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- Exit time (2)
- First passage time (2)
- Marked point processes (2)
- Poisson process (2)
- Conditional McKean-Vlasov equations (1)
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- Dynamic programming (1)
- Fluctuation theory (1)
- Fluctuations of stochastic processes (1)
- Independent and stationary increments processes (1)
- Modified Bessel functions (1)
- Noncooperative stochastic games (1)
- Random walk (1)
- Renewal theory (1)
- Ruin time (1)
- Signed marked random measures (1)
- Stochastic maximum principle (1)
- Switching jump-diffusions (1)
- Time sensitive analysis (1)
Articles 1 - 21 of 21
Full-Text Articles in Physical Sciences and Mathematics
Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp
Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp
Theses and Dissertations
This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.
Multiscale Optimization Via Multilevel Pca-Based Control Space Reduction In Applications To Electrical Impedance Tomography, Maria Minhee Felicia Monica Chun
Multiscale Optimization Via Multilevel Pca-Based Control Space Reduction In Applications To Electrical Impedance Tomography, Maria Minhee Felicia Monica Chun
Theses and Dissertations
A fully developed computational framework for the optimal reconstruction of binary-type images suitable for various models seen in biological and medical applications is developed and validated. This framework enables solutions to the inverse electrical impedance tomography (EIT) problems of cancer detection at different levels of complexity with multiple cancer-affected regions of different sizes based on available measurements usually affected by noise. A new spatial partitioning methodology and efficient scheme for switching between fine and coarse scales are developed to allow higher variations in the geometry of reconstructed binary images with superior performance confirmed computationally on various models. A nominal number …
A Spatiotemporal Bayesian Model For Population Analysis, Mohamed Jaber
A Spatiotemporal Bayesian Model For Population Analysis, Mohamed Jaber
Theses and Dissertations
Spatiotemporal population analysis based on incomplete, redundant, and unidentified observations is critically important, yet it is a very challenging problem. Different approaches have been proposed and several methods have been implemented to address this problem. Capture-recapture methods have been widely used and have become the standard sampling and analytical framework for ecological statistics with applications to population analysis. Despite the fact that capture-recapture methods have been commonly used, these methods do not consider the spatial structure of the population. Moreover, conventional capturerecapture methods do not use any explicit spatial information with regard to the spatial nature of the sampling and …
Machine Learning Approach To Predict Mortality Rates Based On Hospital Clinical Data, Rebecca Smith
Machine Learning Approach To Predict Mortality Rates Based On Hospital Clinical Data, Rebecca Smith
Theses and Dissertations
This thesis integrates fundamental concepts from conventional statistics with the more explanatory, algorithmic, and computational techniques offered by machine learning to predict early mortality risk of surgical patients. Well-known classification methods, including Random Forest, Decision Trees, Nearest Neighbor, Stochastic Gradient Descent, Logistic Regression, Na¨ıve Bayes, Bayes Network, Neural Networks, and Support Vector Machines, are utilized to predict mortality risk of elective general surgical patients treated between January 2005 and September 2010 at the Cleveland Clinic [33]. Clinical factors include surgery type, age, gender, race, BMI, underlying chronic conditions, surgical risk indices, surgical timing predictors, the 30-day mortality, and in-hospital complication …
Pattern Based Classification Of Chronic Kidney Disease Patients, Melissa Megan Moreno Cole
Pattern Based Classification Of Chronic Kidney Disease Patients, Melissa Megan Moreno Cole
Theses and Dissertations
We apply a pattern-based classification method to identify clinical and genomic features associated with the progression of Chronic Kidney Disease (CKD). We analyze the African-American Study of Chronic Kidney Disease with Hypertension (AASK) dataset and construct a decision-tree classification model, consisting 15 combinatorial patterns of clinical features and single nucleotide polymorphisms (SNPs), seven of which are associated with slow progression and eight with rapid progression of renal disease among AASK patients. We identify four clinical features and two SNPs that can accurately predict CKD progression. These features are validated with using sophisticated machine learning techniques including Random Forest, Nearest Neighbor, …
