximum-likelihood estimator (MLE) of the precision matrix of a multivariate normal distribution. If V=1, the distribution is identical to the chi-square distribution with nu degrees of freedom.

\[f(X \mid nu, T) = \frac{{\mid T \mid}^{nu/2}{\mid X \mid}^{(nu-k-1)/2}}{2^{nu k/2} \Gamma_p(nu/2)} \exp\left\{ -\frac{1}{2} Tr(TX) \right\}\]

where \(k\) is the rank of \(X\).

Support	\(X(p x p)\) positive definite matrix
Mean	\(nu V\)
Variance	\(nu (v_{ij}^2 + v_{ii} v_{jj})\)

Parameters:

nutensor_like of int

Degrees of freedom, > 0.

Vtensor_like of float

p x p positive definite matrix.

Notes

The Wishart distribution is generally unusable as a prior distribution for MCMC sampling. The probability of sampling a symmetric positive definite matrix is effectively zero, since MCMC proposals in unconstrained space almost never land exactly on the SPD manifold.

For modeling covariance matrices, you should instead use LKJCholeskyCov or LKJCorr.

However, the Wishart distribution may be used as a likelihood with observed in some cases, where the distribution is evaluated at fixed observed values rather than sampled during MCMC.

Methods

Wishart.dist(nu, V, *args, **kwargs)

Create a tensor variable corresponding to the cls distribution.