Efficient History Matching of a High Dimensional Individual-Based HIV Transmission Model

Abstract

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. History matching is a model (pre-)calibration method that has been applied to computer models from a wide range of scientific disciplines. In this work we apply history matching to an individualbased epidemiological model of HIV that has 96 input and 50 output parameters, a model of much larger scale than others that have been calibrated before using this or similar methods. Apart from demonstrating that history matching can analyze models of this complexity, a central contribution of this work is that the history match is carried out using linear regression, a statistical tool that is elementary and easier to implement than the Gaussian process-based emulators that have previously been used. Furthermore, we address a practical difficulty with history matching, namely, the sampling of tiny, nonimplausible spaces, by introducing a sampling algorithm adjusted to the specific needs of this method. The effectiveness and simplicity of the history matching method presented here shows that it is a useful tool for the calibration of computationally expensive, high dimensional, individual-based models.

Known Boundary Emulation of Complex Computer Models

“…We wish to update the emulator, and hence our beliefs about f (x), at the input point x ∈ X in light of a single known boundary K, where K is a d−1 dimensional hyperplane perpendicular to the x 1 direction (but we note that our results naturally extend to lower dimensional boundaries). To capture the simulator behaviour along K, we evaluate f (x) at a large number, m, of points on K which we denote y (1) , . .…”

“…Emulators have now been successfully employed across several scientific disciplines, including cosmology [41,42,8,38,20,43,32], climate modelling [46,35,25,22] (the later employing emulation to in-crease the efficiency of an Approximate Bayesian Computation algorithm), epidemiology [2,3,1,31,30], systems biology [45,24], oil reservoir modelling [11,12], environmental science [16], traffic modelling [7], vulcanology [5] and even to Bayesian analysis itself [44]. The development of improved emulation strategies therefore has the potential to benefit multiple scientific areas, allowing more accurate analyses with lower computational cost.…”

Model dispersion with PRISM; an alternative to MCMC for rapid analysis of models

“…To solve this problem, we use projections; a method described by Vernon et al (2010); Vernon et al (2018) for visualizing the emulator's performances. Projections are three dimensional figures made for active parameters that allow for the behavior of the model to be studied, and have been used extensively several times in the past Andrianakis et al 2015;Andrianakis et al 2016Andrianakis et al , 2017Vernon et al 2018). In the following, we describe how these projections are made and what information can be derived from them.…”

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

“…It is worth noting that reasonably accurate emulators can often be constructed just using such regression models. This can be a sensible first step (see Andrianakis et al 2016b), before one attempts the construction of a full emulator of the form given in equation (15).…”