Inference

This module contains classes and functions for statistical inference from data.

The module currently contains the following classes:

• InferenceModel: Define a probabilistic model for inference.

• InformationModelSelection: Perform model selection using information theoretic criteria.

• BayesModelSelection: Estimate model posterior probabilities.

• BayesParameterEstimation: Perform Bayesian parameter estimation (estimate posterior density) via MCMC or ImportanceSampling.

• MLE: Compute maximum likelihood parameter estimate.

The goal in inference can be twofold: 1) given a model, parameterized by parameter vector \(\theta\), and some data \(\mathcal{D}\), learn the value of the parameter vector that best explains the data; 2) given a set of candidate models \(\lbrace m_{i} \rbrace_{i=1:M}\) and some data \(\mathcal{D}\), learn which model best explains the data. UQpy currently supports the following inference algorithms for parameter estimation (see e.g. [10] for theory on parameter estimation in frequentist vs. Bayesian frameworks):

• Maximum Likelihood estimation,

• Bayesian approach: estimation of posterior pdf via sampling methods (MCMC/ImportanceSampling).

and the following algorithms for model selection:

• Model selection using information theoretic criteria,

• Bayesian model class selection, i.e., estimation of model posterior probabilities.

The capabilities of UQpy and associated classes are summarized in the following figure.