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Abstract Osteoarthritis (OA) is a chronic condition often associated with pain, affecting approximately fourteen percent of the population, and increasing in prevalence. A globally aging population have made treating OA-associated pain as well as maintaining mobility and activity a public health priority. OA affects all mammals, and the use of spontaneous animal models is one promising approach for improving translational pain research and the development of effective treatment strategies. Accelerometers are a common tool for collecting high-frequency activity data on animals to study the effects of treatment on pain related activity patterns. There has recently been increasing interest in their use to understand treatment effects in human pain conditions. However, activity patterns vary widely across subjects; furthermore, the effects of treatment may manifest in higher or lower activity counts or in subtler ways like changes in the frequency of certain types of activities. We use a zero inflated Poisson hidden semi-Markov model to characterize activity patterns and subsequently derive estimators of the treatment effect in terms of changes in activity levels or frequency of activity type. We demonstrate the application of our model, and its advance over traditional analysis methods, using data from a naturally occurring feline OA-associated pain model. 

We study the problem of sparse signal detection on a spatial domain. We propose a novel approach to model continuous signals that are sparse and piecewise-smooth as the product of independent Gaussian (PING) processes with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of the Gaussian components in the product, and sparsity is controlled by the number of components. The bivariate kurtosis of the PING process implies that more components in the product results in the thicker tail and sharper peak at zero. We develop an efficient computation algorithm based on spectral methods. The simulation results demonstrate superior estimation using the PING prior over Gaussian process prior for different image regressions. We apply our method to a longitudinal magnetic resonance imaging dataset to detect the regions that are affected by multiple sclerosis computation in this domain. Supplementary materials for this article are available online.