Spatial data relating to non-overlapping areal units are prevalent in fields such as economics, environmental science, epidemiology and social science, and a large suite of modeling tools have been developed for analysing these data. Many utilize conditional autoregressive (CAR) priors to capture the spatial autocorrelation inherent in these data, and software packages such as CARBayes and R-INLA have been developed to make these models easily accessible to others. Such spatial data are typically available for multiple time periods, and the development of methodology for capturing temporally changing spatial dynamics is the focus of much current research. A sizeable proportion of this literature has focused on extending CAR priors to the spatio-temporal domain, and this article presents the R package CARBayesST, which is the first dedicated software package for spatio-temporal areal unit modeling with conditional autoregressive priors. The software package allows to fit a range of models focused on different aspects of spacetime modeling, including estimation of overall space and time trends, and the identification of clusters of areal units that exhibit elevated values. This paper outlines the class of models that the software package implement, before applying them to simulated and two real examples from the fields of epidemiology and housing market analysis.

Subjects with a diagnosis of schizophrenia (Scz) overweight unexpected evidence in probabilistic inference: such evidence becomes "aberrantly salient." A neurobiological explanation for this effect is that diminished synaptic gain (e.g., hypofunction of cortical NMDARs) in Scz destabilizes quasi-stable neuronal network states (or "attractors"). This attractor instability account predicts that (1) Scz would overweight unexpected evidence but underweight consistent evidence, (2) belief updating would be more vulnerable to stochastic fluctuations in neural activity, and (3) these effects would correlate. Hierarchical Bayesian belief updating models were tested in two independent datasets ( = 80 male and = 167 female) comprising human subjects with Scz, and both clinical and nonclinical controls (some tested when unwell and on recovery) performing the "probability estimates" version of the beads task (a probabilistic inference task). Models with a standard learning rate, or including a parameter increasing updating to "disconfirmatory evidence," or a parameter encoding belief instability were formally compared. The "belief instability" model (based on the principles of attractor dynamics) had most evidence in all groups in both datasets. Two of four parameters differed between Scz and nonclinical controls in each dataset: belief instability and response stochasticity. These parameters correlated in both datasets. Furthermore, the clinical controls showed similar parameter distributions to Scz when unwell, but were no different from controls once recovered. These findings are consistent with the hypothesis that attractor network instability contributes to belief updating abnormalities in Scz, and suggest that similar changes may exist during acute illness in other psychiatric conditions. Subjects with a diagnosis of schizophrenia (Scz) make large adjustments to their beliefs following unexpected evidence, but also smaller adjustments than controls following consistent evidence. This has previously been construed as a bias toward "disconfirmatory" information, but a more mechanistic explanation may be that in Scz, neural firing patterns ("attractor states") are less stable and hence easily altered in response to both new evidence and stochastic neural firing. We model belief updating in Scz and controls in two independent datasets using a hierarchical Bayesian model, and show that all subjects are best fit by a model containing a belief instability parameter. Both this and a response stochasticity parameter are consistently altered in Scz, as the unstable attractor hypothesis predicts.

Population-level disease risk across a set of non-overlapping areal units varies in space and time, and a large research literature has developed methodology for identifying clusters of areal units exhibiting elevated risks. However, almost no research has extended the clustering paradigm to identify groups of areal units exhibiting similar temporal disease trends. We present a novel Bayesian hierarchical mixture model for achieving this goal, with inference based on a Metropolis-coupled Markov chain Monte Carlo ((MC)$^3$) algorithm. The effectiveness of the (MC)$^3$ algorithm compared to a standard Markov chain Monte Carlo implementation is demonstrated in a simulation study, and the methodology is motivated by two important case studies in the United Kingdom. The first concerns the impact on measles susceptibility of the discredited paper linking the measles, mumps, and rubella vaccination to an increased risk of Autism and investigates whether all areas in the Scotland were equally affected. The second concerns respiratory hospitalizations and investigates over a 10 year period which parts of Glasgow have shown increased, decreased, and no change in risk.

An article published in 1998 by Andrew Wakefield in The Lancet (volume 351, pages 637-641) led to concerns surrounding the safety of the measles, mumps and rubella vaccine, by associating it with an increased risk of autism. The paper was later retracted after multiple epidemiological studies failed to find any association, but a substantial decrease in UK vaccination rates was observed in the years following publication. This paper proposes a novel spatio-temporal Bayesian hierarchical model with accompanying software (the R package CARBayesST) to simultaneously address three key epidemiological questions about vaccination rates: (i) what impact did the controversy have on the overall temporal trend in vaccination rates in Scotland; (ii) did the magnitude of the spatial inequality in measles susceptibility in Scotland increase due to the measles, mumps and rubella vaccination scare; and (iii) are there any covariate effects, such as deprivation, that impacted on measles susceptibility in Scotland. The efficacy of the model is tested by simulation, before being applied to measles susceptibility data in Scotland among a series of cohorts of children who were aged 2.5-4.5, in September of the years 1998 to 2014.

Air pollution continues to be a key health issue in Scotland, despite recent improvements in concentrations. The Scottish Government published the Cleaner Air For Scotland strategy in 2015, and will introduce Low Emission Zones (LEZs) in the four major cities (Aberdeen, Dundee, Edinburgh and Glasgow) by 2020. However, there is no epidemiological evidence quan-* Corresponding author -Duncan Lee, lar disease; and (ii) reducing concentrations in city centres with low resident populations only provides a small health benefit.