Browsing by Subject "Stochastic approximation"
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Item Checking the censored two-sample accelerated life model using integrated cumulative hazard difference(Texas Tech University, 2004-08) Lee, Seung-HwanIn this dissertation, soma lack-of-fit tests will be discussed for the censored two-sample accelerated life model. Conventional scale estimators with two-sample censored data such as rank-based estimators and minimum distance estimators have difficulties to apply easily due to the fact that their asymptotic variances involve the unknown density, or they require soma strict conditions. The object of this work is to provide an asymptotically equivalent martingale-based stochastic process of some estimating functions, which is easier to apply than existing methods from the literature. An extreme value of the observed process compared with simulated realizations of the approximation process would indicate the model misspecifications. The approximation process involving the martingale structure can be achieved through some approximation procedures of the observed process under the two-sample scale model. The p-value applied to the approximation of the observed process leads to the construction of the lack-of-fit tests. Comparison of the processes enables one to get some information visually from the graph about how the model is misspecified.Item Deterministic approximations in stochastic programming with applications to a class of portfolio allocation problems(2001-08) Dokov, Steftcho Pentchev; Morton, David P.Optimal decision making under uncertainty involves modeling stochastic systems and developing solution methods for such models. The need to incorporate randomness in many practical decision-making problems is prompted by the uncertainties associated with today’s fast-paced technological environment. The complexity of the resulting models often exceeds the capabilities of commercially available optimization software, and special purpose solution techniques are required. Three main categories of solution approaches exist for attacking a particular stochastic programming instance. These are: large-scale mathematical programming algorithms, Monte-Carlo sampling-based techniques, and deterministically valid bound-based approximations. This research contributes to the last category. First, second-order lower and upper bounds are developed on the expectation of a convex function of a random vector. Here, a “second-order bound” means that only the first and second moments of the underlying random parameters are needed to compute the bound. The vector’s random components are assumed to be independent and to have bounded support contained in a hyper-rectangle. Applications to stochastic programming test problems and analysis of numerical performance are also presented. Second, assuming additional relevant moment information is available, higher-order upper bounds are developed. In this case the underlying random vector can have support contained in either a hyper-rectangle or a multidimensional simplex, and the random parameters can be either dependent or independent. The higher-order upper bounds form a decreasing sequence converging to the true expectation, and yielding convergence of the optimal decisions. Finally, applications of the higher-order upper bounds to a class of portfolio optimization problems are presented. Mean-variance and mean-varianceskewness efficient portfolio frontiers are considered in the context of a specific portfolio allocation model as well as in general and connected with applications of the higher-order upper bounds in utility theoryItem Mathematical models of host-pathogen genetics in plant pathosystems(Texas Tech University, 2001-12) Kesinger, Jacob C.Not availableItem Numerical methods for approximation of square roots of positive definite matrices in matrix-vector products(Texas Tech University, 1999-05) Boyd, Sarah KathrynTwo numerical methods are developed for calculating the product of the square root of a matrix with a vector, given the matrix and vector, where the matrix is positive definite. Modified forms of Newton's method and Eulers method are developed and analyzed. The methods are applicable, for example, in approximating solutions of stochastic differential equations. An analysis of Newton's method shows that the method is quadratically convergent. Numerical results indicate that the two methods are accurate and computationally fast.Item Radio frequency interference modeling and mitigation in wireless receivers(2011-08) Gulati, Kapil; Evans, Brian L. (Brian Lawrence), 1965-; Andrews, Jeffrey G.; Popova, Elmira; Vikalo, Haris; Vishwanath, SriramIn wireless communication systems, receivers have generally been designed under the assumption that the additive noise in system is Gaussian. Wireless receivers, however, are affected by radio frequency interference (RFI) generated from various sources such as other wireless users, switching electronics, and computational platforms. RFI is well modeled using non-Gaussian impulsive statistics and can severely degrade the communication performance of wireless receivers designed under the assumption of additive Gaussian noise. Methods to avoid, cancel, or reduce RFI have been an active area of research over the past three decades. In practice, RFI cannot be completely avoided or canceled at the receiver. This dissertation derives the statistics of the residual RFI and utilizes them to analyze and improve the communication performance of wireless receivers. The primary contributions of this dissertation are to (i) derive instantaneous statistics of co-channel interference in a field of Poisson and Poisson-Poisson clustered interferers, (ii) characterize throughput, delay, and reliability of decentralized wireless networks with temporal correlation, and (iii) design pre-filters to mitigate RFI in wireless receivers.Item Spectral and discrete approximations to stochastic Fredholm integral equations(Texas Tech University, 1996-05) Novosel, Steven JosephIn this paper two numerical methods, a discrete difference and a spectral method, are given to solve a stochastic Fredholm integral equation. Theoretical support is provided to show that a solution does exist to the equation, and that both methods converge to this solution. In addition, three numerical examples are provided, one that uses only the difference method and two that use both methods, to show that both methods do approximate the solution to the problem.Item Stochastic methods in computational stereo(2011-05) Coffman, Thayne Richard; Bovik, Alan C. (Alan Conrad), 1958-; Aggarwal, J. K.; Evans, Brian L.; Miikkulainen, Risto; Powers, Edward J.Computational stereo estimates 3D structure by analyzing visual changes between two or more passive images of a scene that are captured from different viewpoints. It is a key enabler for ubiquitous autonomous systems, large-scale surveying, virtual reality, and improved techniques for compression, tracking, and object recognition. The fact that computational stereo is an under-constrained inverse problem causes many challenges. Its computational and memory requirements are high. Typical heuristics and assumptions, used to constrain solutions or reduce computation, prevent treatment of key realities such as reflection, translucency, ambient lighting changes, or moving objects in the scene. As a result, a general solution is lacking. Stochastic models are common in computational stereo, but stochastic algorithms are severely under-represented. In this dissertation I present two stochastic algorithms and demonstrate their advantages over deterministic approaches. I first present the Quality-Efficient Stochastic Sampling (QUESS) approach. QUESS reduces the number of match quality function evaluations needed to estimate dense stereo correspondences. This facilitates the use of complex quality metrics or metrics that take unique values at non-integer disparities. QUESS is shown to outperform two competing approaches, and to have more attractive memory and scaling properties than approaches based on exhaustive sampling. I then present a second novel approach based on the Hough transform and extend it with distributed ray tracing (DRT). DRT is a stochastic anti-aliasing technique common to computer rendering but which has not been used in computational stereo. I demonstrate that the DRT-enhanced approach outperforms the unenhanced approach, a competing variation that uses re-accumulation in the Hough domain, and another baseline approach. DRT’s advantages are particularly strong for reduced image resolution and/or reduced accumulator matrix resolution. In support of this second approach, I develop two novel variations of the Hough transform that use DRT, and demonstrate that they outperform competing variations on a traditional line segment detection problem. I generalize these two examples to draw broader conclusions, suggest future work, and call for a deeper exploration by the community. Both practical and academic gaps in the state of the art can be reduced by a renewed exploration of stochastic computational stereo techniques.