arXiv subjects

Andrew Golightly

Publications and source records attributed to Andrew Golightly.

At least 19 recordsLinked to original sources

arXiv2026

Robust, partially alive particle Metropolis-Hastings via the Frankenfilter

When a hidden Markov model permits the conditional likelihood of an observation given the hidden process to be zero, all particle simulations from one observation time to the next could produce zeros. If so, the filtering distribution cannot be estimated and the estimated parameter likelihood is zero. The alive particle filter addresses this by simulating a random number of particles for each inter-observation interval, stopping after a target number of non-zero conditional likelihoods. For outlying observations or poor parameter values, a non-zero result can be extremely unlikely, and computational costs prohibitive. We introduce the Frankenfilter, a principled, partially alive particle filter that targets a user-defined amount of success whilst fixing lower and upper bounds on the number of simulations. The Frankenfilter produces unbiased estimators of the likelihood, suitable for pseudo-marginal Metropolis--Hastings (PMMH). We demonstrate that PMMH with the Frankenfilter is more robust to outliers and mis-specified initial parameter values than PMMH using standard particle filters, and is typically at least 2-3 times more efficient. We also provide advice for choosing the amount of success. In the case of n exact observations, this is particularly simple: target n successes.

stat.ME↗

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.

stat.CO↗

arXiv2025

Reaction-diffusion models of invasive tree pest spread: quantifying the expansion of oak processionary moth in the UK

UK woodlands, forests, and urban treescapes are under threat from invasive species, exacerbated by climate change, trade, and transport. Invasive tree pests debilitate their host and disrupt forest ecosystems, thus it is imperative to quantitatively model and predict their spread. Addressing this, we model the spread of an invasive pest using a spatiotemporal reaction-diffusion equation, representing the spatial distribution as a population density field. We solve this intractable equation numerically and, from the solution, we determine first arrival times of the pest at locations in the field. The adopted model permits us to obtain the expansion rate of pest spread directly from the model parameters, which we infer in the Bayesian paradigm, using a Markov chain Monte Carlo scheme. We apply our framework to the ongoing spread of oak processionary moth in the UK, an outbreak which continues to grow despite management efforts. We demonstrate that our approach effectively captures the spread of the pest and that this has occurred at a non-constant expansion rate. The proposed framework is a powerful tool for quantitatively modelling the spread of an invasive tree pest and could underpin future prediction and management approaches.

q-bio.PE↗

arXiv2025

Simulation-based inference using splitting schemes for partially observed diffusions in chemical reaction networks

We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This is challenging for two main reasons. First, the (multi-dimensional) SDEs cannot be explicitly solved and are driven by multiplicative and non-commutative noise, requiring the development of advanced numerical schemes for their approximation and simulation. Second, not all components of the SDEs are directly observed, as the available discrete-time data are typically incomplete and/or perturbed with measurement error. We tackle these issues via three contributions. First, we show that these models can be rewritten as perturbed conditionally Cox-Ingersoll-Ross-type SDEs, i.e., each coordinate, conditioned on all other coordinates being fixed, follows an SDE with linear drift and square root diffusion coefficient perturbed by additional Brownian motions. Second, for this class of SDEs, we develop a numerical splitting scheme that preserves structural properties of the model, such as oscillations, state space and invariant distributions, unlike the commonly used Euler-Maruyama scheme. Our numerical method is robust for large integration time steps. Third, we propose a sequential Monte Carlo approximate Bayesian computation algorithm incorporating "data-conditional" simulation and sequential learning of summary statistics, allowing inference for multidimensional partially observed systems, further developing previous results on fully observed systems based on the Euler-Maruyama scheme. We validate our approach on models of interest in chemical reaction networks, such as the stochastic Repressilator, Lotka-Volterra, and two-pool systems, demonstrating its effectiveness, in terms of both numerical and inferential accuracy, and reduced computational cost.

stat.ME↗

arXiv2024

Towards Data-Conditional Simulation for ABC Inference in Stochastic Differential Equations

