glearn.priors.Uniform.pdf_jacobian

Uniform.pdf_jacobian(x)

Jacobian of the probability density function of the prior distribution.

Parameters:

xfloat or array_like[float]

Input hyperparameter or an array of hyperparameters.

Returns:

jacfloat or array_like[float]

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

See also

glearn.priors.Prior.log_pdf_jacobian()

glearn.priors.Uniform.pdf()

glearn.priors.Uniform.pdf_hessian()

Notes

The first derivative of the probability density function is

\[\frac{\mathrm{d}p(\theta)}{\mathrm{d}\theta} = 0.\]

When an array of hyperparameters are given, it is assumed that prior for each hyperparameter is independent of others.

Examples

Create uniform prior in the interval \([0.2, 0.9]\):

>>> from glearn import priors
>>> prior = priors.Uniform(0.2, 0.9)

>>> # Evaluate the Jacobian of the PDF
>>> t = [0, 0.5, 1]
>>> prior.pdf_jacobian(t)
array([0., 0., 0.])