glearn.priors.Prior#

class glearn.priors.Prior(half=False)#

Base class for prior distributions.

Warning

This class is a base class and does not implement a kernel function. Use the derivative of this class instead.

See also

glearn.priors.Uniform
glearn.priors.Normal
glearn.priors.StudentT
glearn.priors.Cauchy
glearn.priors.Gamma
glearn.priors.InverseGamma
glearn.priors.Erlang
glearn.priors.BetaPrime

Examples

Create Prior Objects:

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

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

>>> # Evaluate PDF function at multiple locations
>>> t = [0, 0.5, 1]
>>> prior.pdf(t)
array([       nan, 1.56293452, 0.36089409])

>>> # Evaluate the Jacobian of the PDF
>>> prior.pdf_jacobian(t)
array([        nan, -3.12586904, -1.08268227])

>>> # Evaluate the Hessian of the PDF
>>> prior.pdf_hessian(t)
array([[         nan,   0.        ,   0.        ],
       [  0.        , -12.50347615,   0.        ],
       [  0.        ,   0.        ,   3.60894089]])

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

>>> # Evaluate the Jacobian of the log-PDF
>>> prior.log_pdf_jacobian(t)
array([ -6.90775528, -10.05664278, -11.05240845])

>>> # Evaluate the Hessian of the log-PDF
>>> prior.log_pdf_hessian(t)
array([[-10.60379622,   0.        ,   0.        ],
       [  0.        ,  -3.35321479,   0.        ],
       [  0.        ,   0.        ,  -1.06037962]])

>>> # Plot the distribution and its first and second derivative
>>> prior.plot()
../_images/prior_inverse_gamma.png

Where to Use the Prior object:

Define a covariance model (see glearn.Covariance) where its scale parameter is a prior function.

>>> # Generate a set of sample points
>>> from glearn.sample_data import generate_points
>>> points = generate_points(num_points=50)

>>> # Create covariance object of the points with the above kernel
>>> from glearn import covariance
>>> cov = glearn.Covariance(points, kernel=kernel, scale=prior)
Attributes:
use_log_scalebool, default=True

If True, the input argument to the functions is assumed to be the logarithm of the hyperparameter \(\theta\). If False, the input argument to the functions is assumed to be the hyperparameter \(\theta\).

halfbool, default=False

If True, the probability distribution is assumed to be the half-distribution.

Methods

log_pdf(hyperparam)

Logarithm of the probability density function of the prior distribution.

log_pdf_jacobian(hyperparam)

Jacobian of the logarithm of the probability density function of the prior distribution.

log_pdf_hessian(hyperparam)

Hessian of the logarithm of the probability density function of the prior distribution.

plot([interval, log_scale, ...])

Plot the kernel function and its first and second derivative.