Browsing by Subject "stochastic"
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Item Design of Wastewater Ponds Based on Stochastic Storage Analysis(University of Texas at Austin, 1989-02) Al-Omari, K.A.; Buchberger, S.G.Item Modeling Space-Time Data Using Stochastic Differential Equations(2009) Duan, Jason A.; Gelfand, Alan E.; Sirmans, C. F.; Duan, Jason A.This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic differential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that affords meaningful interpretation for the results of statistical inference. Other applications of stochastic logistic differential equations with space-time varying parameters include modeling population growth and product diffusion, which motivate our first, point-referenced data application. We propose a method to discretize both time and space in order to fit the model. We demonstrate the inference for the geostatistical model through a simulated dataset. Then, we fit the Cox process model to a real dataset taken from the greater Dallas metropolitan area.Item A new strategy for management and reconfiguration of self-contained power systems(IEEE, 2006-07) Davey, K.R.; Hebner, R.E.Power systems on naval vessels and airplanes are good examples of self-contained power systems. These types of systems are useful for testing reconfiguration, particularly ones that might be implemented continuously, not just under compromised conditions. Determining the best operating condition in real time is challenging, since it discourages stochastic approaches. A fixed grid representation of the dynamic loads is recommended, employing a phasor algorithm to update the load impedances. A new subspace approach for solving the reconfiguration is presented and compared to branch and bound algorithms. Reconfiguration is studied for a test system with 16 million switch options. Also discussed is how this information can be used in the design of the power grid a priori.Item Reliability of Stochastic Models: Generating Hydrologic Series(University of Texas at Austin, 1980-01) Gan, T.Y.; Beard, L.R.Item A Tractable State-Space Model for Symmetric Positive-Definite Matrices(2014-12) Windle, Jesse; Carvalho, Carlos M.; Carvalho, Carlos M.The Bayesian analysis of a state-space model includes computing the posterior distribution of the system's parameters as well as its latent states. When the latent states wander around R-n there are several well-known modeling components and computational tools that may be profitably combined to achieve this task. When the latent states are constrained to a strict subset of R-n these models and tools are either impaired or break down completely. State-space models whose latent states are covariance matrices arise in finance and exemplify the challenge of devising tractable models in the constrained setting. To that end, we present a state-space model whose observations and latent states take values on the manifold of symmetric positive-definite matrices and for which one may easily compute the posterior distribution of the latent states and the system's parameters as well as filtered distributions and one-step ahead predictions. Employing the model within the context of finance, we show how one can use realized covariance matrices as data to predict latent time-varying covariance matrices. This approach out-performs factor stochastic volatility.