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

Augmented Reality in Higher Education: a Case Study in Medical Education

During lockdown, we piloted a variety of augmented reality (AR) experiences in collaboration with subject matter experts from different fields aiming at creating remote teaching and training experiences. In this paper, we present a case study on how AR can be used as a teaching aid for medical education with pertinent focus on remote and social distanced learning. We describe the process of creating an AR experience that can enhance the knowledge and understanding of anatomy for medical students. The Anatomy Experience is an AR enhanced learning experience developed in collaboration with the Medical School of the University of Edinburgh aiming to assist medical students understand the complex geometry of different parts of the human body. After conducting a focus group study with medical students, trainees, and trainers, we received very positive feedback on the Anatomy Experience and its effects on understanding anatomy, enriching the learning process, and using it as a tool for anatomy teaching.Comment: 4 pages, 2 figures, 9th International Conference of the Immersive Learning Research Network (iLRN2023

Efficiency of delayed-acceptance random walk Metropolis algorithms

Delayed-acceptance Metropolis-Hastings (DA-MH) and delayed-acceptance pseudo-marginal Metropolis-Hastings (DAPsMMH) 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. We focus on the random walk Metropolis (RWM) and consider the DAPsMRWM, of which the DARWM is a special case. We provide a framework for incorporating relatively general deterministic approximations into the theoretical analysis of high-dimensional targets. Then, justified by a limiting diffusion argument, we develop theoretical expressions for limiting efficiency and acceptance rates in high dimension. The results provide insight into the effect of the accuracy of the deterministic approximation, the scale of the RWM jump and the nature of the stochastic approximation on the efficiency of the delayed acceptance algorithm. The predicted properties are verified against simulation studies, all of which are strictly outside of the domain of validity of our limit results. The theory also informs a practical strategy for algorithm tuning

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 It\^o 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.Comment: 29 page

Adaptive, delayed-acceptance MCMC for targets with expensive likelihoods

When conducting Bayesian inference, delayed acceptance (DA) Metropolis-Hastings (MH) algorithms and DA pseudo-marginal MH algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased estimate thereof, but a computationally cheap approximation is available. A first accept-reject stage is applied, with the cheap approximation substituted for the true posterior in the MH acceptance ratio. Only for those proposals which pass through the first stage is the computationally expensive true posterior (or unbiased estimate thereof) evaluated, with a second accept-reject stage ensuring that detailed balance is satisfied with respect to the intended true posterior. In some scenarios there is no obvious computationally cheap approximation. A weighted average of previous evaluations of the computationally expensive posterior provides a generic approximation to the posterior. If only the k-nearest neighbours have non-zero weights then evaluation of the approximate posterior can be made computationally cheap provided that the points at which the posterior has been evaluated are stored in a multi-dimensional binary tree, known as a KD-tree. The contents of the KD-tree are potentially updated after every computationally intensive evaluation. The resulting adaptive, delayed-acceptance [pseudo-marginal] Metropolis-Hastings algorithm is justified both theoretically and empirically. Guidance on tuning parameters is provided and the methodology is applied to a discretely observed Markov jump process characterising predator-prey interactions and an ODE system describing the dynamics of an autoregulatory gene network

The Cellular Composition of the Uveal Immune Environment

The uveal tract consists of the iris, the ciliary body and the choroid; these three distinct tissues form a continuous layer within the eye. Uveitis refers to inflammation of any region of the uveal tract. Despite being grouped together anatomically, the iris, ciliary body and choroid are distinct functionally, and inflammatory diseases may affect only one part and not the others. Cellular structure of tissues direct their function, and understanding the cellular basis of the immune environment of a tissue in health, the "steady state" on which the perturbations of disease are superimposed, is vital to understanding the pathogenesis of those diseases. A contemporary understanding of the immune system accepts that haematopoietic and yolk sac derived leukocytes, though vital, are not the only players of importance. An array of stromal cells, connective tissue cells such as fibroblasts and endothelial cells, may also have a role in the inflammatory reaction seen in several immune-mediated diseases. In this review we summarise what is known about the cellular composition of the uveal tract and the roles these disparate cell types have to play in immune homeostasis. We also discuss some unanswered questions surrounding the constituents of the resident leukocyte population of the different uveal tissues, and we look ahead to the new understanding that modern investigative techniques such as single cell transcriptomics, multi-omic data integration and highly-multiplexed imaging techniques may bring to the study of the uvea and uveitis, as they already have to other immune mediated inflammatory diseases