arXiv subjects

Sarah E. Heaps

Publications and source records attributed to Sarah E. Heaps.

9 recordsLinked to original sources

arXiv2026

Habitual lifestyle timing explains circadian timing, but daily lifestyle changes do not, in free-living humans across 2000 days

Background: Both between- and within-subject variations in circadian timing matter for health. If lifestyle changes could be used to regulate circadian timing, they would offer accessible and scalable routes to chronotherapy, but this link remains unclear under real-life conditions. Here, we explore how lifestyle 'traits' (such as typical wake time) and 'states' (day-to-day deviations from traits, such as waking up later than typical) explain between- and within-subject variation in acrophase (peak time) of the circadian rhythm of heart rate (CRHR). Methods: We collected free-living wearable data (smartwatch, continuous glucose monitor) from healthy volunteers for up to 4 weeks. The CRHR was derived from activity-adjusted heart rate, and acrophase was defined as time-of-day at daily CRHR peak. Sleep, food, and physical activity 'factors' were calculated and split into traits and states. Using a linear mixed-effects model, we tested how traits and states associate with between- and within-subject acrophase variance. Findings: Data from 105 healthy volunteers (66 female, age = 42.5 $\pm$ 15.7 years) spanning ~2000 days (18.8 $\pm$ 8.30 days each) were analysed. Traits were substantially more influential than states, explaining 42.3% versus 0.9% of total acrophase variance. Accordingly, traits explained 86.5% of between-subject variance, whereas states explained only 1.8% of within-subject variance. Sleep, food and physical activity factors contributed both jointly and uniquely, and lifestyle timing mattered most. Interpretation: Between-subject lifestyle traits explained acrophase better than within-subject lifestyle states. This asymmetry, alongside the considerable overlap between factors, supports sustained, holistic, timing-focused lifestyle adjustments as chronotherapy targets, testable through future interventional studies.

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arXiv2026

Bayesian inference of sparsity in stable vector autoregressive processes

Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be learned from these data. To this end, graphical vector autoregressions are a popular tool because zeros among the autoregressive coefficients and error precision matrix have natural interpretations in terms of Granger non-causality and contemporaneous conditional independence. In applications where system dynamics are subject to functional or structural constraints, assuming the process is stable can be advantageous. However, enforcing stability demands restricting the autoregressive coefficients to lie in a constrained space with a complex geometry called the stationary region. The resulting inferential challenges are compounded when sparsity is also a requirement. Working in the Bayesian paradigm, we tackle the problem of developing a prior that simultaneously enforces stationarity and sparsity through parameter expansion, constructing a spike-and-slab prior with support constrained to the stationary region. A mixture of G-Wishart distributions provides a sparse prior for the error precision matrix. Computational inference is carried out using Metropolis-within-Gibbs, exploiting the No-U-Turn Sampler and reversible-jump steps. We demonstrate the inferential and predictive benefits of our approach through simulations and applications in macroeconomics and neuroscience.

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arXiv2025

Nested ensemble Kalman filter for static parameter inference in nonlinear state-space models

The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e. particle filters), the EnKF leverages either the linear Gaussian structure of the SSM or an approximation thereof, to maintain diversity of the sampled latent states (the so-called ensemble members) via shifting-based updates. Joint parameter and state inference using an EnKF is typically achieved by augmenting the state vector with the static parameter. In this case, it is assumed that both parameters and states follow a linear Gaussian state-space model, which may be unreasonable in practice. In this paper, we combine the reweighting and shifting methods by replacing the particle filter used in the SMC^2 algorithm of Chopin et al. (2013), with the ensemble Kalman filter. Hence, parameter particles are weighted according to the estimated observed-data likelihood from the latest observation computed by the EnKF, and particle diversity is maintained via a resample-move step that targets the marginal parameter posterior under the EnKF. Extensions to the resulting algorithm are proposed, such as the use of a delayed acceptance kernel in the rejuvenation step and incorporation of nonlinear observation models. We illustrate the resulting methodology via several applications.

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arXiv2023

Bayesian inference on the order of stationary vector autoregressions

Vector autoregressions (VARs) are a widely used tool for modelling multivariate time-series. It is common to assume a VAR is stationary; this can be enforced by imposing the stationarity condition which restricts the parameter space of the autoregressive coefficients to the stationary region. However, implementing this constraint is difficult due to the complex geometry of the stationary region. Fortunately, recent work has provided a solution for autoregressions of fixed order $p$ based on a reparameterization in terms of a set of interpretable and unconstrained transformed partial autocorrelation matrices. In this work, focus is placed on the difficult problem of allowing $p$ to be unknown, developing a prior and computational inference that takes full account of order uncertainty. Specifically, the multiplicative gamma process is used to build a prior which encourages increasing shrinkage of the partial autocorrelations with increasing lag. Identifying the lag beyond which the partial autocorrelations become equal to zero then determines $p$. Based on classic time-series theory, a principled choice of truncation criterion identifies whether a partial autocorrelation matrix is effectively zero. Posterior inference utilizes Hamiltonian Monte Carlo via Stan. The work is illustrated in a substantive application to neural activity data to investigate ultradian brain rhythms.

