arXiv subjects

Theodore Kypraios

Publications and source records attributed to Theodore Kypraios.

At least 19 recordsLinked to original sources

arXiv2026

Neural Posterior Estimation for Stochastic Epidemic Models Using Final Outcome Data

Neural posterior estimation (NPE) is a simulation-based approach to Bayesian inference that trains a neural network to approximate the posterior distribution from simulated parameter - data pairs, bypassing likelihood evaluation. We apply NPE -- to our knowledge for the first time -- to stochastic susceptible-infectious-removed (SIR) epidemic models observed through final outcome data, considering both homogeneously mixing and household-structured populations. Such data arise naturally in retrospective outbreak investigations and household transmission studies, yet inference is computationally challenging: data-augmentation Markov chain Monte Carlo (MCMC) can be slow to mix in large populations and difficult to implement, while Approximate Bayesian Computation (ABC) suffers from low acceptance rates, particularly for large populations or unlikely outcomes. The discrete, low-dimensional nature of such observations makes this setting particularly well suited to NPE. We show that a logNormal posterior approximation, parameterised by a feed-forward neural network, accurately recovers reference posteriors across a range of population sizes and transmission regimes, and extends naturally to joint inference on global and local transmission rates in the household model. Once trained, the network produces approximate posterior distributions in seconds and generalises reliably to population sizes and structures not seen during training. Performance on both synthetic and real outbreak datasets is consistently strong, with results in close agreement with published analyses.

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arXiv2026

Bayesian Inference for Non-Conjugate Distance Dependent Chinese Restaurant Process Models

The distance dependent Chinese Restaurant Process (ddCRP) provides a flexible prior distribution for clustering observations, incorporating covariate information through pairwise distances and accommodating a rich variety of cluster structures. When cluster parameters are conjugate to the likelihood, Bayesian inference is straightforward. In the non-conjugate setting, however, inference becomes substantially more challenging due to the trans-dimensional parameter spaces that arise as cluster assignments change. We develop a reversible jump Markov chain Monte Carlo (RJMCMC) framework to address this challenge, targeting the dimension-changing nature of cluster parameter vectors when observation assignments are updated. We introduce and compare several proposal strategies for birth and death moves, including prior-based, independence, and data-driven moment-matching proposals that target regions of high posterior density. For fixed-dimensional moves, we propose a posterior resampling strategy that improves acceptance rates while maintaining computational efficiency. Through a simulation study and an application to Old Faithful eruption durations, we demonstrate moment-matched proposals offer a principled, data-driven alternative to prior-based proposals. The resulting methodology provides a general RJMCMC framework for ddCRP models with non-conjugate likelihoods, demonstrated here on both discrete and continuous observation models.

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arXiv2025

Estimating the duration of RT-PCR positivity for SARS-CoV-2 from doubly interval censored data with undetected infections

Monitoring the incidence of new infections during a pandemic is critical for an effective public health response. General population prevalence surveys for SARS-CoV-2 can provide high-quality data to estimate incidence. However, estimation relies on understanding the distribution of the duration that infections remain detectable. This study addresses this need using data from the Coronavirus Infection Survey (CIS), a long-term, longitudinal, general population survey conducted in the UK. Analyzing these data presents unique challenges, such as doubly interval censoring, undetected infections, and false negatives. We propose a Bayesian nonparametric survival analysis approach, estimating a discrete-time distribution of durations and integrating prior information derived from a complementary study. Our methodology is validated through a simulation study, including its resilience to model misspecification, and then applied to the CIS dataset. This results in the first estimate of the full duration distribution in a general population, as well as methodology that could be transferred to new contexts.

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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.

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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.

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arXiv2019

Scalable Bayesian Inference for Population Markov Jump Processes

Bayesian inference for Markov jump processes (MJPs) where available observations relate to either system states or jumps typically relies on data-augmentation Markov Chain Monte Carlo. State-of-the-art developments involve representing MJP paths with auxiliary candidate jump times that are later thinned. However, these algorithms are i) unfeasible in situations involving large or infinite capacity systems and ii) not amenable for all observation types. In this paper we establish and present a general data-augmentation framework for population MJPs based on uniformized representations of the underlying non-stationary jump processes. This leads to multiple novel MCMC samplers which enable exact (in the Monte Carlo sense) inference tasks for model parameters. We show that proposed samplers outperform existing popular approaches, and offer substantial efficiency gains in applications to partially observed stochastic epidemics, immigration processes and predator-prey dynamical systems.