Optimization Framework For Reconstructing Biomedical Images By Efficient Sample-Based Parameterization, Paul Richard Arbic Ii
Optimization Framework For Reconstructing Biomedical Images By Efficient Sample-Based Parameterization, Paul Richard Arbic Ii
Theses and Dissertations
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various biomedical applications is developed and validated. The methodology includes derivative-free optimization supported by a set of sample solutions with customized geometry generated synthetically. The entire framework has an easy to follow design due to a nominal number of tuning parameters which makes the approach simple for practical implementation in various settings, adjusting it to new models, and enhancing the performance. High efficiency in computational time is achieved through applying the coordinate descent method to work with individual controls in the predefined custom order. This technique …
Discrete Moment Problems With Logconcave And Logconvex Distributions, Talal Alharbi
Discrete Moment Problems With Logconcave And Logconvex Distributions, Talal Alharbi
Theses and Dissertations
We introduce new shape constraints, logconcavity and logconvexity, to discrete moment problems for bounding the k-out-of-n type probabilities and expectations of higher order convex functions of discrete random variables with non-negative and finite support. The bounds are obtained as the optimum values of non-convex and convex nonlinear optimization problems, where the non-convex problem is reformulated as a bilinear optimization problem. We present numerical experiments to show the improvement in the tightness of the bounds when the shape of underlying unknown probability distribution is prescribed into discrete moment problems. We apply our optimization based bounding methodology in an insurance problem to …
Optimal Control Of The Second Order Elliptic Equations With Biomedical Applications, Saleheh Seif
Optimal Control Of The Second Order Elliptic Equations With Biomedical Applications, Saleheh Seif
Theses and Dissertations
Dissertation analyzes optimal control of systems with distributed parameters described by the general boundary value problems in a bounded Lipschitz domain for the linear second order uniformly elliptic partial differential equations (PDE) with bounded measurable coefficients. Broad class of elliptic optimal control problems under Dirichlet or Neumann boundary conditions are considered, where the control parameter is the density of sources, and the cost functional is the L2-norm difference of the weak solution of the elliptic problem from measurement along the boundary or subdomain. The optimal control problems are fully discretized using the method of finite differences. Two types of discretization …
Identification Of Parameters In Systems Biology, Roby Poteau
Identification Of Parameters In Systems Biology, Roby Poteau
Theses and Dissertations
Systems Biology is an actively emerging interdisciplinary area between biology and applied mathematics, based on the idea of treating biological systems as a whole entity which is more than the sum of its interrelated components. One of the major goals of systems biology is to reveal, understand, and predict such properties through the development of mathematical models based on experimental data. In many cases, predictive models of systems biology are described by large systems of nonlinear differential equations. Quantitative identification of such systems requires the solution of inverse problems on the identification of parameters of the system. This dissertation explores …
Ensemble Correlation Coefficient For Variable Association Detection, Wejdan Deebani
Ensemble Correlation Coefficient For Variable Association Detection, Wejdan Deebani
Theses and Dissertations
Subjects in a population are represented by their characteristics, and the characteristics are represented by variables. Identifying the relationship between these variables is essential for prediction, hypothesis testing, and decision making. The relation between two variables is often quantified using a correlation factor. Once correlations between response and independent variables are known, they can be used to make predictions regarding response variables. That is, if two variables are correlated, by observing one, we can make predictions about the other one. A more accurate prediction can be made where there is a strong relationship between variables. Several correlation factors have been …
Multi-Class Logical Analysis Of Data With Relaxed Patterns And Its Extension To Survival Analysis, Travaughn Coren Bain
Multi-Class Logical Analysis Of Data With Relaxed Patterns And Its Extension To Survival Analysis, Travaughn Coren Bain
Theses and Dissertations
