arXiv subjects

Ian Vernon

Publications and source records attributed to Ian Vernon.

16 recordsLinked to original sources

arXiv2024

Investigating Complex HPV Dynamics Using Emulation and History Matching

The study of transmission and progression of human papillomavirus (HPV) is crucial for understanding the incidence of cervical cancers, and has been identified as a priority worldwide. The complexity of the disease necessitates a detailed model of HPV transmission and its progression to cancer; to infer properties of the above we require a careful process that can match to imperfect or incomplete observational data. In this paper, we describe the HPVsim simulator to satisfy the former requirement; to satisfy the latter we couple this stochastic simulator to a process of emulation and history matching using the R package hmer. With these tools, we are able to obtain a comprehensive collection of parameter combinations that could give rise to observed cancer data, and explore the implications of the variability of these parameter sets as it relates to future health interventions.

stat.AP↗

arXiv2024

Bayesian Emulation of Grey-Box Multi-Model Ensembles Exploiting Known Interior Structure

Computer models are widely used to study complex real world physical systems. However, there are major limitations to their direct use including: their complex structure; large numbers of inputs and outputs; and long evaluation times. Bayesian emulators are an effective means of addressing these challenges providing fast and efficient statistical approximation for computer model outputs. It is commonly assumed that computer models behave like a ``black-box'' function with no knowledge of the output prior to its evaluation. This ensures that emulators are generalisable but potentially limits their accuracy compared with exploiting such knowledge of constrained or structured output behaviour. We assume a ``grey-box'' computer model and develop a methodological toolkit for its analysis. This includes: multi-model ensemble subsampling to identifying a representative model subset to reduce computational expense; constructing a targeted Bayesian design for optimisation or decision support; a ``divide-and-conquer'' approach to emulating sums of outputs; structured emulators exploiting known constrained and structured behaviour of constituent outputs through splitting the parameter space and imposing truncations; emulation of sums of time series outputs; and emulation of multi-model ensemble outputs. Combining these methods establishes a hierarchical emulation framework which achieves greater physical interpretability and more accurate emulator predictions. This research is motivated by and applied to the commercially important TNO OLYMPUS Well Control Optimisation Challenge from the petroleum industry which we re-express as a decision support under uncertainty problem. We thus encourage users to examine their ``black-box'' simulators to achieve superior emulator accuracy.

stat.ME↗

arXiv2023

FLAMINGO: Calibrating large cosmological hydrodynamical simulations with machine learning

To fully take advantage of the data provided by large-scale structure surveys, we need to quantify the potential impact of baryonic effects, such as feedback from active galactic nuclei (AGN) and star formation, on cosmological observables. In simulations, feedback processes originate on scales that remain unresolved. Therefore, they need to be sourced via subgrid models that contain free parameters. We use machine learning to calibrate the AGN and stellar feedback models for the FLAMINGO cosmological hydrodynamical simulations. Using Gaussian process emulators trained on Latin hypercubes of 32 smaller-volume simulations, we model how the galaxy stellar mass function and cluster gas fractions change as a function of the subgrid parameters. The emulators are then fit to observational data, allowing for the inclusion of potential observational biases. We apply our method to the three different FLAMINGO resolutions, spanning a factor of 64 in particle mass, recovering the observed relations within the respective resolved mass ranges. We also use the emulators, which link changes in subgrid parameters to changes in observables, to find models that skirt or exceed the observationally allowed range for cluster gas fractions and the stellar mass function. Our method enables us to define model variations in terms of the data that they are calibrated to rather than the values of specific subgrid parameters. This approach is useful, because subgrid parameters are typically not directly linked to particular observables, and predictions for a specific observable are influenced by multiple subgrid parameters.

astro-ph.CO↗

arXiv2022

Bayesian Emulation for Computer Models with Multiple Partial Discontinuities

Computer models are 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 slow to evaluate computer model, and greatly aids the vastly more computationally intensive uncertainty quantification calculations that an important scientific analysis often requires. We examine the problem of emulating computer models that possess multiple, partial discontinuities occurring at known non-linear location. We introduce the TENSE framework, based on carefully designed correlation structures that respect the discontinuities while enabling full exploitation of any smoothness/continuity elsewhere. This leads to a single emulator object that can be updated by all runs simultaneously, and also used for efficient design. This approach avoids having to split the input space into multiple subregions. We apply the TENSE framework to the TNO Challenge II, emulating the OLYMPUS reservoir model, which possess multiple such discontinuities.