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arXiv2019

A comparative study of estimation methods in quantum tomography

As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum likelihood, least squares, generalised least squares, positive least squares, thresholded least squares and projected least squares. The common thread of the analysis is that each estimator projects the measurement data onto a parameter space with respect to a specific metric, thus allowing us to study the relationships between different estimators. The asymptotic behaviour of the least squares and the projected least squares estimators is studied in detail for the case of the covariant measurement and a family of states of varying ranks. This gives insight into the rank-dependent risk reduction for the projected estimator, and uncovers an interesting non-monotonic behaviour of the Bures risk. These asymptotic results complement recent non-asymptotic concentration bounds of \cite{GutaKahnKungTropp} which point to strong optimality properties, and high computational efficiency of the projected linear estimators. To illustrate the theoretical methods we present results of an extensive simulation study. An app running the different estimators has been made available online.

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arXiv2018

On Bayesian inferential tasks with infinite-state jump processes: efficient data augmentation

Advances in sampling schemes for Markov jump processes have recently enabled multiple inferential tasks. However, in statistical and machine learning applications, we often require that these continuous-time models find support on structured and infinite state spaces. In these cases, exact sampling may only be achieved by often inefficient particle filtering procedures, and rapidly augmenting observed datasets remains a significant challenge. Here, we build on the principles of uniformization and present a tractable framework to address this problem, which greatly improves the efficiency of existing state-of-the-art methods commonly used in small finite-state systems, and further scales their use to infinite-state scenarios. We capitalize on the marginal role of variable subsets in a model hierarchy during the process jumps, and describe an algorithm that relies on measurable mappings between pairs of states and carefully designed sets of synthetic jump observations. The proposed method enables the efficient integration of slice sampling techniques and it can overcome the existing computational bottleneck. We offer evidence by means of experiments addressing inference and clustering tasks on both simulated and real data sets.

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arXiv2017

Identification and Estimation of Quantum Linear Input-Output Systems

The system identification problem is to estimate dynamical parameters from the output data, obtained by performing measurements on the output fields. We investigate system identification for quantum linear systems. Our main objectives are to address the following general problems: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realisation from sufficient input-output data? (3) How well can we estimate the parameters governing the dynamics? We investigate these problems in two contrasting approaches; using time-dependent inputs or time-stationary (quantum noise) inputs.

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arXiv2017

Auxiliary Variables for Bayesian Inference in Multi-Class Queueing Networks

Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the present paper, we focus on the underlying continuous-time Markov chains induced by these networks, and we present a flexible method for drawing parameter inference in multi-class Markovian cases with switching and different service disciplines. The approach is directed towards the inferential problem with missing data and introduces a slice sampling technique with mappings to the measurable space of task transitions between service stations. The method deals with time and tractability issues, can handle prior system knowledge and overcomes common restrictions on service rates across existing inferential frameworks. Finally, the proposed algorithm is validated on synthetic data and applied to a real data set, obtained from a service delivery tasking tool implemented in two university hospitals.

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arXiv2017

Bayes factors for partially observed stochastic epidemic models

We consider the problem of model choice for stochastic epidemic models given partial observation of a disease outbreak through time. Our main focus is on the use of Bayes factors. Although Bayes factors have appeared in the epidemic modelling literature before, they can be hard to compute and little attention has been given to fundamental questions concerning their utility. In this paper we derive analytic expressions for Bayes factors given complete observation through time, which suggest practical guidelines for model choice problems. We extend the power posterior method for computing Bayes factors so as to account for missing data and apply this approach to partially observed epidemics. For comparison, we also explore the use of a deviance information criterion for missing data scenarios. The methods are illustrated via examples involving both simulated and real data.

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arXiv2017

Efficient SMC$^2$ schemes for stochastic kinetic models

Fitting stochastic kinetic models represented by Markov jump processes within the Bayesian paradigm is complicated by the intractability of the observed data likelihood. There has therefore been considerable attention given to the design of pseudo-marginal Markov chain Monte Carlo algorithms for such models. However, these methods are typically computationally intensive, often require careful tuning and must be restarted from scratch upon receipt of new observations. Sequential Monte Carlo (SMC) methods on the other hand aim to efficiently reuse posterior samples at each time point. Despite their appeal, applying SMC schemes in scenarios with both dynamic states and static parameters is made difficult by the problem of particle degeneracy. A principled approach for overcoming this problem is to move each parameter particle through a Metropolis-Hastings kernel that leaves the target invariant. This rejuvenation step is key to a recently proposed SMC$^2$ algorithm, which can be seen as the pseudo-marginal analogue of an idealised scheme known as iterated batch importance sampling. Computing the parameter weights in SMC$^2$ requires running a particle filter over dynamic states to unbiasedly estimate the intractable observed data likelihood contributions at each time point. In this paper, we propose to use an auxiliary particle filter inside the SMC$^2$ scheme. Our method uses two recently proposed constructs for sampling conditioned jump processes and we find that the resulting inference schemes typically require fewer state particles than when using a simple bootstrap filter. Using two applications, we compare the performance of the proposed approach with various competing methods, including two global MCMC schemes.

