Global sensitivity analysis for statistical model parameters

TL;DR

This paper introduces a novel framework for applying global sensitivity analysis to statistical models, overcoming challenges like parameter correlation and stochasticity, and demonstrates its effectiveness on complex models.

Contribution

The paper develops a new GSA framework tailored for statistical models, enabling parameter influence analysis and model reduction despite inherent difficulties.

Findings

Identified non-influential parameters in a 95-parameter Gaussian process model.

Constructed a reduced model with 79 parameters maintaining predictive accuracy.

Demonstrated the framework's effectiveness on synthetic and real statistical models.

Abstract

Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical models. Such analyses may enable reduced or parsimonious modeling and greater predictive capability. However, difficulties such as parameter correlation, model stochasticity, multivariate model output, and unknown parameter distributions prohibit a direct application of GSA tools to statistical models. By leveraging a loss function associated with the statistical model, we introduce a novel framework to address these difficulties and enable efficient GSA for statistical model parameters. Theoretical and computational properties are considered and illustrated on a synthetic example. The framework is applied to a Gaussian process model from the literature, which depends on 95 parameters. Non-influential parameters are discovered through GSA and a reduced model with equal or stronger predictive capability is constructed by using only 79 parameters.