This dissertation builds on a previously successful optimization based linear program multi-class classification method, called Logical Analysis of Data (LAD), and improves its generalization capability by introducing relaxed constraint modifications and then further extends and applies it to Survival Analysis. First, we propose the relaxed modifications onto the constraints of the mixed integer linear program (MILP) in the pattern generation phase of LAD. Our modifications are aimed at minimizing the degree of over-fitting to noise, allowing for added flexibility to widen the solution space in hopes to discover more robust classification rules. The proposed method introduces relaxed homogeneity and minimum …
Integrated Representation And Discrimination Models For Functional Data Classification, Rana Haber
Integrated Representation And Discrimination Models For Functional Data Classification, Rana Haber
Theses and Dissertations
The modus operandi for machine learning is to map functional data to numerical summaries, filter the data, and/or subject it to global signature extractions with the objecive of building robust feature vectors that uniquely characterize each function and then proceed with training algorithms that seek to optimally partition the feature space S ⊂ Rn into labeled regions. This holds true even when the original data are functional in nature, i.e. curves or surfaces that inherently vary over a continuum such as time or space. Functional data are often reduced to summary statistics, locally-sensitive features, and global signatures with the objective …
Two-Stage Mixed Integer Stochastic Programming And Its Application To Bond Portfolio Optimization, Nasser Aedh Alreshidi
Two-Stage Mixed Integer Stochastic Programming And Its Application To Bond Portfolio Optimization, Nasser Aedh Alreshidi
Theses and Dissertations
We consider a two-stage stochastic bond portfolio optimization problem, where an investor aims to optimize the cost of bond portfolio under different scenarios while ensuring predefined liabilities during a given planning horizon. The investor needs to optimally decide whether to buy, hold, or sell bonds based upon present market conditions under different scenarios and varying assumptions, where the scenarios are determined based on interest rates and buying prices of the bonds. Three stochastic integer programming models are proposed and applied to real-data from Saudi Sukuk (Bond) Market. The case-study results demonstrate the varying optimal decisions made to manage bond portfolio …
Weighted Aggregation Methods For Linear And Nonlinear Cluster Analysis With Applications To Cancer Research, Meshal Shutaywi
Weighted Aggregation Methods For Linear And Nonlinear Cluster Analysis With Applications To Cancer Research, Meshal Shutaywi
Theses and Dissertations
Due to advancements in data acquisition, large amount of data are collected on a daily basis. Analysis of the collected data is an important task to discover the patterns, extract the features, and make informed decisions. A vital step in data analysis is dividing the subjects (elements, individuals) in different groups based on their similarities. One way to group the subjects is clustering. Clustering methods can be divided into two categories, linear and non-linear. K-means is a commonly used linear clustering method, while Kernel K-means is a non-linear technique. Kernel K-means projects the elements to a new space using a …
Parametric Methods For Analysis Of Survival Times With Applications To Organ Transplantation, Farag Hamad
Parametric Methods For Analysis Of Survival Times With Applications To Organ Transplantation, Farag Hamad
Theses and Dissertations
In this dissertation, we have two main objectives. First, we introduce a hybrid method to model hazard function. Different approaches have been used for modeling survival times including parametric, semi-parametric, and non-parametric models. Non-parametric and semi-parametric models are commonly used for survival time analysis due to their flexibility. However, the parametric models are in high demand because of their predictive power. A challenging task is to extend semi-parametric methods and design full parametric models for analysis of survival times by estimating a set of unknown parameters. In the proposed method, the nonparametric estimate of the survival function by Kaplan Meier …
Time Sensitive Functionals Of Marked Random Measures In Real Time, Kizza M. Nandyose Frisbee
Time Sensitive Functionals Of Marked Random Measures In Real Time, Kizza M. Nandyose Frisbee
Theses and Dissertations
