  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.

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