arXiv subjects

Robert J. B. Goudie

Publications and source records attributed to Robert J. B. Goudie.

14 recordsLinked to original sources

arXiv2026

Chained Markov melding using divide and conquer sequential Monte Carlo

Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding. However, when adjacent submodels share common quantities, as in chained Markov melding, posterior inference can be challenging for existing MCMC-based approaches. In this paper, we propose a new multi-stage sampler for chained Markov models involving an arbitrary number of submodels. The proposed sampler adopts a divide-and-conquer sequential Monte Carlo approach for the tree-structured model that fits naturally with the structure of chained Markov melding. The resulting multi-stage sampler provides a flexible alternative for sampling from complex joint models, as its separate sampling scheme for different submodels avoids the need for directly sampling from the full model. We demonstrate applications of the sampler through two examples. The first is a toy example involving 11 submodels of various types. The second example considers an ecologically integrated population model that combines multiple datasets to estimate immigration and reproduction rates.

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arXiv2026

A Bayesian Prevalence Incidence Cure model for estimating survival using Electronic Health Records with incomplete baseline diagnoses

Retrospective cohorts can be extracted from Electronic Health Records (EHR) to study prevalence, time until disease or event occurrence and cure proportion in real world scenarios. However, EHR are collected for patient care rather than research, so typically have complexities, such as patients with missing baseline disease status. Prevalence-Incidence (PI) models, which use a two-component mixture model to account for this missing data, have been proposed. However, PI models are biased in settings in which some individuals will never experience the endpoint (they are 'cured'). To address this, we propose a Prevalence Incidence Cure (PIC) model, a 3 component mixture model that combines the PI model framework with a cure model. Our PIC model enables estimation of the prevalence, time-to-incidence, and the cure proportion, and allows for covariates to affect these. We adopt a Bayesian inference approach, and focus on the interpretability of the prior. We show in a simulation study that the PIC model has smaller bias than a PI model for the survival probability; and compare inference under vague, informative and misspecified priors. We illustrate our model using a dataset of 1964 patients undergoing treatment for Diabetic Macular Oedema, demonstrating improved fit under the PIC model.

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arXiv2025

Translating predictive distributions into informative priors

When complex Bayesian models exhibit implausible behaviour, one solution is to assemble available information into an informative prior. Challenges arise as prior information is often only available for the observable quantity, or some model-derived marginal quantity, rather than directly pertaining to the (usually latent) parameters in our model. We propose a method for translating available prior information, in the form of an elicited distribution for the observable or model-derived marginal quantity, into an informative joint prior. Our approach proceeds given a parametric class of prior distributions with as yet undetermined hyperparameters, and minimises the difference between the supplied elicited distribution and corresponding prior predictive distribution. We employ a global, multi-stage Bayesian optimisation procedure to locate optimal values for the hyperparameters. Three examples illustrate our approach: a cure-fraction survival model, where censoring implies that the observable quantity is _a priori_ a mixed discrete/continuous quantity; a setting in which prior information pertains to $R^{2}$ -- a model-derived quantity; and a nonlinear regression model.

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arXiv2024

A General Framework for Cutting Feedback within Modularised Bayesian Inference

Standard Bayesian inference can build models that combine information from various sources, but this inference may not be reliable if components of a model are misspecified. Cut inference, as a particular type of modularized Bayesian inference, is an alternative which splits a model into modules and cuts the feedback from the suspect module. Previous studies have focused on a two-module case, but a more general definition of a "module" remains unclear. We present a formal definition of a "module" and discuss its properties. We formulate methods for identifying modules; determining the order of modules; and building the cut distribution that should be used for cut inference within an arbitrary directed acyclic graph structure. We justify the cut distribution by showing that it not only cuts the feedback but also is the best approximation satisfying this condition to the joint distribution in the Kullback-Leibler divergence. We also extend cut inference for the two-module case to a general multiple-module case via a sequential splitting technique and demonstrate this via illustrative applications.

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arXiv2024

Dynamic factor analysis for sparse and irregular longitudinal data: an application to metabolite measurements in a COVID-19 study