In this dissertation, we study marked random measures that model stochastic networks (under attacks), status of queueing systems during vacation modes, responses to cancer treatments (such as chemotherapy and radiation), hostile actions in economics and warfare. We extend the recently developed time sensitivity technique for investigating the processes’ behavior about a fixed threshold to a novel time sensitive technique in three important directions: (1) real-time monotone stochastic processes; (2) two-dimensional signed random measures; and (3) antagonistic stochastic games with two active players and one passive player. The need for the time sensitive feature in our study (i.e., an analytical association …
The Capacitated Transfer Point Covering Problem (Tpcp): Expanding Delivery Network Coverage With Minimal Resources, Jeffrey Allen Mcdougall
The Capacitated Transfer Point Covering Problem (Tpcp): Expanding Delivery Network Coverage With Minimal Resources, Jeffrey Allen Mcdougall
Theses and Dissertations
Retail delivery services have begun using unmanned systems in attempts to reduce the time from a customer’s order to when the product arrives at its intended destination. Utilizing these systems are beneficial to both the customer and retailer, however they create problems for the dispatchers making decisions about the delivery. Promised delivery times are now quick enough that orders cannot be grouped and dispatched at predetermined or cyclic departure times. The limited range of emerging delivery vehicles, specifically unmanned aerial systems, creates gaps in last mile retail distribution networks and excludes significant numbers of potential customers. Distributers must use a …
Parametric And Non-Parametric Regression Models With Applications To Climate Change, Osita Eluemuno Onyejekwe
Parametric And Non-Parametric Regression Models With Applications To Climate Change, Osita Eluemuno Onyejekwe
Theses and Dissertations
In this dissertation we have studied the climate factors that contribute to climate change using univariate and multivariate parametric methods as well as nonparametric models. In this study, we have three major contributions. First, the extent of mountain glaciers around the globe and their responses to climate factors are investigated using multivariate methods and we have proposed a predictive model to estimate the mountain glacier response to climate factors. Second, we have addressed the important problem of bandwidth selection in presence of correlated noise in nonparametric regression analysis. We have proposed a denoising method based on an ensemble bandwidth optimization …
On Logconcavity Of Multivariate Discrete Distributions, Majed Ghazi Alharbi
On Logconcavity Of Multivariate Discrete Distributions, Majed Ghazi Alharbi
Theses and Dissertations
The contribution of this dissertation to the literature is twofold. First, we use a geometric perspective to present all possible subdivisions of R³ into tetrahedra with disjoint interiors and adopt a combinatorial approach to obtain a special subdivision of Rⁿ into simplices with disjoint interiors, where two simplices are called neighbors if they share a common facet. We then use the neighborhood relationship of the simplices in each subdivision to fully describe the sufficient conditions for the strong unimodality/logconcavity of the trivariate discrete distributions and further extend these results to present a new sufcient condition for the strong unimodality/logconcavity of …
New Bounds For The K-Out-Of-N Type Probabilities And Their Applications, Ahmed M. Binmahfoudh
New Bounds For The K-Out-Of-N Type Probabilities And Their Applications, Ahmed M. Binmahfoudh
Theses and Dissertations
The contribution of the shape information of the underlying distribution in probability bounding problem is investigated and an efficient linear programming based bounding methodology, which takes advantage of the advanced optimization techniques, probability theory, and the state-of-the-art tools, to obtain robust and efficiently computable bounds for the probabilities that at least k and exactly k-out-of-n events occur is developed. The k-out-of-n type probability bounding problem is formulated as linear programs under the assumption that the probability distribution is unimodal. The dual feasible bases structures of the relaxed versions of linear programs involved are fully described. The bounds for the probability …
Discrete And Continuous Operational Calculus In Stochastic Games, Kenneth Ibe Iwezulu
Discrete And Continuous Operational Calculus In Stochastic Games, Kenneth Ibe Iwezulu
Theses and Dissertations
First, we consider a class of antagonistic stochastic games between two players A and B. The game is specified in terms of two "hostile" stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. This game is observed upon random epochs of time and the outcome of the game is not known in real time. The game ends at the time when the underlying fixed threshold of either player is crossed (referred to as the first passage time). The first passage time is then shifted to an epoch, i.e. upon one of the observation instants of time. …