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Mathematics & Statistics

## Friday, December 7, 2007

Title
Speaker
Time
Place

Financial Calculus Review
Ling Wu
1:00pm-2:00pm
PHY 013

Abstract

This presentation reviews the fundamentals of Financial calculus. It starts with an introduction the basic finacial terminology like derivatives, hedging, arbitrage, etc. Next, a few discrete models for pricing options are introduced followed by the famous Black-Sholes model (which is the continuous one). Applications and extensions of Black-Sholes model will also be discussed.

## Friday, November 30, 2007

Title
Speaker
Time
Place

Geographic Information Systems Software
Keith Hackett
1:00pm-2:00pm
PHY 013

Abstract

Resampling data to remove spatial biases, a practical approach using Geographic Information Systems (GIS) software and inverse distance squared weighting.

As is often the case, individuals or organizations often seek out the expertise of a statistician to aid them with the interpretation of data. However, in many instances, statistical advice is not sought out during the crucial stage of sampling design. Therefore, data are often collected in a nonrandom manner which can lead to bias. A method of resampling data which were not collected using a random sampling design will be demonstrated. The presentation will give a brief introduction to Geographic Information Systems (GIS) as well as an example of using inverse-distance-squared weighting using SAS software.

## Friday, November 9, 2007

Title
Speaker

Time
Place

Valuation of European Contingent Claims on Power with Spikes: the Non-Markovian Approach
Valery A. Kholodnyi
Managing Director of Quantitative Research and Risk Analysis
Platts Analytics, a Division of the McGraw-Hill Companies
Boulder, CO
1:00pm-2:00pm
PHY 013

Abstract

As the power markets are becoming deregulated worldwide, the modeling of spikes in power prices is becoming a key problem in energy risk management, physical assets valuation, and derivatives pricing. For example, power prices in the United States Midwest in June 1998 rose to $7,500 per megawatt hour (MWh) compared with typical prices of around$30/MWh as a result of unseasonably hot weather, planned and unplanned outages, and transmission constraints.

In this talk, we present a new approach to modeling spikes in power prices proposed by the author. In contrast to other approaches, we model power prices with spikes as a non-Markovian stochastic process. This allows for modeling spikes directly as self-reversing jumps. This also allows for the analytical valuation of European contingent claims on power with spikes. Moreover, we obtain a linear evolution equation for the values of these European contingent claims. We also explore a formal analogy between this linear evolution equation in the special case of spikes with constant magnitude and the Schrödinger equation for a two-component spinor describing a nonrelativistic spin ½ particle in an electromagnetic field.

We end our talk with a discussion of the presented approach as a rich source of practically useful research projects for both gradate and undergraduate students.

## Friday, November 2, 2007

Title
Speaker
Time
Place

Prediction Models for Carbon Dioxide Emissions and the Atmosphere
Shou Hsing Shih
1:00pm-2:00pm
PHY 013

Abstract

The object of the present study is to develop statistical models for predicting the carbon dioxide emissions and the atmosphere in the United States. We used monthly emissions data from 1981 to 2003 that was collected by the Carbon Dioxide Information Analysis Center. For the carbon dioxide in the atmosphere, we used the data that was collected in Mauna Loa from 1965 to 2004 by the Scripps Institution of Oceanography.

The developed statistical models take into consideration trends and seasonal effects. The quality of the prediction process is illustrated using the actual data.

## Friday, October 26, 2007

Title
Speaker
Time
Place

Modeling of Global Warming
Chris Tsokos
1:00pm-2:00pm
PHY 013

Abstract

The lecture is centered on the “GLOBAL WARMING PROBLEM”. Temperature and carbon dioxide are two fundamental components that play a central role in the global warming. One of the basic objectives of this study is to develop stochastic models to obtain short and long-term estimates on the temperature and carbon dioxide $$(\mathrm{CO}_2)$$. The prediction models structured using data for the underlying entities for the Continental United States. The role and the scope of the study also emphasized.

## Friday, October 19, 2007

Title

Speaker
Time
Place

Power and sample size for case-control association studies with copy number polymorphism: application of mixture-based likelihood ratio test
Wonkuk Kim
1:00pm-2:00pm
PHY 013

Abstract

Recent studies suggest that copy number polymorphisms (CNPs) may play an important role in disease susceptibility and onset. Measurements of CNPs are based on a quantitative measurement such as the average ratio of intensity signals. Conventionally, subjects are assigned to a specific CNP category, and cases and controls are compared using a chi-square test of independence. Given a CNP, the quantitative measurement has a fixed distribution that is the same for case and control subjects so that both case and control measurements are a mixture of distributions. The talk describes how to apply the likelihood ratio test (LRT) based on the underlying quantitative measurement and how to calculate its power, sample size and relative efficiency (as compared to the chi-square test of independence on CNP counts) for case-control sampling design. An example of the application of the likelihood ratio test statistic (LRTS) will be given for a comparison of CNP distributions in individuals of European or Chinese ancestry. The LRTS is more powerful than the chi-square test, due to misclassification of the most common category into a less common category. The efficiency of the chi-square test can approach zero as the frequency of the at-risk category approaches zero. Although both non-centrality parameters (NCPs) of the chi-square test and the LRTS converge to zero, the NCP of the chi-square test approaches zero faster than the NCP of the LRTS.

