arXiv subjects

James M. McGree

Publications and source records attributed to James M. McGree.

At least 19 recordsLinked to original sources

arXiv2026

Computationally Efficient Experimental Design with Generalized Posteriors

The hybrid approach to experimental design aims to control frequentist operating characteristics of Bayesian decision procedures. These operating characteristics are assessed by simulating sampling distributions of posterior summaries under assumed data-generation processes that also define posterior distributions. Model misspecification can distort effect estimation and compromise control over operating characteristics. Generalized posterior distributions are defined using generalized likelihoods that characterize data generation under fewer assumptions, enhancing the robustness of Bayesian analysis and study design. However, widely applicable and computationally efficient design methodology with generalized posteriors is lacking. We propose an efficient method to determine suitable sample sizes and decision criteria associated with generalized posteriors under the hybrid approach. Using theoretical results to model posterior summaries as linear functions of the sample size, we efficiently assess operating characteristics throughout the sample size space given simulations conducted at only two sample sizes. While the benefits of the proposed methodology are illustrated by redesigning an adaptive clinical trial with time-to-event outcomes, we overview our framework's broader applicability to experiments involving Bayesian analogues to M-estimation.

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arXiv2025

General Bayesian L2 calibration of mathematical models

A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the system; and (b) calibration parameters: unknown characteristics of the physical system that cannot be controlled or directly measured. Of interest is the estimation of the calibration parameter using physical observations. Since the mathematical model will be an inexact representation of the physical system: the aim is to estimate values for the calibration parameters to make the mathematical model ``close" to the physical system. Closeness is defined as the squared $L^2$ norm of the difference between the mathematical model and the physical system. Different Bayesian and general Bayesian methods are introduced, developed and compared for this task.

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arXiv2025

A subsampling approach for large data sets when the Generalised Linear Model is potentially misspecified

Subsampling is a computationally efficient and scalable method to draw inference in large data settings based on a subset of the data rather than needing to consider the whole dataset. When employing subsampling techniques, a crucial consideration is how to select an informative subset based on the queries posed by the data analyst. A recently proposed method for this purpose involves randomly selecting samples from the large dataset based on subsampling probabilities. However, a major drawback of this approach is that the derived subsampling probabilities are typically based on an assumed statistical model which may be difficult to correctly specify in practice. To address this limitation, we propose to determine subsampling probabilities based on a statistical model that we acknowledge may be misspecified. To do so, we propose to evaluate the subsampling probabilities based on the Mean Squared Error (MSE) of the predictions from a model that is not assumed to completely describe the large dataset. We apply our subsampling approach in a simulation study and for the analysis of two real-world large datasets, where its performance is benchmarked against existing subsampling techniques. The findings suggest that there is value in adopting our approach over current practice.

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arXiv2025

A general Bayesian approach to design adaptive clinical trials with time-to-event outcomes

Clinical trials are an integral component of medical research. Trials require careful design to, for example, maintain the safety of participants, use resources efficiently and allow clinically meaningful conclusions to be drawn. Adaptive clinical trials (i.e. trials that can be altered based on evidence that has accrued) are often more efficient, informative and ethical than standard or non-adaptive trials because they require fewer participants, target more promising treatments, and can stop early with sufficient evidence of effectiveness or harm. The design of adaptive trials requires the pre-specification of adaptions that are permissible throughout the conduct of the trial. Proposed adaptive designs are then usually evaluated through simulation which provides indicative metrics of performance (e.g. statistical power and type-1 error) under different scenarios. Trial simulation requires assumptions about the data generating process to be specified but correctly specifying these in practice can be difficult, particularly for new and emerging diseases. To address this, we propose an approach to design adaptive clinical trials without needing to specify the complete data generating process. To facilitate this, we consider a general Bayesian framework where inference about the treatment effect on a time-to-event outcome can be performed via the partial likelihood. As a consequence, the proposed approach to evaluate trial designs is robust to the specific form of the baseline hazard function. The benefits of this approach are demonstrated through the redesign of a recent clinical trial to evaluate whether a third dose of a vaccine provides improved protection against gastroenteritis in Australian Indigenous infants.