stat.ME↗

arXiv2022

Emulation and History Matching using the hmer Package

Modelling complex real-world situations such as infectious diseases, geological phenomena, and biological processes can present a dilemma: the computer model (referred to as a simulator) needs to be complex enough to capture the dynamics of the system, but each increase in complexity increases the evaluation time of such a simulation, making it difficult to obtain an informative description of parameter choices that would be consistent with observed reality. While methods for identifying acceptable matches to real-world observations exist, for example optimisation or Markov chain Monte Carlo methods, they may result in non-robust inferences or may be infeasible for computationally intensive simulators. The techniques of emulation and history matching can make such determinations feasible, efficiently identifying regions of parameter space that produce acceptable matches to data while also providing valuable information about the simulator's structure, but the mathematical considerations required to perform emulation can present a barrier for makers and users of such simulators compared to other methods. The hmer package provides an accessible framework for using history matching and emulation on simulator data, leveraging the computational efficiency of the approach while enabling users to easily match to, visualise, and robustly predict from their complex simulators.

stat.CO↗

arXiv2022

Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces

Heavy atomic nuclei have an excess of neutrons over protons, which leads to the formation of a neutron skin whose thickness is sensitive to details of the nuclear force. This links atomic nuclei to properties of neutron stars, thereby relating objects that differ in size by orders of magnitude. The nucleus ${}^{208}$Pb is of particular interest because it exhibits a simple structure and is experimentally accessible. However, computing such a heavy nucleus has been out of reach for ab initio theory. By combining advances in quantum many-body methods, statistical tools, and emulator technology, we make quantitative predictions for the properties of ${}^{208}$Pb starting from nuclear forces that are consistent with symmetries of low-energy quantum chromodynamics. We explore $10^9$ different nuclear-force parameterisations via history matching, confront them with data in select light nuclei, and arrive at an importance-weighted ensemble of interactions. We accurately reproduce bulk properties of ${}^{208}$Pb and determine the neutron skin thickness, which is smaller and more precise than a recent extraction from parity-violating electron scattering but in agreement with other experimental probes. This work demonstrates how realistic two- and three-nucleon forces act in a heavy nucleus and allows us to make quantitative predictions across the nuclear landscape.

nucl-th↗

arXiv2020

Efficient Emulation of Computer Models Utilising Multiple Known Boundaries of Differing Dimensions

Emulation has been successfully applied across a wide variety of scientific disciplines for efficiently analysing computationally intensive models. We develop known boundary emulation strategies which utilise the fact that, for many computer models, there exist hyperplanes in the input parameter space for which the model output can be evaluated far more efficiently, whether this be analytically or just significantly faster using a more efficient and simpler numerical solver. The information contained on these known hyperplanes, or boundaries, can be incorporated into the emulation process via analytical update, thus involving no additional computational cost. In this article, we show that such analytical updates are available for multiple boundaries of various dimensions. We subsequently demonstrate which configurations of boundaries such analytical updates are available for, in particular by presenting a set of conditions that such a set of boundaries must satisfy. We demonstrate the powerful computational advantages of the known boundary emulation techniques developed on both an illustrative low-dimensional simulated example and a scientifically relevant and high-dimensional systems biology model of hormonal crosstalk in the roots of an Arabidopsis plant.

stat.ME↗

arXiv2019

Understanding Hormonal Crosstalk in Arabidopsis Root Development via Emulation and History Matching

A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 x 10^(-7) of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations.

stat.AP↗

arXiv2019

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.

stat.ME↗

arXiv2018

Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions

Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. Results: Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embedded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty. The approach is demonstrated via application to two models of hormonal crosstalk in Arabidopsis root development, which have 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches to observed trend data. The biological consequences of the resulting comparison, including the evaluation of gene functions, are described.

q-bio.MN↗

arXiv2017

A Bayesian computer model analysis of Robust Bayesian analyses

We harness the power of Bayesian emulation techniques, designed to aid the analysis of complex computer models, to examine the structure of complex Bayesian analyses themselves. These techniques facilitate robust Bayesian analyses and/or sensitivity analyses of complex problems, and hence allow global exploration of the impacts of choices made in both the likelihood and prior specification. We show how previously intractable problems in robustness studies can be overcome using emulation techniques, and how these methods allow other scientists to quickly extract approximations to posterior results corresponding to their own particular subjective specification. The utility and flexibility of our method is demonstrated on a reanalysis of a real application where Bayesian methods were employed to capture beliefs about river flow. We discuss the obvious extensions and directions of future research that such an approach opens up.

