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Summary Statistical modelling of functional magnetic resonance imaging data is challenging as the data are both spatially and temporally correlated. Spatially, measurements are taken at thousands of contiguous regions, called voxels, and temporally measurements are taken at hundreds of time points at each voxel. Recent advances in Bayesian hierarchical modelling have addressed the challenges of spatiotemporal structure in functional magnetic resonance imaging data with models incorporating both spatial and temporal priors for signal and noise. Whereas there has been extensive research on modelling the functional magnetic resonance imaging signal (i.e. the convolution of the experimental design with the functional choice for the haemodynamic response function) and its spatial variability, less attention has been paid to realistic modelling of the temporal dependence that typically exists within the functional magnetic resonance imaging noise, where a low order auto-regressive process is typically adopted. Furthermore, the auto-regressive order is held constant across voxels (e.g. AR(1) at each voxel). Motivated by an event-related functional magnetic resonance imaging experiment, we propose a novel hierarchical Bayesian model with automatic selection of the auto-regressive orders of the noise process that vary spatially over the brain. With simulation studies we show that our model is more statistically efficient and we apply it to our motivating example.

SUMMARY Many facets of neuromuscular activation patterns and control can be assessed via electromyography and are important for understanding the control of locomotion. After spinal cord injury, muscle activation patterns can affect locomotor recovery. We present a novel application of reversible jump Markov chain Monte Carlo simulation to estimate activation patterns from electromyographic data. We assume the data to be a zero-mean, heteroscedastic process. The variance is explicity modeled using a step function. The number and location of points of discontinuity, or change-points, in the step function, the inter-changepoint variances, and the overall mean are jointly modeled along with the mean and variance from baseline data. The number of change-points is considered a nuisance parameter and is integrated out of the posterior distribution. Whereas current methods of detecting activation patterns are deterministic or provide only point estimates, ours provides distributional estimates of muscle activation. These estimates, in turn, are used to estimate physiologically relevant quantities such as muscle coactivity, total integrated energy, and average burst duration and to draw valid statistical inferences about these quantities.

To define predictors of survival time in late human immunodeficiency virus type 1 (HIV-1) disease, long- and short-duration survivors were studied after their CD4+ T cells fell to