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arXiv2025

Gibbs optimal design of experiments

Bayesian optimal design is a well-established approach to planning experiments. A distribution for the responses, i.e. a statistical model, is assumed which is dependent on unknown parameters. A utility function is then specified giving gain in information in estimating the true values of the parameters, using the Bayesian posterior distribution. A Bayesian optimal design is given by maximising expectation of the utility with respect to the distribution implied by statistical model and prior distribution for the true parameter values. The approach accounts for the experimental aim, via specification of the utility, and of assumed sources of uncertainty. However, it is predicated on the statistical model being correct. Recently, a new type of statistical inference, known as Gibbs inference, has been proposed. This is Bayesian-like, i.e. uncertainty for unknown quantities is represented by a posterior distribution, but does not necessarily require specification of a statistical model. The resulting inference is less sensitive to misspecification of the statistical model. This paper introduces Gibbs optimal design: a framework for optimal design of experiments under Gibbs inference. A computational approach to find designs in practice is outlined and the framework is demonstrated on exemplars including linear models, and experiments with count and time-to-event responses.

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arXiv2024

Bayesian design for mathematical models of fruit growth based on misspecified prior information

Bayesian design can be used for efficient data collection over time when the process can be described by the solution to an ordinary differential equation (ODE). Typically, Bayesian designs in such settings are obtained by maximising the expected value of a utility function that is derived from the joint probability distribution of the parameters and the response, given prior information about an appropriate ODE. However, in practice, appropriately defining such information \textit{a priori} can be difficult due to incomplete knowledge about the mechanisms that govern how the process evolves over time. In this paper, we propose a method for finding Bayesian designs based on a flexible class of ODEs. Specifically, we consider the inclusion of spline terms into ODEs to provide flexibility in modelling how the process changes over time. We then propose to leverage this flexibility to form designs that are efficient even when the prior information is misspecified. Our approach is motivated by a sampling problem in agriculture where the goal is to provide a better understanding of fruit growth where prior information is based on studies conducted overseas, and therefore is potentially misspecified.

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arXiv2023

Being Bayesian in the 2020s: opportunities and challenges in the practice of modern applied Bayesian statistics

Building on a strong foundation of philosophy, theory, methods and computation over the past three decades, Bayesian approaches are now an integral part of the toolkit for most statisticians and data scientists. Whether they are dedicated Bayesians or opportunistic users, applied professionals can now reap many of the benefits afforded by the Bayesian paradigm. In this paper, we touch on six modern opportunities and challenges in applied Bayesian statistics: intelligent data collection, new data sources, federated analysis, inference for implicit models, model transfer and purposeful software products.

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arXiv2022

Robust simulation design for generalized linear models in conditions of heteroscedasticity or correlation

A meta-model of the input-output data of a computationally expensive simulation is often employed for prediction, optimization, or sensitivity analysis purposes. Fitting is enabled by a designed experiment, and for computationally expensive simulations, the design efficiency is of importance. Heteroscedasticity in simulation output is common, and it is potentially beneficial to induce dependence through the reuse of pseudo-random number streams to reduce the variance of the meta-model parameter estimators. In this paper, we develop a computational approach to robust design for computer experiments without the need to assume independence or identical distribution of errors. Through explicit inclusion of the variance or correlation structures into the meta-model distribution, either maximum likelihood estimation or generalized estimating equations can be employed to obtain an appropriate Fisher information matrix. Robust designs can then be computationally sought which maximize some relevant summary measure of this matrix, averaged across a prior distribution of any unknown parameters.

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arXiv2022

A model robust sub-sampling approach for Generalised Linear Models in Big data settings

In today's modern era of Big data, computationally efficient and scalable methods are needed to support timely insights and informed decision making. One such method is sub-sampling, where a subset of the Big data is analysed and used as the basis for inference rather than considering the whole data set. A key question when applying sub-sampling approaches is how to select an informative subset based on the questions being asked of the data. A recent approach for this has been proposed based on determining sub-sampling probabilities for each data point, but a limitation of this approach is that appropriate sub-sampling probabilities rely on an assumed model for the Big data. In this article, to overcome this limitation, we propose a model robust approach where a set of models is considered, and the sub-sampling probabilities are evaluated based on the weighted average of probabilities that would be obtained if each model was considered singularly. Theoretical support for such an approach is provided. Our model robust sub-sampling approach is applied in a simulation study and in two real world applications where performance is compared to current sub-sampling practices. The results show that our model robust approach outperforms alternative approaches.

