Calibration of stochastic computer simulators using likelihood emulation

We calibrate a stochastic computer simulation model of ‘moderate’ computational expense. The simulator is an imperfect representation of reality, and we recognise this discrepancy to ensure a reliable calibration. The calibration model combines a Gaussian process emulator of the likelihood surface with importance sampling. Changing the discrepancy specification changes only the importance weights, which lets us investigate sensitivity to different discrepancy specifications at little computational cost. We present a case study of a natural history model that has been used to characterise UK bowel cancer incidence. Data sets and computer code are provided as supplementary material

Biodistribution of 64 Cu in Inflamed Rats Following Administration of Two Anti-Inflammatory Copper Complexes

64Cu was administered in two anti-inflammatory formulations to normal rats and to rats with 2 forms of local inflammation, namely (a) an acute paw oedema (elicited with carrageenan) or (b) a chronic granulomatous response to an implanted irritant (Mycobacterium tuberculosis in a polyurethane sponge). The copper formulations used were (i) a slow release one consisting of Cu(II) salicylate applied dermally with ethanol/DMSO and (ii) short acting hydrophilic complex (Cu(I)Cu(II)-penicillamine)5- given subcutaneously. Three types of changes in copper biodistribution with these forms of inflammation were discerned based on determination of 64Cu and copper content in the following organs: inflammatory locus (foot or sponge implant), kidney, liver, spleen, adrenals, brain, blood, thymus, heart, and skin (site of application). The most evident changes were in the kidneys, liver, spleen, adrenals, thymus and serum from animals with chronic granulomatous inflammation. In contrast, a short term acute inflammatory stress (carrageenan paw oedema) had little effect. While copper D-penicillamine (applied subcutaneously) appeared to move as a bolus through the animals, the results with the percutaneous copper salicylate formulation are consistent with it providing a slow release source of copper(II). Exogenous 64Cu from both formulations was sequestered at inflammatory sites (relative to serum). This may partly explain how applied copper complexes can be anti-inflammatory

Known Boundary Emulation of Complex Computer Models

Computer models are now widely used across a range of scientific disciplines to describe various complex physical systems, however to perform full uncertainty quantification we often need to employ emulators. An emulator is a fast statistical construct that mimics the complex computer model, and greatly aids the vastly more computationally intensive uncertainty quantification calculations that a serious scientific analysis often requires. In some cases, the complex model can be solved far more efficiently for certain parameter settings, leading to boundaries or hyperplanes in the input parameter space where the model is essentially known. We show that for a large class of Gaussian process style emulators, multiple boundaries can be formally incorporated into the emulation process, by Bayesian updating of the emulators with respect to the boundaries, for trivial computational cost. The resulting updated emulator equations are given analytically. This leads to emulators that possess increased accuracy across large portions of the input parameter space. We also describe how a user can incorporate such boundaries within standard black box GP emulation packages that are currently available, without altering the core code. Appropriate designs of model runs in the presence of known boundaries are then analysed, with two kinds of general purpose designs proposed. We then apply the improved emulation and design methodology to an important systems biology model of hormonal crosstalk in Arabidopsis Thaliana

Exchangeable Computer Models

Analysts often use deterministic computer models to predict the behavior of com- plex physical systems when observational data are limited. However, inferences based partially or entirely on simulated data require adequate assessments of model uncer- tainty that can be hard to quantify. The deterministic nature of computer models limits the information we can extract from simulations to separate model signal from model error. In this paper we present a new approach to assess the uncertainty of computer models to which we refer as multi-deterministic. Evaluations from a multi- deterministic computer model can be considered to be a collection of deterministic simulators which share the same input and output space, do not present obvious the- oretical or computational advantages, and generate disparate predictions. To quantify the uncertainty of predictions from multi-deterministic models we use the construct of a latent model about which we learn from observed evaluations. We assume that outcomes from multi-deterministic models are sequences of second-order exchangeable functions (SOEF) and use Bayes linear methods to assess the latent model a posteriori. We demonstrate our methods using multi-deterministic results from a galaxy forma- tion model called Galform for which the system condition is the specification of dark matter over time and space