stat.ME↗

arXiv2016

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

We explore the parameter space of the semi-analytic galaxy formation model GALFORM, studying the constraints imposed by measurements of the galaxy stellar mass function (GSMF) and its evolution. We use the Bayesian Emulator method to quickly eliminate vast implausible volumes of the parameter space and zoom in on the most interesting regions, allowing us to identify a set of models that match the observational data within model uncertainties. We find that the GSMF strongly constrains parameters related to quiescent star formation in discs, stellar and AGN feedback and threshold for disc instabilities, but weakly restricts other parameters. Constraining the model using local data alone does not usually select models that match the evolution of the GSMF well. Nevertheless, we show that a small subset of models provides acceptable match to GSMF data out to redshift 1.5. We explore the physical significance of the parameters of these models, in particular exploring whether the model provides a better description if the mass loading of the galactic winds generated by starbursts ($β_{0,\text{burst}}$) and quiescent disks ($β_{0,\text{disc}}$) is different. Performing a principal component analysis of the plausible volume of the parameter space, we write a set of relations between parameters obeyed by plausible models with respect to GSMF evolution. We find that while $β_{0,\text{disc}}$ is strongly constrained by GSMF evolution data, constraints on $β_{0,\text{burst}}$ are weak. Although it is possible to find plausible models for which $β_{0,\text{burst}} = β_{0,\text{disc}}$, most plausible models have $β_{0,\text{burst}}>β_{0,\text{disc}}$, implying - for these - larger SN feedback efficiency at higher redshifts.

astro-ph.GA↗

arXiv2014

Galaxy Formation: Bayesian History Matching for the Observable Universe

Cosmologists at the Institute of Computational Cosmology, Durham University, have developed a state of the art model of galaxy formation known as Galform, intended to contribute to our understanding of the formation, growth and subsequent evolution of galaxies in the presence of dark matter. Galform requires the specification of many input parameters and takes a significant time to complete one simulation, making comparison between the model's output and real observations of the Universe extremely challenging. This paper concerns the analysis of this problem using Bayesian emulation within an iterative history matching strategy, and represents the most detailed uncertainty analysis of a galaxy formation simulation yet performed.

stat.ME↗

arXiv2013

Efficient uniform designs for multi-wave computer experiments

In this paper we tackle the problem of generating uniform designs in very small subregions of computer model input space that have been identified in previous experiments as worthy of further study. The method is capable of producing uniform designs in subregions of computer model input space defined by a membership function that consists of a continuous function passing a threshold test, and does so far more efficiently than current methods when these subregions are small. Our application is designing for regions of input space that are not ruled out by history matching, a statistical methodology applied in numerous diverse scientific applications whereby model runs are used to cut out regions of input space that are incompatible with real world observations. History matching defines a membership function for a region of input space that is not ruled out yet by observations in the form of a distance metric called implausibility. We use this distance metric to drive a new type of Evolutionary Monte Carlo algorithm with a uniform distribution on the not ruled out yet region as its target distribution. The algorithm can locate and generate uniform points within extremely small subspaces of the computer model input space with complex and even disconnected topologies. We illustrate the performance of the technique in comparison to current methods with a number of idealised examples. We then apply our algorithm to generating an optimal design for the not ruled out yet region of a galaxy simulation model called GALFORM following 4 previous waves of history matching where the target region is 0.001% the volume of the input space.

stat.ME↗

arXiv2001

Branes on the Horizon

Models with extra dimensions are often invoked to resolve cosmological problems. We investigate the possibility of apparent acausality as seen by a brane-based observer resulting from signal propagation through the extra dimensions. Null geodesics are first computed in static and cosmological single-brane models, following which we derive the equations of motion for the inter-brane distance in a two-brane scenario, which we use to examine possible acausality in this more complex setup. Despite observing significant effective acausality in some situations there is no a priori solution to the horizon problem using this mechanism. In the two-brane scenario there can be significant late time violation of gravitational Lorentz invariance, resulting in the gravitational horizon being larger than the particle horizon, leading to potential signals in gravitational wave detectors.

hep-ph↗

arXiv2000

Brane World Cosmology Without the Z_2 Symmetry

The Friedmann equation for a positive tension brane situated between two bulk spacetimes that posses the same 5D cosmological constant, but which does not posses a Z_2 symmetry of the metric itself is derived, and the possible effects of dropping the Z_2 symmetry on the expansion of our Universe are examined; cosmological constraints are discussed. The global solutions for the metric in the infinite extra dimension case are found and comparison with the symmetric case is made. We show that any brane world senario of this type must revert to a Z_2 symmetric form at late times, and hence rule out certain proposed scenarios.

hep-ph↗