pymc.MvStudentT#
- class pymc.MvStudentT(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, **kwargs)[source]#
Multivariate Student-T log-likelihood.
\[f(\mathbf{x}| \nu,\mu,\Sigma) = \frac {\Gamma\left[(\nu+p)/2\right]} {\Gamma(\nu/2)\nu^{p/2}\pi^{p/2} \left|{\Sigma}\right|^{1/2} \left[ 1+\frac{1}{\nu} ({\mathbf x}-{\mu})^T {\Sigma}^{-1}({\mathbf x}-{\mu}) \right]^{-(\nu+p)/2}}\]Support
\(x \in \mathbb{R}^p\)
Mean
\(\mu\) if \(\nu > 1\) else undefined
Variance
- \(\frac{\nu}{\mu-2}\Sigma\)
if \(\nu>2\) else undefined
- Parameters:
- nutensor_like of
float Degrees of freedom, should be a positive scalar.
- Sigmatensor_like of
float, optional Scale matrix. Use scale in new code.
- mutensor_like of
float, optional Vector of means.
- scaletensor_like of
float, optional The scale matrix.
- tautensor_like of
float, optional The precision matrix.
- choltensor_like of
float, optional The cholesky factor of the scale matrix.
- lowerbool, default=True
Whether the cholesky fatcor is given as a lower triangular matrix.
- nutensor_like of
Methods
MvStudentT.dist(nu, *[, Sigma, mu, scale, ...])Creates a tensor variable corresponding to the cls distribution.