arXiv subjects

Antony Overstall

Publications and source records attributed to Antony Overstall.

7 recordsLinked to original sources

arXiv2024

fdesigns: Bayesian Optimal Designs of Experiments for Functional Models in R

This paper describes the R package fdesigns that implements a methodology for identifying Bayesian optimal experimental designs for models whose factor settings are functions, known as profile factors. This type of experiments which involve factors that vary dynamically over time, presenting unique challenges in both estimation and design due to the infinite-dimensional nature of functions. The package fdesigns implements a dimension reduction method leveraging basis functions of the B-spline basis system. The package fdesigns contains functions that effectively reduce the design problem to the optimisation of basis coefficients for functional linear functional generalised linear models, and it accommodates various options. Applications of the fdesigns package are demonstrated through a series of examples that showcase its capabilities in identifying optimal designs for functional linear and generalised linear models. The examples highlight how the package's functions can be used to efficiently design experiments involving both profile and scalar factors, including interactions and polynomial effects.

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arXiv2023

Zero-Truncated Modelling in a Meta-Analysis on Suicide Data after Bariatric Surgery

Meta-analysis is a well-established method for integrating results from several independent studies to estimate a common quantity of interest. However, meta-analysis is prone to selection bias, notably when particular studies are systematically excluded. This can lead to bias in estimating the quantity of interest. Motivated by a meta-analysis to estimate the rate of completed-suicide after bariatric surgery, where studies which reported no suicides were excluded, a novel zero-truncated count modelling approach was developed. This approach addresses heterogeneity, both observed and unobserved, through covariate and overdispersion modelling, respectively. Additionally, through the Horvitz-Thompson estimator, an approach is developed to estimate the number of excluded studies, a quantity of potential interest for researchers. Uncertainty quantification for both estimation of suicide rates and number of excluded studies is achieved through a parametric bootstrapping approach.\end{abstract}

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arXiv2019

Bayesian optimal design for ordinary differential equation models with application in biological science

Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of non-linear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations governing the transport of amino acids through cell membranes in human placentas. Decision-theoretic Bayesian design of experiments for such nonlinear models is conceptually very attractive, allowing the formal incorporation of prior knowledge to overcome the parameter dependence of frequentist design and being less reliant on asymptotic approximations. However, the necessary approximation and maximization of the, typically analytically intractable, expected utility results in a computationally challenging problem. These issues are further exacerbated if the solution to the differential equations is not available in closed-form. This paper proposes a new combination of a probabilistic solution to the equations embedded within a Monte Carlo approximation to the expected utility with cyclic descent of a smooth approximation to find the optimal design. A novel precomputation algorithm reduces the computational burden, making the search for an optimal design feasible for bigger problems. The methods are demonstrated by finding new designs for a number of common models derived from differential equations, and by providing optimal designs for the placenta experiment.

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arXiv2018

acebayes: An R Package for Bayesian Optimal Design of Experiments via Approximate Coordinate Exchange

We describe the R package acebayes and demonstrate its use to find Bayesian optimal experimental designs. A decision-theoretic approach is adopted, with the optimal design maximising an expected utility. Finding Bayesian optimal designs for realistic problems is challenging, as the expected utility is typically intractable and the design space may be high-dimensional. The package implements the approximate coordinate exchange algorithm to optimise (an approximation to) the expected utility via a sequence of conditional one-dimensional optimisation steps. At each step, a Gaussian process regression model is used to approximate, and subsequently optimise, the expected utility as the function of a single design coordinate (the value taken by one controllable variable for one run of the experiment). In addition to functions for bespoke design problems with user-defined utility functions, acebayes provides functions tailored to finding designs for common generalised linear and nonlinear models. The package provides a step-change in the complexity of problems that can be addressed, enabling designs to be found for much larger numbers of variables and runs than previously possible. We provide tutorials on the application of the methodology for four illustrative examples of varying complexity where designs are found for the goals of parameter estimation, model selection and prediction. These examples demonstrate previously unseen functionality of acebayes.

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arXiv2018

Bayesian prediction for physical models with application to the optimization of the synthesis of pharmaceutical products using chemical kinetics

Quality control in industrial processes is increasingly making use of prior scientific knowledge, often encoded in physical models that require numerical approximation. Statistical prediction, and subsequent optimization, is key to ensuring the process output meets a specification target. However, the numerical expense of approximating the models poses computational challenges to the identification of combinations of the process factors where there is confidence in the quality of the response. Recent work in Bayesian computation and statistical approximation (emulation) of expensive computational models is exploited to develop a novel strategy for optimizing the posterior probability of a process meeting specification. The ensuing methodology is motivated by, and demonstrated on, a chemical synthesis process to manufacture a pharmaceutical product, within which an initial set of substances evolve according to chemical reactions, under certain process conditions, into a series of new substances. One of these substances is a target pharmaceutical product and two are unwanted by-products. The aim is to determine the combinations of process conditions and amounts of initial substances that maximize the probability of obtaining sufficient target pharmaceutical product whilst ensuring unwanted by-products do not exceed a given level. The relationship between the factors and amounts of substances of interest is theoretically described by the solution to a system of ordinary differential equations incorporating temperature dependence. Using data from a small experiment, it is shown how the methodology can approximate the multivariate posterior predictive distribution of the pharmaceutical target and by-products, and therefore identify suitable operating values. Materials to replicate the analysis can be found at www.github.com/amo105/chemicalkinetics.

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arXiv2016

Bayesian Design of Experiments using Approximate Coordinate Exchange

The construction of decision-theoretic Bayesian designs for realistically-complex nonlinear models is computationally challenging, as it requires the optimization of analytically intractable expected utility functions over high-dimensional design spaces. We provide the most general solution to date for this problem through a novel approximate coordinate exchange algorithm. This methodology uses a Gaussian process emulator to approximate the expected utility as a function of a single design coordinate in a series of conditional optimization steps. It has flexibility to address problems for any choice of utility function and for a wide range of statistical models with different numbers of variables, numbers of runs and randomization restrictions. In contrast to existing approaches to Bayesian design, the method can find multi-variable designs in large numbers of runs without resorting to asymptotic approximations to the posterior distribution or expected utility. The methodology is demonstrated on a variety of challenging examples of practical importance, including design for pharmacokinetic models and design for mixed models with discrete data. For many of these models, Bayesian designs are not currently available. Comparisons are made to results from the literature, and to designs obtained from asymptotic approximations.

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arXiv2015

Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model

We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for multivariate covariance-separable emulators are developed and techniques to improve the adequacy of an emulator are discussed and implemented. A variety of emulators are compared for a humanitarian relief simulator, modelling aid missions to Sicily after a volcanic eruption and earthquake, and a sensitivity analysis is conducted to determine the sensitivity of the simulator output to changes in the input variables. The results from parametric and nonparametric emulators are compared in terms of prediction accuracy, uncertainty quantification and scientific interpretability.

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