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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 θ, and some data 𝒟, learn the value of the parameter vector that best explains the data; 2) given a set of candidate models {mi}i = 1 : M and some data 𝒟, learn which model best explains the data. :pyUQpy currently supports the following inference algorithms for parameter estimation (see e.g. MCMC2 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 :pyUQpy and associated classes are summarized in the following figure.

image

Inference Models <inference_models> Maximum Likelihood Estimation <mle> Bayes Parameter Estimation <bayes_parameter_estimation> Information Theoretic Model Selection <info_model_selection> Bayes Model Selection <bayes_model_selection>