## Friday, October 12, 2007

Title
Speaker

Time
Place

Some Simple Applications of Statistics in Condensed-Matter Physics
David Rabson
Department of Physics, USF
1:00pm-2:00pm
PHY 013

Abstract

While probability theory has long been used in physics, where its application is known as Statistical Mechanics, the branches of physics dealing with the condensed states of matter (solids and liquids, roughly) tend to use statistical inference (as opposed to statistical mechanics) less often than do astrophysicists or high-energy physicists. I will describe three recent projects in which I've used simple statistical techniques straight out of elementary textbooks:

• The first application is to the ballistic-to-diffusive crossover in electron transport in a quantum wire and concerns non-parametric mode estimation.
• The second is straightforward bootstrapping to estimate confidence bounds in a quality-control protocol for tunnel junctions intended for magnetic random-access computer memory chips.
• The third shows how to get a paper out in a subfield of biophysics where previous authors simply didn't think to apply statistics.

## Friday, October 5, 2007

Title
Speaker
Time
Place

Stochastic Modelling of Drug Dosage and Prescription Processes
1:00pm-2:00pm
PHY 013

Abstract

In this presentation, an attempt has been made to answer two of the most important questions in providing the best medical care to patients. The problems are:

• How much dosage of a drug is to be prescribed?
• How frequently the drug is to be administered?
Knowing the significance of these problems, we develop a simple mathematical model that provides answers to the problems. Moreover, model determines both the drug dosage level and the inter-dosage time. This model is also extended to random fluctuations in the turnover rate of a patient.

## Friday, September 28, 2007

Title

Speaker

Time
Place

Determination of Root Water Uptake — Calculation From Soil Moisture Data and Conceptualization for Modeling
Nirjhar Shah
Department of Civil Engineering, USF
1:00pm-2:00pm
PHY 013

Abstract

The talk will describe a dynamic model of water uptake from plants growing in naturally vegetated areas subjected to a rainfall and evaporation time series. The model results are compared and contrasted with popular pre-existing models. Also, the effects of the uptake pattern on the movement of water across multiple soil layers are also analyzed. The results showed that contrary to common modeling approaches, root water uptake is both a function of root distribution and variability in water content. Following the comparison of derived root water uptake versus the traditionally used models, a modeling framework based on physical root distribution and hydraulic characteristics of zylems is presented. The framework using empirical data is found to provide results that closely match the observed root water uptake values. The results greatly increased the confidence in the framework and warrant a further, more detailed investigation.

## Friday, September 21, 2007

Title
Speaker
Time
Place

Statistical Modeling the Conditions Under Which Tropical Storms Form: Estimating the Birth of a Storm
Rebecca D. Wooten
1:00pm-2:00pm
PHY 013

Abstract

The relationship between statistics and physics looking at the correlation between wind speed and pressure versus wind speed and temperature play a significant role in hurricane prediction. Contrary to previous studies, this study indicates that a drop in pressure is more a result of the storm and less a cause. It shows that temperature is a key indicator that a storm will form in conjunction with a drop in pressure. Real data and developed statistical models were used to prove our conjecture. The key attributing variables and their interactions that estimate the wind speed of a given storm have been identified and ranked with respect to contribution.

## Friday, September 14, 2007

Title
Speaker
Time
Place

Analyzing Carbon Dioxide Concentration at Barrow, Alaska
Julie Cholet
1:00pm-2:00pm
PHY 013

Abstract

The annual cycle of atmospheric carbon dioxide concentration at a given location reflects the environmental activity in areas from which contributing air masses originate. Data of this sort have been interpreted as indicators of cyclic phenomena, such as the length and timing of the growing season. Though most research to date has involved data from Mauna Loa, Hawaii, which has both the longest continuous record and the best understood, Barrow, Alaska has nearly as long a history of carbon dioxide measurement, and the shape of its annual cycle shows a much more pronounced influence from northern forested regions. This makes it provacative as a possible source of information about photosynthetic and decomposition activity in those regions. This discussion will address the challenges of working with carbon dioxide data in general, and from Barrow, Alaska in particular. It will investigate various methods for using the data to determine whether changes in forest growing season characteristics have occurred over time.