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arXiv2017

Bayesian nonparametrics for stochastic epidemic models

The vast majority of models for the spread of communicable diseases are parametric in nature and involve underlying assumptions about how the disease spreads through a population. In this article we consider the use of Bayesian nonparametric approaches to analysing data from disease outbreaks. Specifically we focus on methods for estimating the infection process in simple models under the assumption that this process has an explicit time-dependence.

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arXiv2017

A rare event approach to high dimensional Approximate Bayesian computation

Approximate Bayesian computation (ABC) methods permit approximate inference for intractable likelihoods when it is possible to simulate from the model. However they perform poorly for high dimensional data, and in practice must usually be used in conjunction with dimension reduction methods, resulting in a loss of accuracy which is hard to quantify or control. We propose a new ABC method for high dimensional data based on rare event methods which we refer to as RE-ABC. This uses a latent variable representation of the model. For a given parameter value, we estimate the probability of the rare event that the latent variables correspond to data roughly consistent with the observations. This is performed using sequential Monte Carlo and slice sampling to systematically search the space of latent variables. In contrast standard ABC can be viewed as using a more naive Monte Carlo estimate. We use our rare event probability estimator as a likelihood estimate within the pseudo-marginal Metropolis-Hastings algorithm for parameter inference. We provide asymptotics showing that RE-ABC has a lower computational cost for high dimensional data than standard ABC methods. We also illustrate our approach empirically, on a Gaussian distribution and an application in infectious disease modelling.

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arXiv2016

Modelling and Bayesian analysis of the Abakaliki Smallpox Data

The celebrated Abakaliki smallpox data have appeared numerous times in the epidemic modelling literature, but in almost all cases only a specific subset of the data is considered. There is one previous analysis of the full data set, but this relies on approximation methods to derive a likelihood. The data themselves continue to be of interest due to concerns about the possible re-emergence of smallpox as a bioterrorism weapon. We present the first full Bayesian analysis using data-augmentation Markov chain Monte Carlo methods which avoid the need for likelihood approximations. Results include estimates of basic model parameters as well as reproduction numbers and the likely path of infection. Model assessment is carried out using simulation-based methods.

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arXiv2016

Evaluating hospital infection control measures for antimicrobial-resistant pathogens using stochastic transmission models: application to Vancomycin-Resistant Enterococci in intensive care units

Nosocomial pathogens such as Methicillin-Resistant {\em Staphylococcus aureus} (MRSA) and Vancomycin-resistant {\em Enterococci} (VRE) are the cause of significant morbidity and mortality among hospital patients. It is important to be able to assess the efficacy of control measures using data on patient outcomes. In this paper we describe methods for analysing such data using patient-level stochastic models which seek to describe the underlying unobserved process of transmission. The methods are applied to detailed longitudinal patient-level data on VRE from a study in a US hospital with eight intensive care units (ICUs). The data comprise admission and discharge dates, dates and results of screening tests, and dates during which precautionary measures were in place for each patient during the study period. Results include estimates of the efficacy of the control measures, the proportion of unobserved patients colonized with VRE and the proportion of patients colonized on admission.

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arXiv2016

Bayesian model choice via mixture distributions with application to epidemics and population process models

We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the Bayes factors. Our motivation is the setting where the observed data are a partially observed realisation of a stochastic population process, although the methods have far wider applicability. The methods allow for missing data and for parameters to be shared between models. Illustrative examples including epidemics, population processes and regression models are given, showing that the methods are competitive compared to existing approaches.

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arXiv2015

Reconstructing transmission trees for communicable diseases using densely sampled genetic data

Whole genome sequencing of pathogens from multiple hosts in an epidemic offers the potential to investigate who infected whom with unparalleled resolution, potentially yielding important insights into disease dynamics and the impact of control measures. We considered disease outbreaks in a setting with dense genomic sampling, and formulated stochastic epidemic models to investigate person-to-person transmission, based on observed genomic and epidemiological data. We constructed models in which the genetic distance between sampled genotypes depends on the epidemiological relationship between the hosts. A data augmented Markov chain Monte Carlo algorithm was used to sample over the transmission trees, providing a posterior probability for any given transmission route. We investigated the predictive performance of our methodology using simulated data, demonstrating high sensitivity and specificity, particularly for rapidly mutating pathogens with low transmissibility. We then analyzed data collected during an outbreak of methicillin-resistant Staphylococcus aureus in a hospital, identifying probable transmission routes and estimating epidemiological parameters. Our approach overcomes limitations of previous methods, providing a framework with the flexibility to allow for unobserved infection times, multiple independent introductions of the pathogen, and within-host genetic diversity, as well as allowing forward simulation.

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