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 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: string

Name of the random variable

X: array-like

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

y: array-like

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

sigma: scalar, Variable, or Covariance

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

noise: scalar, Variable, or Covariance

Previous parameterization of sigma.

jitter: scalar

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


Extra keyword arguments that are passed to MvNormal distribution constructor.