We develop a Bayesian inference method for discretely-observed stochastic differential equations (SDEs). Inference is challenging for most SDEs, due to the analytical intractability of the likelihood function. Nevertheless, forward simulation via numerical methods is straightforward, motivating the use of approximate Bayesian computation (ABC). We propose a conditional simulation scheme for SDEs that is based on lookahead strategies for sequential Monte Carlo (SMC) and particle smoothing using backward simulation. This leads to the simulation of trajectories that are consistent with the observed trajectory, thereby increasing the ABC acceptance rate. We additionally employ an invariant neural network, previously developed for Markov processes, to learn the summary statistics function required in ABC. The neural network is incrementally retrained by exploiting an ABC-SMC sampler, which provides new training data at each round. Since the SDEs simulation scheme differs from standard forward simulation, we propose a suitable importance sampling correction, which has the added advantage of guiding the parameters towards regions of high posterior density, especially in the first ABC-SMC round. Our approach achieves accurate inference and is about three times faster than standard (forward-only) ABC-SMC. We illustrate our method in five simulation studies, including three examples from the Chan-Karaolyi-Longstaff-Sanders SDE family, a stochastic bi-stable model (Schl{ö}gl) that is notoriously challenging for ABC methods, and a two dimensional biochemical reaction network.

stat.ME↗

arXiv2024

Sequential Bayesian inference for stochastic epidemic models of cumulative incidence

Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time window, a continuous-time discrete-valued Markov process provides a natural description of the dynamics of each model component, typically taken to be the number of susceptible, exposed, infected or removed individuals. Fitting the SEIR model to time-course data is a challenging problem due incomplete observations and, consequently, the intractability of the observed data likelihood. Whilst sampling based inference schemes such as Markov chain Monte Carlo are routinely applied, their computational cost typically restricts analysis to data sets of no more than a few thousand infective cases. Instead, we develop a sequential inference scheme that makes use of a computationally cheap approximation of the most natural Markov process model. Crucially, the resulting model allows a tractable conditional parameter posterior which can be summarised in terms of a set of low dimensional statistics. This is used to rejuvenate parameter samples in conjunction with a novel bridge construct for propagating state trajectories conditional on the next observation of cumulative incidence. The resulting inference framework also allows for stochastic infection and reporting rates. We illustrate our approach using synthetic and real data applications.

stat.ME↗

arXiv2023

Accelerating Bayesian inference for stochastic epidemic models using incidence data

We consider the case of performing Bayesian inference for stochastic epidemic compartment models, using incomplete time course data consisting of incidence counts that are either the number of new infections or removals in time intervals of fixed length. We eschew the most natural Markov jump process representation for reasons of computational efficiency, and focus on a stochastic differential equation representation. This is further approximated to give a tractable Gaussian process, that is, the linear noise approximation (LNA). Unless the observation model linking the LNA to data is both linear and Gaussian, the observed data likelihood remains intractable. It is in this setting that we consider two approaches for marginalising over the latent process: a correlated pseudo-marginal method and analytic marginalisation via a Gaussian approximation of the observation model. We compare and contrast these approaches using synthetic data before applying the best performing method to real data consisting of removal incidence of oak processionary moth nests in Richmond Park, London. Our approach further allows comparison between various competing compartment models.

stat.CO↗

arXiv2023

Using extreme value theory to evaluate the leading pedestrian interval road safety intervention

Improving road safety is hugely important with the number of deaths on the world's roads remaining unacceptably high; an estimated 1.35 million people die each year as a result of road traffic collisions (WHO, 2020). Current practice for treating collision hotspots is almost always reactive: once a threshold level of collisions has been overtopped during some pre-determined observation period, treatment is applied (e.g. road safety cameras). Traffic collisions are rare, so prolonged observation periods are necessary. However, traffic conflicts are more frequent and are a margin of the social cost; hence, traffic conflict before/after studies can be conducted over shorter time periods. We investigate the effect of implementing the leading pedestrian interval (LPI) treatment (Van Houten et al. 2000) at signalised intersections as a safety intervention in a city in north America. Pedestrian-vehicle traffic conflict data were collected from treatment and control sites during the before and after periods. We implement a before/after study on post-encroachment times (PETs) where small PET values denote a near-miss. Hence, extreme value theory is employed to model extremes of our PET processes, with adjustments to the usual modelling framework to account for temporal dependence and treatment effects.