It is of scientific interest to identify essential biomarkers in biological processes underlying diseases to facilitate precision medicine. Factor analysis (FA) has long been used to address this goal: by assuming latent biological pathways drive the activity of measurable biomarkers, a biomarker is more influential if its absolute factor loading is larger. Although correlation between biomarkers has been properly handled under this framework, correlation between latent pathways are often overlooked, as one classical assumption in FA is the independence between factors. However, this assumption may not be realistic in the context of pathways, as existing biological knowledge suggests that pathways interact with one another rather than functioning independently. Motivated by sparsely and irregularly collected longitudinal measurements of metabolites in a COVID-19 study of large sample size, we propose a dynamic factor analysis model that can account for the potential cross-correlations between pathways, through a multi-output Gaussian processes (MOGP) prior on the factor trajectories. To mitigate against overfitting caused by sparsity of longitudinal measurements, we introduce a roughness penalty upon MOGP hyperparameters and allow for non-zero mean functions. To estimate these hyperparameters, we develop a stochastic expectation maximization (StEM) algorithm that scales well to the large sample size. In our simulation studies, StEM leads across all sample sizes considered to a more accurate and stable estimate of the MOGP hyperparameters than a comparator algorithm used in previous research. Application to the motivating example identifies a kynurenine pathway that affects the clinical severity of patients with COVID-19. In particular, a novel biomarker taurine is discovered, which has been receiving increased attention clinically, yet its role was overlooked in a previous analysis.

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arXiv2024

Dynamic Factor Analysis with Dependent Gaussian Processes for High-Dimensional Gene Expression Trajectories

The increasing availability of high-dimensional, longitudinal measures of gene expression can facilitate understanding of biological mechanisms, as required for precision medicine. Biological knowledge suggests that it may be best to describe complex diseases at the level of underlying pathways, which may interact with one another. We propose a Bayesian approach that allows for characterising such correlation among different pathways through Dependent Gaussian Processes (DGP) and mapping the observed high-dimensional gene expression trajectories into unobserved low-dimensional pathway expression trajectories via Bayesian Sparse Factor Analysis. Our proposal is the first attempt to relax the classical assumption of independent factors for longitudinal data and has demonstrated a superior performance in recovering the shape of pathway expression trajectories, revealing the relationships between genes and pathways, and predicting gene expressions (closer point estimates and narrower predictive intervals), as demonstrated through simulations and real data analysis. To fit the model, we propose a Monte Carlo Expectation Maximization (MCEM) scheme that can be implemented conveniently by combining a standard Markov Chain Monte Carlo sampler and an R package GPFDA (Konzen and others, 2021), which returns the maximum likelihood estimates of DGP hyperparameters. The modular structure of MCEM makes it generalizable to other complex models involving the DGP model component. Our R package DGP4LCF that implements the proposed approach is available on CRAN.

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arXiv2022

Combining chains of Bayesian models with Markov melding

A challenge for practitioners of Bayesian inference is specifying a model that incorporates multiple relevant, heterogeneous data sets. It may be easier to instead specify distinct submodels for each source of data, then join the submodels together. We consider chains of submodels, where submodels directly relate to their neighbours via common quantities which may be parameters or deterministic functions thereof. We propose chained Markov melding, an extension of Markov melding, a generic method to combine chains of submodels into a joint model. One challenge we address is appropriately capturing the prior dependence between common quantities within a submodel, whilst also reconciling differences in priors for the same common quantity between two adjacent submodels. Estimating the posterior of the resulting overall joint model is also challenging, so we describe a sampler that uses the chain structure to incorporate information contained in the submodels in multiple stages, possibly in parallel. We demonstrate our methodology using two examples. The first example considers an ecological integrated population model, where multiple data sets are required to accurately estimate population immigration and reproduction rates. We also consider a joint longitudinal and time-to-event model with uncertain, submodel-derived event times. Chained Markov melding is a conceptually appealing approach to integrating submodels in these settings.

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arXiv2022

Generalized Geographically Weighted Regression Model within a Modularized Bayesian Framework

Geographically weighted regression (GWR) models handle geographical dependence through a spatially varying coefficient model and have been widely used in applied science, but its general Bayesian extension is unclear because it involves a weighted log-likelihood which does not imply a probability distribution on data. We present a Bayesian GWR model and show that its essence is dealing with partial misspecification of the model. Current modularized Bayesian inference models accommodate partial misspecification from a single component of the model. We extend these models to handle partial misspecification in more than one component of the model, as required for our Bayesian GWR model. Information from the various spatial locations is manipulated via a geographically weighted kernel and the optimal manipulation is chosen according to a Kullback-Leibler (KL) divergence. We justify the model via an information risk minimization approach and show the consistency of the proposed estimator in terms of a geographically weighted KL divergence.

