glearn.priors.Uniform.pdf_hessian

Uniform.pdf_hessian(x)

Hessian of the probability density function of the prior distribution.

Parameters:

xfloat or array_like[float]

Input hyperparameter or an array of hyperparameters.

Returns:

hessfloat or array_like[float]

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

See also

glearn.priors.Prior.log_pdf_hessian()

glearn.priors.Uniform.pdf()

glearn.priors.Uniform.pdf_jacobian()

Notes

The second derivative of the probability density function is

\[\frac{\mathrm{d}^2p(\theta)}{\mathrm{d}\theta^2} = 0.\]

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 Hessian of the PDF
>>> t = [0, 0.5, 1]
>>> prior.pdf_hessian(t)
array([[0., 0., 0.],
       [0., 0., 0.],
       [0., 0., 0.]])