Calibration of Complex Computer Simulators using Likelihood Emulation

TL;DR

This paper presents a novel calibration method for complex, stochastic computer simulators used in health modeling, combining likelihood emulation with importance sampling to efficiently estimate unknown inputs and account for model discrepancy.

Contribution

It introduces a likelihood emulation approach integrated with importance sampling for calibrating computationally expensive, stochastic simulators, enabling flexible discrepancy assessment.

Findings

Efficient calibration of a bowel cancer model with 25 unknown inputs.

Ability to evaluate different discrepancy assumptions with minimal additional computation.

Successful application to a health-related natural history simulator.

Abstract

We calibrate a Natural History Model, which is a class of computer simulator used in the health industry, and here has been used to characterise bowel cancer incidence for the UK. The simulator tracks the development of bowel cancer in a sample of people, and its output mostly stratifies bowel cancer occurrence by patient age and bowel cancer type. Its output relies on 25 unknown inputs, which we are required to calibrate. In order to do this we must address that not only is the output count data, but it is also stochastic, due to the simulation procedure. We cannot feasibly achieve calibration of the simulator using Monte Carlo methods alone, as it is of `moderate' computational expense. To achieve a reliable calibration, we must also specify its discrepancy: how, when calibrated, it differs from reality. We propose a method for calibration that combines a statistical emulator for the likelihood function with importance sampling. The emulator provides an interim sample of inputs at which the simulator is run, from which the likelihood is calculated. Importance sampling is then used to re-weight the inputs and provide a final sample of calibrated inputs. Re-calculating the importance weights incurs little computational cost, and so we can easily investigate how different discrepancy specifications affect calibration.