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Cardiovascular disease (CVD) is the most common cause of death in industrialized countries. One underlying cause is atherosclerosis, which is a systemic disease characterized by plaques of retained lipids, inflammatory cells, apoptotic cells, calcium and extracellular matrix (ECM) proteins in the arterial wall. The biologic composition of an atherosclerotic plaque determines whether the plaque is more or less vulnerable, that is prone to rupture or erosion. Here, the ECM and tissue repair play an important role in plaque stability, vulnerability and progression. This review will focus on ECM remodelling in atherosclerotic plaques, with focus on how ECM biomarkers might predict plaque vulnerability and outcome.

Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism, environmental noise, serial correlation and dependence on time varying factors. This paper addresses these issues via suitable Bayesian modelling. In doing so we utilise a general class of stochastic regression models appropriate for spatio-temporal count data with an excess number of zeros. The developed regression framework does incorporate serial correlation and time varying covariates through an Ornstein Uhlenbeck process formulation. In addition, we explore the effect of different priors, including default options and variations of mixtures of g-priors. The effect of different distance kernels for the epidemic model component is investigated. We proceed by developing branching process-based methods for testing scenarios for disease control, thus linking traditional epidemiological models with stochastic epidemic processes, useful in policy-focused decision making. The approach is illustrated with an application to a sheep pox dataset from the Evros region, Greece.

We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a nontrivial likelihood given the latent path. Due to the non-Markovian and high-dimensional nature of the latent path, estimating posterior expectations is computationally challenging. We present a reparameterization framework based on the Davies and Harte method for sampling stationary Gaussian processes and use it to construct a Markov chain Monte Carlo algorithm that allows computationally efficient Bayesian inference. The algorithm is based on a version of hybrid Monte Carlo simulation that delivers increased efficiency when used on the high-dimensional latent variables arising in this context. We specify the methodology on a stochastic volatility model, allowing for memory in the volatility increments through a fractional specification. The method is demonstrated on simulated data and on the S&P 500/VIX time series. In the latter case, the posterior distribution favours values of the Hurst parameter smaller than 1/2 , pointing towards medium-range dependence.

Evaluation of large‐scale intervention programmes against human immunodeficiency virus (HIV) is becoming increasingly important, but impact estimates frequently hinge on knowledge of changes in behaviour such as the frequency of condom use over time, or other self‐reported behaviour changes, for which we generally have limited or potentially biased data. We employ a Bayesian inference methodology that incorporates an HIV transmission dynamics model to estimate condom use time trends from HIV prevalence data. Estimation is implemented via particle Markov chain Monte Carlo methods, applied for the first time in this context. The preliminary choice of the formulation for the time varying parameter reflecting the proportion of condom use is critical in the context studied, because of the very limited amount of condom use and HIV data available. We consider various novel formulations to explore the trajectory of condom use over time, based on diffusion‐driven trajectories and smooth sigmoid curves. Numerical simulations indicate that informative results can be obtained regarding the amplitude of the increase in condom use during an intervention, with good levels of sensitivity and specificity performance in effectively detecting changes. The application of this method to a real life problem demonstrates how it can help in evaluating HIV interventions based on a small number of prevalence estimates, and it opens the way to similar applications in different contexts.