Emulating computer models with high-dimensional count output.

Area of Science:

• Computational epidemiology
• Statistical modeling
• Uncertainty quantification

Background:

• Computer models are vital for real-world studies but often complex, expensive, and require calibration.
• Emulators serve as cost-effective surrogates for these simulators, trained on limited data to predict outcomes with uncertainty.
• Epidemiological models frequently produce high-dimensional, spatially and temporally indexed, stochastic count data.

Purpose of the Study:

• To develop and evaluate a Poisson lognormal PCA (PLNPCA) emulator for high-dimensional count data from complex computer models.
• To apply the PLNPCA emulator to a COVID-19 epidemiological model for England and Wales.
• To compare the PLNPCA emulator's performance against emulators trained on aggregated model outputs.

Main Methods:

• Utilized a Poisson lognormal PCA (PLNPCA) approach for emulation.
• Trained the emulator on a subset of simulations from a complex computer model.
• Applied the emulator to spatially and temporally indexed count data from a COVID-19 model.

Main Results:

• The PLNPCA emulator demonstrated comparable performance to emulators trained on aggregated data.
• The emulator successfully captured correlations within the high-dimensional output.
• It provided representative high-dimensional samples of count data, mirroring the true model output.

Conclusions:

• The PLNPCA emulator is a viable and effective tool for emulating high-dimensional count outputs from complex computer models.
• This method preserves desirable properties, including the prediction of full output and capturing output correlations.
• The approach is particularly relevant for epidemiological applications requiring accurate uncertainty quantification.