arXiv subjects

Darren J. Wilkinson

Publications and source records attributed to Darren J. Wilkinson.

12 recordsLinked to original sources

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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arXiv2026

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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arXiv2024

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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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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arXiv2017

A Network Epidemic Model for Online Community Commissioning Data

A statistical model assuming a preferential attachment network, which is generated by adding nodes sequentially according to a few simple rules, usually describes real-life networks better than a model assuming, for example, a Bernoulli random graph, in which any two nodes have the same probability of being connected, does. Therefore, to study the propogation of "infection" across a social network, we propose a network epidemic model by combining a stochastic epidemic model and a preferential attachment model. A simulation study based on the subsequent Markov Chain Monte Carlo algorithm reveals an identifiability issue with the model parameters. Finally, the network epidemic model is applied to a set of online commissioning data.

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arXiv2016

Online state and parameter estimation in Dynamic Generalised Linear Models

Inference for streaming time-series is tightly coupled with the problem of Bayesian on-line state and parameter inference. In this paper we will introduce Dynamic Generalised Linear Models, the class of models often chosen to model continuous and discrete time-series data. We will look at three different approaches which allow on-line estimation and analyse the results when applied to different real world datasets related to inference for streaming data. Sufficient statistics based methods delay known problems, such as particle impoverishment, especially when applied to long running time-series, while providing reasonable parameter estimations when compared to exact methods, such as Particle Marginal Metropolis-Hastings. State and observation forecasts will also be analysed as a performance metric. By benchmarking against a "gold standard" (off-line) method, we can better understand the performance of on-line methods in challenging real-world scenarios.

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arXiv2015

Bayesian hierarchical modelling for inferring genetic interactions in yeast

Quantitative Fitness Analysis (QFA) is a high-throughput experimental and computational methodology for measuring the growth of microbial populations. QFA screens can be used to compare the health of cell populations with and without a mutation in a query gene in order to infer genetic interaction strengths genome-wide, examining thousands of separate genotypes. We introduce Bayesian, hierarchical models of population growth rates and genetic interactions that better reflect QFA experimental design than current approaches. Our new approach models population dynamics and genetic interaction simultaneously, thereby avoiding passing information between models via a univariate fitness summary. Matching experimental structure more closely, Bayesian hierarchical approaches use data more efficiently and find new evidence for genes which interact with yeast telomeres within a published dataset.

q-bio.QM↗

arXiv2014

Scalable Inference for Markov Processes with Intractable Likelihoods

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo (MCMC) techniques can lead to exact inference in such models but in practice can suffer performance issues including long burn-in periods and poor mixing. On the other hand approximate Bayesian computation techniques can allow rapid exploration of a large parameter space but yield only approximate posterior distributions. Here we consider the combined use of approximate Bayesian computation (ABC) and MCMC techniques for improved computational efficiency while retaining exact inference on parallel hardware.

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arXiv2014

Likelihood free inference for Markov processes: a comparison

Approaches to Bayesian inference for problems with intractable likelihoods have become increasingly important in recent years. Approximate Bayesian computation (ABC) and "likelihood free" Markov chain Monte Carlo techniques are popular methods for tackling inference in these scenarios but such techniques are computationally expensive. In this paper we compare the two approaches to inference, with a particular focus on parameter inference for stochastic kinetic models, widely used in systems biology. Discrete time transition kernels for models of this type are intractable for all but the most trivial systems yet forward simulation is usually straightforward. We discuss the relative merits and drawbacks of each approach whilst considering the computational cost implications and efficiency of these techniques. In order to explore the properties of each approach we examine a range of observation regimes using two example models. We use a Lotka--Volterra predator prey model to explore the impact of full or partial species observations using various time course observations under the assumption of known and unknown measurement error. Further investigation into the impact of observation error is then made using a Schlögl system, a test case which exhibits bi-modal state stability in some regions of parameter space.

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arXiv2014

Bayesian inference for Markov jump processes with informative observations

In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis.

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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.

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arXiv2013

Fast Bayesian parameter estimation for stochastic logistic growth models

The transition density of a stochastic, logistic population growth model with multiplicative intrinsic noise is analytically intractable. Inferring model parameter values by fitting such stochastic differential equation (SDE) models to data therefore requires relatively slow numerical simulation. Where such simulation is prohibitively slow, an alternative is to use model approximations which do have an analytically tractable transition density, enabling fast inference. We introduce two such approximations, with either multiplicative or additive intrinsic noise, each derived from the linear noise approximation of the logistic growth SDE. After Bayesian inference we find that our fast LNA models, using Kalman filter recursion for computation of marginal likelihoods, give similar posterior distributions to slow arbitrarily exact models. We also demonstrate that simulations from our LNA models better describe the characteristics of the stochastic logistic growth models than a related approach. Finally, we demonstrate that our LNA model with additive intrinsic noise and measurement error best describes an example set of longitudinal observations of microbial population size taken from a typical, genome-wide screening experiment.

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