glearn.priors.StudentT.log_pdf

StudentT.log_pdf(hyperparam)

Logarithm of the probability density function of the prior distribution.

Parameters:

xfloat or array_like[float]

Input hyperparameter or an array of hyperparameters.

Returns:

pdffloat or array_like[float]

The logarithm of probability density function of the input hyperparameter(s).

See also

glearn.priors.Prior.log_pdf_jacobian()

glearn.priors.Prior.log_pdf_hessian()

Notes

This function returns \(\log p(\theta)\).

Multiple hyperparameters:

When an array of hyperparameters \(\boldsymbol{\theta} = (\theta_, \dots, \theta_n)\) are given, it is assumed that prior for each hyperparameter is independent of others. The output of this function is then the sum of all log-probabilities

\[\sum_{i=1}^n \log p(\theta_i).\]

Using Log Scale:

If the attribute use_log_scale is True, it is assumed that the input argument \(\theta\) is the log of the hyperparameter, so to convert back to the original hyperparameter, the transformation below is performed

\[\theta \gets 10^{\theta}.\]

Examples

Create the inverse Gamma distribution with the shape parameter \(\alpha=4\) and rate parameter \(\beta=2\).

>>> from glearn import priors
>>> prior = priors.InverseGamma(4, 2)

>>> # Evaluate the log-PDF
>>> prior.log_pdf(t)
-17.15935597045384