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arXiv2022

Bayesian Design with Sampling Windows for Complex Spatial Processes

Optimal design facilitates intelligent data collection. In this paper, we introduce a fully Bayesian design approach for spatial processes with complex covariance structures, like those typically exhibited in natural ecosystems. Coordinate Exchange algorithms are commonly used to find optimal design points. However, collecting data at specific points is often infeasible in practice. Currently, there is no provision to allow for flexibility in the choice of design. We also propose an approach to find Bayesian sampling windows, rather than points, via Gaussian process emulation to identify regions of high design efficiency across a multi-dimensional space. These developments are motivated by two ecological case studies: monitoring water temperature in a river network system in the northwestern United States and monitoring submerged coral reefs off the north-west coast of Australia.

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arXiv2022

SSNbayes: An R package for Bayesian spatio-temporal modelling on stream networks

Spatio-temporal models are widely used in many research areas from ecology to epidemiology. However, most covariance functions describe spatial relationships based on Euclidean distance only. In this paper, we introduce the R package SSNbayes for fitting Bayesian spatio-temporal models and making predictions on branching stream networks. SSNbayes provides a linear regression framework with multiple options for incorporating spatial and temporal autocorrelation. Spatial dependence is captured using stream distance and flow connectivity while temporal autocorrelation is modelled using vector autoregression approaches. SSNbayes provides the functionality to make predictions across the whole network, compute exceedance probabilities and other probabilistic estimates such as the proportion of suitable habitat. We illustrate the functionality of the package using a stream temperature dataset collected in Idaho, USA.

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arXiv2021

Bayesian design for minimising prediction uncertainty in bivariate spatial responses with applications to air quality monitoring

Model-based geostatistical design involves the selection of locations to collect data to minimise an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which, for geostatistical studies, could be to minimise the prediction uncertainty at unobserved locations. In this paper, we propose a new approach to design such studies via a loss function derived through considering the entropy about the model predictions and the parameters of the model. The approach also includes a multivariate extension to generalised linear spatial models, and thus can be used to design experiments with more than one response. Unfortunately, evaluating our proposed loss function is computationally expensive so we provide an approximation such that our approach can be adopted to design realistically sized geostatistical studies. This is demonstrated through a simulated study and through designing an air quality monitoring program in Queensland, Australia. The results show that our designs remain highly efficient in achieving each experimental objective individually, providing an ideal compromise between the two objectives. Accordingly, we advocate that our approach could be adopted more generally in model-based geostatistical design.

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arXiv2021

Bayesian decision-theoretic design of experiments under an alternative model

Traditionally Bayesian decision-theoretic design of experiments proceeds by choosing a design to minimise expectation of a given loss function over the space of all designs. The loss function encapsulates the aim of the experiment, and the expectation is taken with respect to the joint distribution of all unknown quantities implied by the statistical model that will be fitted to observed responses. In this paper, an extended framework is proposed whereby the expectation of the loss is taken with respect to a joint distribution implied by an alternative statistical model. Motivation for this includes promoting robustness, ensuring computational feasibility and for allowing realistic prior specification when deriving a design. To aid in exploring the new framework, an asymptotic approximation to the expected loss under an alternative model is derived, and the properties of different loss functions are established. The framework is then demonstrated on a linear regression versus full-treatment model scenario, on estimating parameters of a non-linear model under model discrepancy and a cubic spline model under an unknown number of basis functions.

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arXiv2020

Bayesian adaptive N-of-1 trials for estimating population and individual treatment effects

This article proposes a novel adaptive design algorithm that can be used to find optimal treatment allocations in N-of-1 clinical trials. This new methodology uses two Laplace approximations to provide a computationally efficient estimate of population and individual random effects within a repeated measures, adaptive design framework. Given the efficiency of this approach, it is also adopted for treatment selection to target the collection of data for the precise estimation of treatment effects. To evaluate this approach, we consider both a simulated and motivating N-of-1 clinical trial from the literature. For each trial, our methods were compared to the multi-armed bandit approach and a randomised N-of-1 trial design in terms of identifying the best treatment for each patient and the information gained about the model parameters. The results show that our new approach selects designs that are highly efficient in achieving each of these objectives. As such, we propose our Laplace-based algorithm as an efficient approach for designing adaptive N-of-1 trials.

