Friday, April 25, 2008
Stochastic Modeling and Statistical Analysis
Option pricing is very important topic in financial risk management. We will first review financial mathematics and introduce the development of stochastic modeling, briefly. The fundamental results in financial mathematics and stochastic modeling are outlined. By using statistical analysis and methods, an example of the most widely used model — Geometric Brownian Motion model (linear model) will be illustrated. We will also show the simulations using different data partitions, and with or without jumps.
Other nonlinear models and the future works will be proposed for my doctoral research at University of South Florida.
Friday, April 18, 2008
Bayesian Multiscale In Situ Process Control for Nanomanufacturing
Department of Industrial & Management Systems Engineering
The fast-developing nanotechnology needs breakthrough innovations in manufacturing to expedite its transfer from laboratories to industry applications at lower cost. Yet much less research and education initiatives have been undertaken in nanomanufacturing to duplicate the success of transforming quality and productivity performance of traditional manufacturing. Standard statistical quality control (SQC) methods are essential to efficient nanomanufacturing. But SQC faces new challenges of scale effects in nanomanufacturing. Particularly, process variables affecting nanostructure growth are manipulated at macroscopic length/time scales. The quality characteristics of nanostructures (e.g., nanowire diameters) would better be characterized at nanoscale. Relating macroscale process variables to nanoscale quality characteristics requires novel multiscale model integration for in situ process control. Process control in nanomanufacturing therefore demands a new paradigm for effective modeling, process change detection, and process adjustment.
Using nanowire growth process as an example, this talk will presents a Bayesian multiscale modeling and control scheme for in situ process control in nanomanufacturing. Other research activities in the speaker’s Nanomanufacturing Quality Control Laboratory (Nano-QCLab) will be introduced too.
Friday, February 22, 2008
There will be no seminar this week.
Friday, February 15, 2008
Optimal Delayed Control of Stochastic Systems with Memory
Manager of the Probability and Statistics Program
Mathematical Sciences Division
US Army Research Office
This talk is based on results obtained in a joint paper (with T. Pang and M. Pemy) entitled “Optimal Control of Stochastic Functional Differential Equations with a Bounded Memory” which is to appear in Stochastics. In this talk, we will discuss a finite time horizon optimal control problem in which the controlled state dynamics is governed by a general system of stochastic functional differential equations with a bounded memory. An infinite-dimensional Hamilton-Jacobi-Bellman (HJB) equation will be derived using a Bellman-type dynamic programming principle.
It will be shown that the value function of the stochastic control problem is the unique viscosity solution of the infinite dimensional HJB equation. Some motivating examples, originated from operations research, communication networks and quantum physics, will also be given.
Friday, February 8, 2008
Power loss due to LD in the two-stage design
A powerful and cost-effective strategy for association studies is the two-stage design, where subsets of individuals and markers are typed in each stage, and for which joint analysis of both phases results in increased power. An implicit assumption is that the disease variant is either typed in Stage I or in high linkage disequilibrium (LD) with a typed marker. When this assumption is violated, a significant power loss may occur if the disease variant is indeed absent from Stage I, but power is recovered when it is included in Stage II. We investigated what factors most significantly determine power to detect association. The variable most significantly affecting power is relative risk, followed by the interaction between relative risk and sampling proportion. On the other hand, we found that typing additional markers at Stage II due to full SNP ascertainment does not significantly affect power, i.e. the multiple testing penalty incurred is comparatively small.
Friday, February 1, 2008
There will be no seminar this week.
Friday, January 25, 2008
Statistical Analysis and Modeling of Lightning
Rebecca D. Wooten
Florida is the lightning capital of the United States. Lightning strikes occur when electrostatic energy within storm conditions is unbalanced and ephemeral discharges of static electricity are set off to help the system find equilibrium. Lightning, meaning the number of lightning strikes per month, is characterized by relative humidity, sea level pressure, sea surface temperature, rain, precipitable water and the outgoing long-wave radiation. In the present study we use real data to identify the probability distribution that characterizes the behavior of the number of lightning strikes, develop a statistical model that identifies that key attributable variables to the subject strikes along with attributing interactions and proceed to estimate the number of lightning strikes with an acceptable degree of confidence. The result of the present study can be effectively used for strategic protection planning, among others.