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arXiv2022

Enforcing stationarity through the prior in vector autoregressions

Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient matrices to lie in the stationary region. However, the stationary region has a highly complex geometry which impedes specification of a prior distribution. In this work, an unconstrained reparameterization of a stationary vector autoregression is presented. The new parameters are partial autocorrelation matrices, which are interpretable, and can be transformed bijectively to the space of unconstrained square matrices through a simple mapping of their singular values. This transformation preserves various structural forms of the partial autocorrelation matrices and readily facilitates specification of a prior. Properties of this prior are described along with an important special case which is exchangeable with respect to the order of the elements in the observation vector. Posterior inference and computation are described and implemented using Hamiltonian Monte Carlo via Stan. The prior and inferential procedures are illustrated with an application to a macroeconomic time series which highlights the benefits of enforcing stationarity and encouraging shrinkage towards a sensible parametric structure. Supplementary materials for this article are available in the ancillary files section.

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arXiv2021

A sparse Bayesian hierarchical vector autoregressive model for microbial dynamics in a wastewater treatment plant

Proper function of a wastewater treatment plant (WWTP) relies on maintaining a delicate balance between a multitude of competing microorganisms. Gaining a detailed understanding of the complex network of interactions therein is essential to maximising not only current operational efficiencies, but also for the effective design of new treatment technologies. Metagenomics offers an insight into these dynamic systems through the analysis of the microbial DNA sequences present. Unique taxa are inferred through sequence clustering to form operational taxonomic units (OTUs), with per-taxa abundance estimates obtained from corresponding sequence counts. The data in this study comprise weekly OTU counts from an activated sludge (AS) tank of a WWTP. To model the OTU dynamics, we develop a Bayesian hierarchical vector autoregressive model, which is a linear approximation to the commonly used generalised Lotka-Volterra (gLV) model. To tackle the high dimensionality and sparsity of the data, they are first clustered into 12 "bins" using a seasonal phase-based approach. The autoregressive coefficient matrix is assumed to be sparse, so we explore different shrinkage priors by analysing simulated data sets before selecting the regularised horseshoe prior for the biological application. We find that ammonia and chemical oxygen demand have a positive relationship with several bins and pH has a positive relationship with one bin. These results are supported by findings in the biological literature. We identify several negative interactions, which suggests OTUs in different bins may be competing for resources and that these relationships are complex. We also identify two positive interactions. Although simpler than a gLV model, our vector autoregression offers valuable insight into the microbial dynamics of the WWTP.

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arXiv2020

Incorporating compositional heterogeneity into Lie Markov models for phylogenetic inference

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard models assume is time-reversible and stationary. These assumptions are biologically questionable and induce a likelihood function which is invariant to a tree's root position. This hampers inference because a tree's biological interpretation depends critically on where it is rooted. Relaxing both assumptions, we introduce a model whose likelihood can distinguish between rooted trees. The model is non-stationary, with step changes in the instantaneous rate matrix at each speciation event. Exploiting recent theoretical work, each rate matrix belongs to a non-reversible family of Lie Markov models. These models are closed under matrix multiplication, so our extension offers the conceptually appealing property that a tree and all its sub-trees could have arisen from the same family of non-stationary models. We adopt a Bayesian approach, describe an MCMC algorithm for posterior inference and provide software. The biological insight that our model can provide is illustrated through an analysis in which non-reversible but stationary, and non-stationary but reversible models cannot identify a plausible root.

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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.

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arXiv2018

Identifying the effect of public holidays on daily demand for gas

To reduce operational costs, gas distribution networks require accurate forecasts of the demand for gas. Amongst domestic and commercial customers, demand relates primarily to the weather and patterns of life and work. Public holidays have a pronounced effect which often spreads into neighbouring days. We call this spread the "proximity effect". Traditionally, the days over which the proximity effect is felt are pre-specified in fixed windows around each holiday, allowing no uncertainty in their identification. We are motivated by an application to modelling daily gas demand in two large British regions. We introduce a novel model which does not fix the days on which the proximity effect is felt. Our approach uses a four-state, non-homogeneous hidden Markov model, with cyclic dynamics, where the classification of days as public holidays is observed, but the assignment of days as "pre-holiday", "post-holiday" or "normal" is unknown. The number of days to the preceding and succeeding holidays guide transitions between states. We apply Bayesian inference and illustrate the benefit of our modelling approach. A preliminary version of the model is now being used by one of the UK's regional distribution networks.

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