class*, mean_func=< object>, cov_func=< object>)[source]#

Marginal Gaussian process.

The gp.Marginal class is an implementation of the sum of a GP prior and additive noise. It has marginal_likelihood, conditional and predict methods. This GP implementation can be used to implement regression on data that is normally distributed. For more information on the prior and conditional methods, see their docstrings.

cov_func: None, 2D array, or instance of Covariance

The covariance function. Defaults to zero.

mean_func: None, instance of Mean

The mean function. Defaults to zero.


# A one dimensional column vector of inputs.
X = np.linspace(0, 1, 10)[:, None]

with pm.Model() as model:
    # Specify the covariance function.
    cov_func =, ls=0.1)

    # Specify the GP.  The default mean function is `Zero`.
    gp =

    # Place a GP prior over the function f.
    sigma = pm.HalfCauchy("sigma", beta=3)
    y_ = gp.marginal_likelihood("y", X=X, y=y, noise=sigma)


# After fitting or sampling, specify the distribution
# at new points with .conditional
Xnew = np.linspace(-1, 2, 50)[:, None]

with model:
    fcond = gp.conditional("fcond", Xnew=Xnew)


Marginal.__init__(*[, mean_func, cov_func])

Marginal.conditional(name, Xnew[, ...])

Returns the conditional distribution evaluated over new input locations Xnew.

Marginal.marginal_likelihood(name, X, y, noise)

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

Marginal.predict(Xnew[, point, diag, ...])

Return the mean vector and covariance matrix of the conditional distribution as numpy arrays, given a point, such as the MAP estimate or a sample from a trace.

Marginal.prior(name, X, *args, **kwargs)