class SimPEG.utils.GaussianMixtureWithNonlinearRelationshipsWithPrior(gmmref, kappa=0.0, nu=0.0, zeta=0.0, prior_type='semi', cluster_mapping=None, init_params='kmeans', max_iter=100, means_init=None, n_init=10, precisions_init=None, random_state=None, reg_covar=1e-06, tol=0.001, verbose=0, verbose_interval=10, warm_start=False, weights_init=None, update_covariances=True, fixed_membership=None)[source]#

Bases: SimPEG.utils.pgi_utils.GaussianMixtureWithPrior

Gaussian mixture class for non-linear relationships with priors.

This class built upon the GaussianMixtureWithPrior, which itself built upon from the WeightedGaussianMixture, built up from the mixture.gaussian_mixture.GaussianMixture class from Scikit-Learn.

In addition to weights samples/observations by the cells volume of the mesh (from WeightedGaussianMixture), and nonlinear relationships for each cluster (from GaussianMixtureWithNonlinearRelationships), this class uses a posterior approach to fit the GMM parameters (from GaussianMixtureWithPrior). It takes prior parameters, passed through WeightedGaussianMixture gmmref. The prior distribution for each parameters (proportions, means, covariances) is defined through a conjugate or semi-conjugate approach (prior_type), to the choice of the user. See Astic & Oldenburg 2019: A framework for petrophysically and geologically guided geophysical inversion ( for more information.

Disclaimer: this class built upon the GaussianMixture class from Scikit-Learn. New functionalitie are added, as well as modifications to existing functions, to serve the purposes pursued within SimPEG. This use is allowed by the Scikit-Learn licensing (BSD-3-Clause License) and we are grateful for their contributions to the open-source community.

Addtional parameters to provide, compared to GaussianMixtureWithPrior:

cluster_mapping(n_components) list

List of mapping describing a nonlinear relationships between physical properties; one per cluster/unit.