Survival Analysis &
Diffusion Processes
Anomaly Detection
and Prediction
Publications
For my thesis I studied and modeling latent mechanisms/phenomena that drive an observable process until some endpoint of interest. In survival and reliability analysis such endpoints are typically the time of failure. The data driven statistical nature of these models make them generally applicable across many areas, including finance, economics, medicine, etc.
Stochastic processes are the theoretical foundation for modeling the latent (unobserved) event-causing mechanisms. Parametric and predictive inference equations are developed based on the first hitting times of the stochastic processes to a random/uncertain barrier set (threshold). In addition, modeling also accommodates time dependent covariates, which vary with time, environment, usage, etc., and are used to improve inferences and predictions.
Click here to view a sample matlab prediction plot. The asterisks represent a latent process, and the density curves the conditionally predicticted distribution for the degradation variable.
Previously, I worked with machine learning algorithms for anomaly detection and prediction. I developed a one-class Bayesian support vector machine algorithm to detect the onset of system anomalies,and trend output classification probabilities, as a way to monitor the health of a system. Click here to see a snap-shot of the Bayesian support vector machine matlab tool. This work involved theory on support vector machines, Bayesian linear models, and gaussian processes.
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