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arXiv2021

Stochastic Approximation Cut Algorithm for Inference in Modularized Bayesian Models

Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model, and prevent feedback from suspect modules, using a cut model. After observing data, this leads to the cut distribution which normally does not have a closed-form. Previous studies have proposed algorithms to sample from this distribution, but these algorithms have unclear theoretical convergence properties. To address this, we propose a new algorithm called the Stochastic Approximation Cut algorithm (SACut) as an alternative. The algorithm is divided into two parallel chains. The main chain targets an approximation to the cut distribution; the auxiliary chain is used to form an adaptive proposal distribution for the main chain. We prove convergence of the samples drawn by the proposed algorithm and present the exact limit. Although SACut is biased, since the main chain does not target the exact cut distribution, we prove this bias can be reduced geometrically by increasing a user-chosen tuning parameter. In addition, parallel computing can be easily adopted for SACut, which greatly reduces computation time.

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arXiv2021

Interoperability of statistical models in pandemic preparedness: principles and reality

We present "interoperability" as a guiding framework for statistical modelling to assist policy makers asking multiple questions using diverse datasets in the face of an evolving pandemic response. Interoperability provides an important set of principles for future pandemic preparedness, through the joint design and deployment of adaptable systems of statistical models for disease surveillance using probabilistic reasoning. We illustrate this through case studies for inferring spatial-temporal coronavirus disease 2019 (COVID-19) prevalence and reproduction numbers in England.

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arXiv2021

A numerically stable algorithm for integrating Bayesian models using Markov melding

When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the prior for this quantity can be implicit, and its prior density must be estimated. We show that error in this density estimate makes the two-stage Markov chain Monte Carlo sampler employed by Markov melding unstable and unreliable. We propose a robust two-stage algorithm that estimates the required prior marginal self-density ratios using weighted samples, dramatically improving accuracy in the tails of the distribution. The stabilised version of the algorithm is pragmatic and provides reliable inference. We demonstrate our approach using an evidence synthesis for inferring HIV prevalence, and an evidence synthesis of A/H1N1 influenza.

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arXiv2021

A Bayesian framework for case-cohort Cox regression: application to dietary epidemiology

The case-cohort study design bypasses resource constraints by collecting certain expensive covariates for only a small subset of the full cohort. Weighted Cox regression is the most widely used approach for analysing case-cohort data within the Cox model, but is inefficient. Alternative approaches based on multiple imputation and nonparametric maximum likelihood suffer from incompatibility and computational issues respectively. We introduce a novel Bayesian framework for case-cohort Cox regression that avoids the aforementioned problems. Users can include auxiliary variables to help predict the unmeasured expensive covariates with a prediction model of their choice, while the models for the nuisance parameters are nonparametrically specified and integrated out. Posterior sampling can be carried out using procedures based on the pseudo-marginal MCMC algorithm. The method scales effectively to large, complex datasets, as demonstrated in our application: investigating the associations between saturated fatty acids and type 2 diabetes using the EPIC-Norfolk study. As part of our analysis, we also develop a new approach for handling compositional data in the Cox model, leading to more reliable and interpretable results compared to previous studies. The performance of our method is illustrated with extensive simulations. The code used to produce the results in this paper can be found at https://github.com/andrewyiu/bayes_cc .

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arXiv2018

MultiBUGS: A parallel implementation of the BUGS modelling framework for faster Bayesian inference

MultiBUGS (https://www.multibugs.org) is a new version of the general-purpose Bayesian modelling software BUGS that implements a generic algorithm for parallelising Markov chain Monte Carlo (MCMC) algorithms to speed up posterior inference of Bayesian models. The algorithm parallelises evaluation of the product-form likelihoods formed when a parameter has many children in the directed acyclic graph (DAG) representation; and parallelises sampling of conditionally-independent sets of parameters. A heuristic algorithm is used to decide which approach to use for each parameter and to apportion computation across computational cores. This enables MultiBUGS to automatically parallelise the broad range of statistical models that can be fitted using BUGS-language software, making the dramatic speed-ups of modern multi-core computing accessible to applied statisticians, without requiring any experience of parallel programming. We demonstrate the use of MultiBUGS on simulated data designed to mimic a hierarchical e-health linked-data study of methadone prescriptions including 425,112 observations and 20,426 random effects. Posterior inference for the e-health model takes several hours in existing software, but MultiBUGS can perform inference in only 28 minutes using 48 computational cores.

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arXiv2017

Joining and splitting models with Markov melding

Analysing multiple evidence sources is often feasible only via a modular approach, with separate submodels specified for smaller components of the available evidence. Here we introduce a generic framework that enables fully Bayesian analysis in this setting. We propose a generic method for forming a suitable joint model when joining submodels, and a convenient computational algorithm for fitting this joint model in stages, rather than as a single, monolithic model. The approach also enables splitting of large joint models into smaller submodels, allowing inference for the original joint model to be conducted via our multi-stage algorithm. We motivate and demonstrate our approach through two examples: joining components of an evidence synthesis of A/H1N1 influenza, and splitting a large ecology model.

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