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
nu: float

Degrees of freedom, should be a positive scalar.

Sigma: matrix

Covariance matrix. Use cov in new code.

mu: array

Vector of means.

cov: matrix

The covariance matrix.

tau: matrix

The precision matrix.

chol: matrix

The cholesky factor of the covariance matrix.

lower: bool, default=True

Whether the cholesky fatcor is given as a lower triangular matrix.

Methods

MvStudentT.__init__(*args, **kwargs)

MvStudentT.dist(nu[, Sigma, mu, cov, tau, ...])

Creates a tensor variable corresponding to the cls distribution.

MvStudentT.logp(nu, mu, cov)

Calculate log-probability of Multivariate Student's T distribution at specified value.

MvStudentT.moment(size, nu, mu, cov)

Attributes

rv_class

rv_op