arXiv subjects

Richard J. Boys

Publications and source records attributed to Richard J. Boys.

12 recordsLinked to original sources

arXiv2020

Parameter inference for a stochastic kinetic model of expanded polyglutamine proteins

The presence of protein aggregates in cells is a known feature of many human age-related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutamine (PolyQ) proteins in cells have been used to gain a better understanding of the biological system, how to focus drug development and how to construct more efficient designs of future laboratory-based in vitro experiments. However, there is considerable uncertainty about the values of some of the parameters governing the system. Currently, appropriate values are chosen by ad hoc attempts to tune the parameters so that the model output matches experimental data. The problem is further complicated by the fact that the data only offer a partial insight into the underlying biological process: the data consist only of the proportions of cell death and of cells with inclusion bodies at a few time points, corrupted by measurement error. Developing inference procedures to estimate the model parameters in this scenario is a significant task. The model probabilities corresponding to the observed proportions cannot be evaluated exactly and so they are estimated within the inference algorithm by repeatedly simulating realisations from the model. In general such an approach is computationally very expensive and we therefore construct Gaussian process emulators for the key quantities and reformulate our algorithm around these fast stochastic approximations. We conclude by examining the fit of our model and highlight appropriate values of the model parameters leading to new insights into the underlying biological processes such as the kinetics of aggregation.

stat.AP↗

arXiv2020

On Bayesian inference for the Extended Plackett-Luce model

The analysis of rank ordered data has a long history in the statistical literature across a diverse range of applications. In this paper we consider the Extended Plackett-Luce model that induces a flexible (discrete) distribution over permutations. The parameter space of this distribution is a combination of potentially high-dimensional discrete and continuous components and this presents challenges for parameter interpretability and also posterior computation. Particular emphasis is placed on the interpretation of the parameters in terms of observable quantities and we propose a general framework for preserving the mode of the prior predictive distribution. Posterior sampling is achieved using an effective simulation based approach that does not require imposing restrictions on the parameter space. Working in the Bayesian framework permits a natural representation of the posterior predictive distribution and we draw on this distribution to address the rank aggregation problem and also to identify potential lack of model fit. The flexibility of the Extended Plackett-Luce model along with the effectiveness of the proposed sampling scheme are demonstrated using several simulation studies and real data examples.

stat.AP↗

arXiv2019

Generalising rate heterogeneity across sites in statistical phylogenetics

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate matrix. Early models assumed the same rate matrix governed substitutions at all sites of the alignment, ignoring variation in evolutionary pressures. Substantial improvements in phylogenetic inference and model fit were achieved by augmenting these models with multiplicative random effects that describe the result of variation in selective constraints and allow sites to evolve at different rates which linearly scale a baseline rate matrix. Motivated by this pioneering work, we consider an extension using a quadratic, rather than linear, transformation. The resulting models allow for variation in the selective coefficients of different types of point mutation at a site in addition to variation in selective constraints. We derive properties of the extended models. For certain non-stationary processes, the extension gives a model that allows variation in sequence composition both across sites and taxa. We adopt a Bayesian approach, describe an MCMC algorithm for posterior inference and provide software. Our quadratic models are applied to alignments spanning the tree of life and compared with site-homogeneous and linear models.

stat.ME↗

arXiv2018

Revealing subgroup structure in ranked data using a Bayesian WAND

Ranked data arise in many areas of application ranging from the ranking of up-regulated genes for cancer to the ranking of academic statistics journals. Complications can arise when rankers do not report a full ranking of all entities; for example, they might only report their top--$M$ ranked entities after seeing some or all entities. It can also be useful to know whether rankers are equally informative, and whether some entities are effectively judged to be exchangeable. When there is important subgroup structure in the data, summaries such as aggregate (overall) rankings can be misleading. In this paper we propose a flexible Bayesian nonparametric model for identifying heterogeneous structure and ranker reliability in ranked data. The model is a Weighted Adapted Nested Dirichlet (WAND) process mixture of Plackett-Luce models and inference proceeds through a simple and efficient Gibbs sampling scheme for posterior sampling. The richness of information in the posterior distribution allows us to infer many details of the structure both between ranker groups and between entity groups (within ranker groups), in contrast to many other (Bayesian) analyses. We also examine how posterior predictive checks can be used to identify lack of model fit. The methodology is illustrated using several simulation studies and real data examples.

stat.ME↗

arXiv2018

Efficient construction of Bayes optimal designs for stochastic process models

Stochastic process models are now commonly used to analyse complex biological, ecological and industrial systems. Increasingly there is a need to deliver accurate estimates of model parameters and assess model fit by optimizing the timing of measurement of these processes. Standard methods to construct Bayes optimal designs, such as the well known \Muller algorithm, are computationally intensive even for relatively simple models. A key issue is that, in determining the merit of a design, the utility function typically requires summaries of many parameter posterior distributions, each determined via a computer-intensive scheme such as MCMC. This paper describes a fast and computationally efficient scheme to determine optimal designs for stochastic process models. The algorithm compares favourably with other methods for determining optimal designs and can require up to an order of magnitude fewer utility function evaluations for the same accuracy in the optimal design solution. It benefits from being embarrassingly parallel and is ideal for running on multi-core computers. The method is illustrated by determining different sized optimal designs for three problems of increasing complexity.