stat.AP↗

arXiv2023

Accelerating inference for stochastic kinetic models

Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are modelled using a continuous-time stochastic process, and, depending on the application area of interest, this will typically take the form of a Markov jump process or an Itô diffusion process. Widespread use of these models is typically precluded by their computational complexity. In particular, performing exact fully Bayesian inference in either modelling framework is challenging due to the intractability of the observed data likelihood, necessitating the use of computationally intensive techniques such as particle Markov chain Monte Carlo (particle MCMC). It is proposed to increase the computational and statistical efficiency of this approach by leveraging the tractability of an inexpensive surrogate derived directly from either the jump or diffusion process. The surrogate is used in three ways: in the design of a gradient-based parameter proposal, to construct an appropriate bridge and in the first stage of a delayed-acceptance step. The resulting approach, which exactly targets the posterior of interest, offers substantial gains in efficiency over a standard particle MCMC implementation.

stat.CO↗

arXiv2023

Bayesian inference for a spatio-temporal model of road traffic collision data

Improving road safety is hugely important with the number of deaths on the world's roads remaining unacceptably high; an estimated 1.35 million people die each year (WHO, 2020). Current practice for treating collision hotspots is almost always reactive: once a threshold level of collisions has been exceeded during some predetermined observation period, treatment is applied (e.g. road safety cameras). However, more recently, methodology has been developed to predict collision counts at potential hotspots in future time periods, with a view to a more proactive treatment of road safety hotspots. Dynamic linear models provide a flexible framework for predicting collisions and thus enabling such a proactive treatment. In this paper, we demonstrate how such models can be used to capture both seasonal variability and spatial dependence in time course collision rates at several locations. The model allows for within- and out-of-sample forecasting for locations which are fully observed and for locations where some data are missing. We illustrate our approach using collision rate data from 8 Traffic Administration Zones in North Florida, USA, and find that the model provides a good description of the underlying process and reasonable forecast accuracy.

stat.AP↗

arXiv2022

Exact Bayesian inference for discretely observed Markov Jump Processes using finite rate matrices

We present new methodologies for Bayesian inference on the rate parameters of a discretely observed continuous-time Markov jump processes with a countably infinite state space. The usual method of choice for inference, particle Markov chain Monte Carlo (particle MCMC), struggles when the observation noise is small. We consider the most challenging regime of exact observations and provide two new methodologies for inference in this case: the minimal extended state space algorithm (MESA) and the nearly minimal extended state space algorithm (nMESA). By extending the Markov chain Monte Carlo state space, both MESA and nMESA use the exponentiation of finite rate matrices to perform exact Bayesian inference on the Markov jump process even though its state space is countably infinite. Numerical experiments show improvements over particle MCMC of between a factor of three and several orders of magnitude.

stat.CO↗

arXiv2021

Augmented pseudo-marginal Metropolis-Hastings for partially observed diffusion processes

We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying Itô stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our starting point is a state-of-the-art correlated pseudo-marginal Metropolis-Hastings algorithm, that uses correlated particle filters to induce strong and positive correlation between successive likelihood estimates. However, unless the measurement error or the dimension of the SDE is small, correlation can be eroded by the resampling steps in the particle filter. We therefore propose a novel augmentation scheme, that allows for conditioning on values of the latent process at the observation times, completely avoiding the need for resampling steps. We integrate over the uncertainty at the observation times with an additional Gibbs step. Connections between the resulting pseudo-marginal scheme and existing inference schemes for diffusion processes are made, giving a unified inference framework that encompasses Gibbs sampling and pseudo marginal schemes. The methodology is applied in three examples of increasing complexity. We find that our approach offers substantial increases in overall efficiency, compared to competing methods.

stat.CO↗

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.

stat.AP↗

arXiv2021

The Neural Moving Average Model for Scalable Variational Inference of State Space Models

