Marginal.marginal_likelihood(name, X, y, sigma=None, noise=None, jitter=1e-06, is_observed=True, **kwargs)[source]#

Returns the marginal likelihood distribution, given the input locations X and the data y.

This is the integral over the product of the GP prior and a normal likelihood.

\[y \mid X,\theta \sim \int p(y \mid f,\, X,\, \theta) \, p(f \mid X,\, \theta) \, df\]

Name of the random variable


Function input values. If one-dimensional, must be a column vector with shape (n, 1).


Data that is the sum of the function with the GP prior and Gaussian noise. Must have shape (n, ).

sigmafloat, Variable, or Covariance, default WhiteNoise

Standard deviation of the Gaussian noise. Can also be a Covariance for non-white noise.

noisefloat, Variable, or Covariance, optional

Deprecated. Previous parameterization of sigma.

jitterfloat, default 1e-6

A small correction added to the diagonal of positive semi-definite covariance matrices to ensure numerical stability.

is_observedbool, default True

Deprecated. Whether to set y as an observed variable in the model.


Extra keyword arguments that are passed to MvNormal distribution constructor.