stat.CO↗

arXiv2018

On the ranking of Test match batsmen

Ranking sportsmen whose careers took place in different eras is often a contentious issue and the topic of much debate. In this paper we focus on cricket and examine what conclusions may be drawn about the ranking of Test batsmen using data on batting scores from the first Test in 1877 onwards. The overlapping nature of playing careers is exploited to form a bridge from past to present so that all players can be compared simultaneously, rather than just relative to their contemporaries. The natural variation in runs scored by a batsman is modelled by an additive log-linear model with year, age and cricket-specific components used to extract the innate ability of an individual cricketer. Incomplete innings are handled via censoring and a zero-inflated component is incorporated into the model to allow for an excess of frailty at the start of an innings. The innings-by-innings variation of runs scored by each batsman leads to uncertainty in their ranking position. A Bayesian approach is used to fit the model and realisations from the posterior distribution are obtained by deploying a Markov Chain Monte Carlo algorithm. Posterior summaries of innate player ability are then used to assess uncertainty in ranking position and this is contrasted with rankings determined via the posterior mean runs scored. Posterior predictive checks show that the model provides a reasonably accurate description of runs scored.

stat.AP↗

arXiv2018

Bayesian inference for a partially observed birth-death process using data on proportions

Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have measurements on all interacting chemical species in the process, observed continuously in time. However, in practice, measurements are taken only at a relatively few time-points. In some situations, only very limited observation of the process is available, such as when experimenters can only observe noisy observations on the proportion of cells that are alive. This makes the inference task even more problematic. We consider a range of data-poor scenarios and investigate the performance of various computationally intensive Bayesian algorithms in determining the posterior distribution using data on proportions from a simple birth-death process.

stat.CO↗

arXiv2016

Bayesian inference for diffusion driven mixed-effects models

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units, SDE driven mixed-effects models allow the quantification of between (as well as within) individual variation. Performing Bayesian inference for such models, using discrete time data that may be incomplete and subject to measurement error is a challenging problem and is the focus of this paper. We extend a recently proposed MCMC scheme to include the SDE driven mixed-effects framework. Fundamental to our approach is the development of a novel construct that allows for efficient sampling of conditioned SDEs that may exhibit nonlinear dynamics between observation times. We apply the resulting scheme to synthetic data generated from a simple SDE model of orange tree growth, and real data consisting of observations on aphid numbers recorded under a variety of different treatment regimes. In addition, we provide a systematic comparison of our approach with an inference scheme based on a tractable approximation of the SDE, that is, the linear noise approximation.

stat.CO↗

arXiv2016

Improved bridge constructs for stochastic differential equations

We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an Itô stochastic differential equation conditional on an observation taken at a fixed future time-point. Such realisations are typically termed diffusion bridges. Since, in general, no closed form expression exists for the transition densities of the process of interest, a widely adopted solution works with the Euler-Maruyama approximation, by replacing the intractable transition densities with Gaussian approximations. However, the density of the conditioned discrete-time process remains intractable, necessitating the use of computationally intensive methods such as Markov chain Monte Carlo. Designing an efficient proposal mechanism which can be applied to a noisy and partially observed system that exhibits nonlinear dynamics is a challenging problem, and is the focus of this paper. By partitioning the process into two parts, one that accounts for nonlinear dynamics in a deterministic way, and another as a residual stochastic process, we develop a class of novel constructs that bridge the residual process via a linear approximation. In addition, we adapt a recently proposed construct to a partial and noisy observation regime. We compare the performance of each new construct with a number of existing approaches, using three applications.

stat.CO↗

arXiv2014

Bayesian identification of protein differential expression in multi-group isobaric labelled mass spectrometry data

In this paper we develop a Bayesian statistical inference approach to the unified analysis of isobaric labelled MS/MS proteomic data across multiple experiments. An explicit probabilistic model of the log-intensity of the isobaric labels' reporter ions across multiple pre-defined groups and experiments is developed. This is then used to develop a full Bayesian statistical methodology for the identification of differentially expressed proteins, with respect to a control group, across multiple groups and experiments. This methodology is implemented and then evaluated on simulated data and on two model experimental datasets (for which the differentially expressed proteins are known) that use a TMT labelling protocol.

stat.AP↗

arXiv2013

Inference for population dynamics in the Neolithic period

We consider parameter estimation for the spread of the Neolithic incipient farming across Europe using radiocarbon dates. We model the arrival time of farming at radiocarbon-dated, early Neolithic sites by a numerical solution to an advancing wavefront. We allow for (technical) uncertainty in the radiocarbon data, lack-of-fit of the deterministic model and use a Gaussian process to smooth spatial deviations from the model. Inference for the parameters in the wavefront model is complicated by the computational cost required to produce a single numerical solution. We therefore employ Gaussian process emulators for the arrival time of the advancing wavefront at each radiocarbon-dated site. We validate our model using predictive simulations.

stat.AP↗

arXiv2012

Bayesian inference for a wavefront model of the Neolithisation of Europe

We consider a wavefront model for the spread of Neolithic culture across Europe, and use Bayesian inference techniques to provide estimates for the parameters within this model, as constrained by radiocarbon data from Southern and Western Europe. Our wavefront model allows for both an isotropic background spread (incorporating the effects of local geography), and a localized anisotropic spread associated with major waterways. We introduce an innovative numerical scheme to track the wavefront, and use Gaussian process emulators to further increase the efficiency of our model, thereby making Markov chain Monte Carlo methods practical. We allow for uncertainty in the fit of our model, and discuss the inferred distribution of the parameter specifying this uncertainty, along with the distributions of the parameters of our wavefront model. We subsequently use predictive distributions, taking account of parameter uncertainty, to identify radiocarbon sites which do not agree well with our model. These sites may warrant further archaeological study, or motivate refinements to the model.

physics.bio-ph↗