Variational inference has had great success in scaling approximate Bayesian inference to big data by exploiting mini-batch training. To date, however, this strategy has been most applicable to models of independent data. We propose an extension to state space models of time series data based on a novel generative model for latent temporal states: the neural moving average model. This permits a subsequence to be sampled without drawing from the entire distribution, enabling training iterations to use mini-batches of the time series at low computational cost. We illustrate our method on autoregressive, Lotka-Volterra, FitzHugh-Nagumo and stochastic volatility models, achieving accurate parameter estimation in a short time.

stat.ML↗

arXiv2021

Efficiency of delayed-acceptance random walk Metropolis algorithms

Delayed-acceptance Metropolis-Hastings and delayed-acceptance pseudo-marginal Metropolis-Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation thereof, but a computationally cheap deterministic approximation is available. An initial accept-reject stage uses the cheap approximation for computing the Metropolis-Hastings ratio; proposals which are accepted at this stage are then subjected to a further accept-reject step which corrects for the error in the approximation. Since the expensive posterior, or the approximation thereof, is only evaluated for proposals which are accepted at the first stage, the cost of the algorithm is reduced and larger scalings may be used. We focus on the random walk Metropolis (RWM) and consider the delayed-acceptance RWM and the delayed-acceptance pseudo-marginal RWM. We provide a framework for incorporating relatively general deterministic approximations into the theoretical analysis of high-dimensional targets. Justified by diffusion approximation arguments, we derive expressions for the limiting efficiency and acceptance rates in high-dimensional settings. These theoretical insights are finally leveraged to formulate practical guidelines for the efficient tuning of the algorithms. The robustness of these guidelines and predicted properties are verified against simulation studies, all of which are strictly outside of the domain of validity of our limit results.

math.ST↗

arXiv2021

Efficient inference for stochastic differential equation mixed-effects models using correlated particle pseudo-marginal algorithms

Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units and, optionally, account for measurement error. Fully Bayesian inference for state-space SDEMEMs is performed, using data at discrete times that may be incomplete and subject to measurement error. However, the inference problem is complicated by the typical intractability of the observed data likelihood which motivates the use of sampling-based approaches such as Markov chain Monte Carlo. A Gibbs sampler is proposed to target the marginal posterior of all parameter values of interest. The algorithm is made computationally efficient through careful use of blocking strategies and correlated pseudo-marginal Metropolis-Hastings steps within the Gibbs scheme. The resulting methodology is flexible and is able to deal with a large class of SDEMEMs. The methodology is demonstrated on three case studies, including tumor growth dynamics and neuronal data. The gains in terms of increased computational efficiency are model and data dependent, but unless bespoke sampling strategies requiring analytical derivations are possible for a given model, we generally observe an efficiency increase of one order of magnitude when using correlated particle methods together with our blocked-Gibbs strategy.

stat.CO↗

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↗

arXiv2019

Ensemble MCMC: Accelerating Pseudo-Marginal MCMC for State Space Models using the Ensemble Kalman Filter

Particle Markov chain Monte Carlo (pMCMC) is now a popular method for performing Bayesian statistical inference on challenging state space models (SSMs) with unknown static parameters. It uses a particle filter (PF) at each iteration of an MCMC algorithm to unbiasedly estimate the likelihood for a given static parameter value. However, pMCMC can be computationally intensive when a large number of particles in the PF is required, such as when the data is highly informative, the model is misspecified and/or the time series is long. In this paper we exploit the ensemble Kalman filter (EnKF) developed in the data assimilation literature to speed up pMCMC. We replace the unbiased PF likelihood with the biased EnKF likelihood estimate within MCMC to sample over the space of the static parameter. On a wide class of different non-linear SSM models, we demonstrate that our new ensemble MCMC (eMCMC) method can significantly reduce the computational cost whilst maintaining reasonable accuracy. We also propose several extensions of the vanilla eMCMC algorithm to further improve computational efficiency. Computer code to implement our methods on all the examples can be downloaded from https://github.com/cdrovandi/Ensemble-MCMC.

stat.CO↗