There is rich literature on the state estimation of wireless sensor networks (WSNs). Most of these works are based on the dynamic state-space model via Kalman filter or similar Markov models. In any network, information exchange is inevitable, and in this paper, we propose a Bayesian non-parametric approach for addressing this issue in the context of state estimation of WSNs. We consider a cluster-based WSN and consider a discrete-time linear Markov model for estimating the state values of the sensor nodes over time. For measuring the amount of information shared by the model parameters across different clusters, we consider non-parametric matrix stick-breaking priors for the cluster-specific model parameters. We demonstrate the usefulness of our proposed model in locating an immobile anomalous node in the network. We compute the time to locate the anomalous object and the false positive rate of our proposed approach. Simulation studies are performed to assess the operating characteristics of the proposed model. The proposed approach will be useful in emergency monitoring, medical genetics, geosciences, and many other disciplines where WSNs are frequently used for decision making.

MOTIVATION: Despite their success in identifying genes that affect complex disease or traits, current genome-wide association studies (GWASs) based on a single SNP analysis are too simple to elucidate a comprehensive picture of the genetic architecture of phenotypes. A simultaneous analysis of a large number of SNPs, although statistically challenging, especially with a small number of samples, is crucial for genetic modeling. METHOD: We propose a two-stage procedure for multi-SNP modeling and analysis in GWASs, by first producing a 'preconditioned' response variable using a supervised principle component analysis and then formulating Bayesian lasso to select a subset of significant SNPs. The Bayesian lasso is implemented with a hierarchical model, in which scale mixtures of normal are used as prior distributions for the genetic effects and exponential priors are considered for their variances, and then solved by using the Markov chain Monte Carlo (MCMC) algorithm. Our approach obviates the choice of the lasso parameter by imposing a diffuse hyperprior on it and estimating it along with other parameters and is particularly powerful for selecting the most relevant SNPs for GWASs, where the number of predictors exceeds the number of observations. RESULTS: The new approach was examined through a simulation study. By using the approach to analyze a real dataset from the Framingham Heart Study, we detected several significant genes that are associated with body mass index (BMI). Our findings support the previous results about BMI-related SNPs and, meanwhile, gain new insights into the genetic control of this trait. AVAILABILITY: The computer code for the approach developed is available at Penn State Center for Statistical Genetics web site, http://statgen.psu.edu.