Nosocomial, or hospital-acquired, infections are a key determinant of patient health in healthcare facilities, leading to longer stays and increased mortality. In addition to the direct effects on infected patients, the burden imposed by nosocomial infections impacts both staff and other patients by increasing the load on the healthcare system. The appropriate infection control response may differ depending on whether the infection was acquired in the hospital or the community. For example, nosocomial outbreaks may require ward closures to reduce the risk of onward transmission, whilst this may not be an appropriate response to repeated importations of infections from outside the facility. Unfortunately, it is often unclear whether an infection detected in a healthcare facility is nosocomial, as the time of infection is unobserved. Given this, there is a strong case for the development of models that can integrate multiple datasets available in hospitals to assess whether an infection detected in a hospital is nosocomial. When assessing nosocomiality, it is beneficial to take into account both whether the timing of infection is consistent with hospital acquisition and whether there are any likely candidates within the hospital who could have been the source of the infection. In this work, we developed a Bayesian model which jointly estimates whether a given infection detected in hospital is nosocomial and whether it came from a set of individuals identified as candidates by hospital staff. The model coherently integrates pathogen genetic information, the timings of epidemiological events, such as symptom onset, and location data on the infected patient and candidate infectors. We illustrated this model on a real hospital dataset showing both its output and how the impact of the different data sources on the assessed probabilities are contingent on what other data has been included in the model, and validated the calibration of the predictions against simulated data.

Likelihood-free inference methods based on neural conditional density estimation were shown to drastically reduce the simulation burden in comparison to classical methods such as ABC. When applied in the context of any latent variable model, such as a Hidden Markov model (HMM), these methods are designed to only estimate the parameters, rather than the joint distribution of the parameters and the hidden states. Naive application of these methods to a HMM, ignoring the inference of this joint posterior distribution, will thus produce an inaccurate estimate of the posterior predictive distribution, in turn hampering the assessment of goodness-of-fit. To rectify this problem, we propose a novel, sample-efficient likelihood-free method for estimating the high-dimensional hidden states of an implicit HMM. Our approach relies on learning directly the intractable posterior distribution of the hidden states, using an autoregressive-flow, by exploiting the Markov property. Upon evaluating our approach on some implicit HMMs, we found that the quality of the estimates retrieved using our method is comparable to what can be achieved using a much more computationally expensive SMC algorithm.

Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe, mechanistically, changes in extrinsic environmental factors including public behaviour and seasonal fluctuations. An elegant approach to capturing environmental stochasticity is to model the force of infection as a stochastic process. However, inference in this context requires solving a computationally expensive "missing data" problem, using data-augmentation techniques. We propose to model the time-varying transmission-potential as an approximate diffusion process using a path-wise series expansion of Brownian motion. This approximation replaces the "missing data" imputation step with the inference of the expansion coefficients: a simpler and computationally cheaper task. We illustrate the merit of this approach through three examples: modelling influenza using a canonical SIR model, capturing seasonality using a SIRS model, and the modelling of COVID-19 pandemic using a multi-type SEIR model.

By invoking a pathwise series expansion of Brownian motion, we propose to approximate a stochastic differential equation (SDE) with an ordinary differential equation (ODE). This allows us to reformulate Bayesian inference for a SDE as the parameter estimation task for an ODE. Unlike a nonlinear SDE, the likelihood for an ODE model is tractable and its gradient can be obtained using adjoint sensitivity analysis. This reformulation allows us to use an efficient sampler, such as NUTS, that rely on the gradient of the log posterior. Applying the reparameterisation trick, variational inference can also be used for the same estimation task. We illustrate the proposed method on a variety of SDE models. We obtain similar parameter estimates when compared to data augmentation techniques.

We apply the reparameterisation trick to obtain a variational formulation of Bayesian inference in nonlinear ODE models. By invoking the linear noise approximation we also extend this variational formulation to a stochastic kinetic model. Our proposed inference method does not depend on any emulation of the ODE solution and only requires the extension of automatic differentiation to an ODE. We achieve this through a novel and holistic approach that uses both forward and adjoint sensitivity analysis techniques. Consequently, this approach can cater to both small and large ODE models efficiently. Upon benchmarking on some widely used mechanistic models, the proposed inference method produced a reliable approximation to the posterior distribution, with a significant reduction in execution time, in comparison to MCMC.

Public sequence databases contain information on the sequence, structure and function of proteins. Genome sequencing projects have led to a rapid increase in protein sequence information, but reliable, experimentally verified, information on protein function lags a long way behind. To address this deficit, functional annotation in protein databases is often inferred by sequence similarity to homologous, annotated proteins, with the attendant possibility of error. Now, the functional annotation in these homologous proteins may itself have been acquired through sequence similarity to yet other proteins, and it is generally not possible to determine how the functional annotation of any given protein has been acquired. Thus the possibility of chains of misannotation arises, a process we term 'error percolation'. With some simple assumptions, we develop a dynamical probabilistic model for these misannotation chains. By exploring the consequences of the model for annotation quality it is evident that this iterative approach leads to a systematic deterioration of database quality.