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arXiv2019

SSNdesign -- an R package for pseudo-Bayesian optimal and adaptive sampling designs on stream networks

Streams and rivers are biodiverse and provide valuable ecosystem services. Maintaining these ecosystems is an important task, so organisations often monitor the status and trends in stream condition and biodiversity using field sampling and, more recently, autonomous in-situ sensors. However, data collection is often costly and so effective and efficient survey designs are crucial to maximise information while minimising costs. Geostatistics and optimal and adaptive design theory can be used to optimise the placement of sampling sites in freshwater studies and aquatic monitoring programs. Geostatistical modelling and experimental design on stream networks pose statistical challenges due to the branching structure of the network, flow connectivity and directionality, and differences in flow volume. Thus, unique challenges of geostatistics and experimental design on stream networks necessitates the development of new open-source software for implementing the theory. We present SSNdesign, an R package for solving optimal and adaptive design problems on stream networks that integrates with existing open-source software. We demonstrate the mathematical foundations of our approach, and illustrate the functionality of SSNdesign using two case studies involving real data from Queensland, Australia. In both case studies we demonstrate that the optimal or adaptive designs outperform random and spatially balanced survey designs. The SSNdesign package has the potential to boost the efficiency of freshwater monitoring efforts and provide much-needed information for freshwater conservation and management.

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arXiv2019

A synthetic likelihood-based Laplace approximation for efficient design of biological processes

Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the design of experiments. Bayesian designs are found by maximising the expectation of a utility function over a design space, and typically this requires sampling from or approximating a large number of posterior distributions. This renders approaches adopted in inference computationally infeasible to implement in design. Consequently, optimal design in such fields has been limited to a small number of dimensions or a restricted range of utility functions. To overcome such limitations, we propose a synthetic likelihood-based Laplace approximation for approximating utility functions for models with intractable likelihoods. As will be seen, the proposed approximation is flexible in that a wide range of utility functions can be considered, and remains computationally efficient in high dimensions. To explore the validity of this approximation, an illustrative example from epidemiology is considered. Then, our approach is used to design experiments with a relatively large number of observations in two motivating applications from epidemiology and ecology.

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arXiv2019

A framework for automated anomaly detection in high frequency water-quality data from in situ sensors

River water-quality monitoring is increasingly conducted using automated in situ sensors, enabling timelier identification of unexpected values. However, anomalies caused by technical issues confound these data, while the volume and velocity of data prevent manual detection. We present a framework for automated anomaly detection in high-frequency water-quality data from in situ sensors, using turbidity, conductivity and river level data. After identifying end-user needs and defining anomalies, we ranked their importance and selected suitable detection methods. High priority anomalies included sudden isolated spikes and level shifts, most of which were classified correctly by regression-based methods such as autoregressive integrated moving average models. However, using other water-quality variables as covariates reduced performance due to complex relationships among variables. Classification of drift and periods of anomalously low or high variability improved when we applied replaced anomalous measurements with forecasts, but this inflated false positive rates. Feature-based methods also performed well on high priority anomalies, but were also less proficient at detecting lower priority anomalies, resulting in high false negative rates. Unlike regression-based methods, all feature-based methods produced low false positive rates, but did not and require training or optimization. Rule-based methods successfully detected impossible values and missing observations. Thus, we recommend using a combination of methods to improve anomaly detection performance, whilst minimizing false detection rates. Furthermore, our framework emphasizes the importance of communication between end-users and analysts for optimal outcomes with respect to both detection performance and end-user needs. Our framework is applicable to other types of high frequency time-series data and anomaly detection applications.

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arXiv2019

Bayesian design of experiments for intractable likelihood models using coupled auxiliary models and multivariate emulation

A Bayesian design is given by maximising an expected utility over a design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models. Although straightforward in principle, there are several challenges to finding Bayesian designs in practice. Firstly, the utility and expected utility are rarely available in closed form and require approximation. Secondly, the design space can be of high-dimensionality. In the case of intractable likelihood models, these problems are compounded by the fact that the likelihood function, whose evaluation is required to approximate the expected utility, is not available in closed form. A strategy is proposed to find Bayesian designs for intractable likelihood models. It relies on the development of an automatic, auxiliary modelling approach, using multivariate Gaussian process emulators, to approximate the likelihood function. This is then combined with a copula-based approach to approximate the marginal likelihood (a quantity commonly required to evaluate many utility functions). These approximations are demonstrated on examples of stochastic process models involving experimental aims of both parameter estimation and model comparison.

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