arXiv subjects

Stuart Barber

Publications and source records attributed to Stuart Barber.

7 recordsLinked to original sources

arXiv2026

Tail-Greedy Unbalanced Haar Wavelet Segmentation for Copy Number Alteration Data

Detecting copy number alterations (CNAs) from next-generation sequencing data remains challenging, particularly for short segments under noisy conditions. Existing segmentation methods often suffer from high false positive rates or fail to reliably detect short aberrations, especially in low-coverage data. In this study, we propose a modified tail-greedy unbalanced Haar (TGUHm) method that introduces a dual-thresholding strategy to improve segmentation accuracy. The proposed approach effectively suppresses spurious spikes while preserving sensitivity to both short and long CNA segments. Extensive simulation studies under Gaussian and heavy-tailed noise demonstrate that TGUHm consistently achieves higher true positive rates and lower false positive rates compared to state-of-the-art methods, including CBS, HaarSeg, and FDRSeg. In particular, the proposed method improves detection accuracy for short segments while maintaining competitive overall performance. Application to real cancer genomic data further confirms the practical utility of the method, revealing biologically meaningful CNAs associated with known cancer-related genes. These results suggest that TGUHm provides a robust and effective framework for CNA detection in challenging sequencing settings.

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arXiv2025

Defining Utility as a Measure of Preference Under Uncertainty in Phase I-II Oncology Dose Finding Trials

The main objective of dose finding trials is to find an optimal dose amongst a candidate set for further research. The trial design in oncology proceeds in stages with a decision as to how to treat the next group of patients made at every stage until a final sample size is reached or the trial stopped early. This work applies a Bayesian decision-theoretic approach to the problem, proposing a new utility function based on both efficacy and toxicity and grounded in von Neumann-Morgenstern (VNM) utility theory. Our proposed framework seeks to better capture real clinical judgements by allowing attitudes to risk to vary when the judgements are of gains or losses, which are defined with respect to an intermediate outcome known as a reference point. We call this method Reference Dependent Decision Theoretic dose finding (R2DT). A simulation study demonstrates that the framework can perform well and produce good operating characteristics. The simulation results demonstrate that R2DT is better at detecting the optimal dose in scenarios where candidate doses are around minimum acceptable efficacy and maximum acceptable toxicity thresholds. The proposed framework shows that a flexible utility function, which better captures clinician beliefs, can lead to trials with good operating characteristics, including a high probability of finding the optimal dose. Our work demonstrates proof-of-concept for this framework, which should be evaluated in a broader range of settings.

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arXiv2021

Mixture models for spherical data with applications to protein bioinformatics

Finite mixture models are fitted to spherical data. Kent distributions are used for the components of the mixture because they allow considerable flexibility. Previous work on such mixtures has used an approximate maximum likelihood estimator for the parameters of a single component. However, the approximation causes problems when using the EM algorithm to estimate the parameters in a mixture model. Hence the exact maximum likelihood estimator is used here for the individual components. This paper is motivated by a challenging prize problem in structural bioinformatics of how proteins fold. It is known that hydrogen bonds play a key role in the folding of a protein. We explore this hydrogen bond geometry using a data set describing bonds between two amino acids in proteins. An appropriate coordinate system to represent the hydrogen bond geometry is proposed, with each bond represented as a point on a sphere. We fit mixtures of Kent distributions to different subsets of the hydrogen bond data to gain insight into how the secondary structure elements bond together, since the distribution of hydrogen bonds depends on which secondary structure elements are involved.

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arXiv2018

Gaussian process modeling of heterogeneity and discontinuities using Voronoi tessellations

Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities. The problem of non-stationarity is dealt with by using a combination of Voronoi tessellation to partition the input space, and a separate Gaussian process to model the data on each region of the partitioned space. Our method is highly flexible because we allow the Voronoi cells to form relationships with each other, which can enable non-convex and disconnected regions to be considered. In such problems, identifying the borders between regions is often of great importance and we propose an adaptive sampling method to gain extra information along such borders. The method is illustrated with simulation studies and application to real data.

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arXiv2014

Bayesian Protein Sequence and Structure Alignment

The structure of a protein is crucial in determining its functionality, and is much more conserved than sequence during evolution. A key task in structural biology is to compare protein structures in order to determine evolutionary relationships, estimate the function of newly-discovered structures, and predict unknown structures. We propose a Bayesian method for protein structure alignment, with the prior on alignments based on functions which penalise ``gaps'' in the aligned sequences. We show how a broad class of penalty functions fits into this framework, and how the resulting posterior distribution can be efficiently sampled. A commonly-used gap penalty function is shown to be a special case, and we propose a new penalty function which alleviates an undesirable feature of the commonly-used penalty. We illustrate our method on benchmark data sets, and find it competes well with popular tools from computational biology. Our method has the benefit of being able to potentially explore multiple competing alignments and quantify their merits probabilistically. The framework naturally allows for further information such as amino acid sequence to be included, and could be adapted to other situations such as flexible proteins or domain swaps.

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arXiv2013

Bayesian alignment of similarity shapes

We develop a Bayesian model for the alignment of two point configurations under the full similarity transformations of rotation, translation and scaling. Other work in this area has concentrated on rigid body transformations, where scale information is preserved, motivated by problems involving molecular data; this is known as form analysis. We concentrate on a Bayesian formulation for statistical shape analysis. We generalize the model introduced by Green and Mardia [Biometrika 93 (2006) 235-254] for the pairwise alignment of two unlabeled configurations to full similarity transformations by introducing a scaling factor to the model. The generalization is not straightforward, since the model needs to be reformulated to give good performance when scaling is included. We illustrate our method on the alignment of rat growth profiles and a novel application to the alignment of protein domains. Here, scaling is applied to secondary structure elements when comparing protein folds; additionally, we find that one global scaling factor is not in general sufficient to model these data and, hence, we develop a model in which multiple scale factors can be included to handle different scalings of shape components.

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arXiv2013

The Rate of Convergence for Approximate Bayesian Computation

Approximate Bayesian Computation (ABC) is a popular computational method for likelihood-free Bayesian inference. The term "likelihood-free" refers to problems where the likelihood is intractable to compute or estimate directly, but where it is possible to generate simulated data $X$ relatively easily given a candidate set of parameters $\theta$ simulated from a prior distribution. Parameters which generate simulated data within some tolerance $\delta$ of the observed data $x^*$ are regarded as plausible, and a collection of such $\theta$ is used to estimate the posterior distribution $\theta\,|\,X\!=\!x^*$. Suitable choice of $\delta$ is vital for ABC methods to return good approximations to $\theta$ in reasonable computational time. While ABC methods are widely used in practice, particularly in population genetics, study of the mathematical properties of ABC estimators is still in its infancy. We prove that ABC estimates converge to the exact solution under very weak assumptions and, under slightly stronger assumptions, quantify the rate of this convergence. Our results can be used to guide the choice of the tolerance parameter $\delta$.

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