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Sensor systems, such as modern wind tunnels, require continual monitoring to validate their quality, as corrupted data will increase both experimental downtime and budget and lead to inconclusive scientific and engineering results. One approach to validate sensor quality is monitoring individual sensor measurements' distribution. Although, in general settings, we do not know how to correct measurements should be distributed for each sensor system. Instead of monitoring sensors individually, our approach relies on monitoring the co-variation of the entire network of sensor measurements, both within and across sensor systems. That is, by monitoring how sensors behave, relative to each other, we can detect anomalies expeditiously. Previous monitoring methodologies, such as those based on Principal Component Analysis, can be heavily influenced by extremely outlying sensor anomalies. We propose two Bayesian mixture model approaches that utilize heavy-tailed Cauchy assumptions. First, we propose a Robust Bayesian Regression, which utilizes a scale-mixture model to induce a Cauchy regression. Second, we extend elements of the Robust Bayesian Regression methodology using additive mixture models that decompose the anomalous and non-anomalous sensor readings into two parametric compartments. Specifically, we use a non-local, heavy-tailed Cauchy component for isolating the anomalous sensor readings, which we refer to as the Modified Cauchy Net. / Doctor of Philosophy / Sensor systems, such as modern wind tunnels, require continual monitoring to validate their quality, as corrupted data will increase both experimental downtime and budget and lead to inconclusive scientific and engineering results. One approach to validate sensor quality is monitoring individual sensor measurements' distribution. Although, in general settings, we do not know how to correct measurements should be distributed for each sensor system. Instead of monitoring sensors individually, our approach relies on monitoring the co-variation of the entire network of sensor measurements, both within and across sensor systems. That is, by monitoring how sensors behave, relative to each other, we can detect anomalies expeditiously. We proposed two Bayesian monitoring approaches called the Robust Bayesian Regression and Modified Cauchy Net, which provide flexible, tunable models for detecting anomalous sensors with the historical data containing anomalous observations.

We live in the data explosion era. The unprecedented amount of data offers a potential wealth of knowledge but also brings about concerns regarding ethical collection and usage. Mistakes stemming from anomalous data have the potential for severe, real-world consequences, such as when building prediction models for housing prices. To combat anomalies, we develop the Cauchy-Net Mixture Model (CNMM). The CNMM is a flexible Bayesian nonparametric tool that employs a mixture between a Dirichlet Process Mixture Model (DPMM) and a Cauchy distributed component, which we call the Cauchy-Net (CN). Each portion of the model offers benefits, as the DPMM eliminates the limitation of requiring a fixed number of a components and the CN captures observations that do not belong to the well-defined components by leveraging its heavy tails. Through isolating the anomalous observations in a single component, we simultaneously identify the observations in the net as warranting further inspection and prevent them from interfering with the formation of the remaining components. The result is a framework that allows for simultaneously clustering observations and making predictions in the face of the anomalous data. We demonstrate the usefulness of the CNMM in a variety of experimental situations and apply the model for predicting housing prices in Fairfax County, Virginia. / Doctor of Philosophy / We live in the data explosion era. The unprecedented amount of data offers a potential wealth of knowledge but also brings about concerns regarding ethical collection and usage. Mistakes stemming from anomalous data have the potential for severe, real-world consequences, such as when building prediction models for housing prices. To combat anomalies, we develop the Cauchy-Net Mixture Model (CNMM). The CNMM is a flexible tool for identifying and isolating the anomalies, while simultaneously discovering cluster structure and making predictions among the nonanomalous observations. The result is a framework that allows for simultaneously clustering and predicting in the face of the anomalous data. We demonstrate the usefulness of the CNMM in a variety of experimental situations and apply the model for predicting housing prices in Fairfax County, Virginia.