pymc.Wishart#
- class pymc.Wishart(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)[source]#
Wishart log-likelihood.
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.
- nutensor_like of
Notes
This distribution is unusable in a PyMC model. You should instead use LKJCholeskyCov or LKJCorr.
Methods
Wishart.dist(nu, V, *args, **kwargs)Creates a tensor variable corresponding to the cls distribution.