- "Resampling Inhomogeneous Marked Point Processes", Ph.D Defense, 12/5/11
- An overview of my research for my Ph.D. dealing with resampling methods for marked point processes where the arrival times come from an inhomogeneous Poisson process and the marks are wide-sense stationary. A copy can be found here.
- "Local averaging for the estimation of a covariance function", Math 287D - Statistical Learning, 3/7/11
- An overview of time series, marked point processes and their associated covariance functions, with an application of local averaging to aid in the estimation of the covariance function for a marked point process. A copy can be found here.
- "A (Very) Brief Overview of Statistical Tests and Modeling", Math 297 - Mathstorm Seminar, 1/19/11
- Mathstorm is a graduate consulting group and I gave a talk highlighting comment methods that one is likely to use. A copy can be found here.
- "Analysis of Observational Studies in the Presence of Treatment Selection Bias", Math 288 - Biostatistics Seminar, 1/21/10
- A summary of papers by (i) Angrist, Imbens, Rubin, (ii) D'Agostino, and (iii) Stukel et al. In the presence of treatment selection bias in an observation study, how can one draw causal inference? This talk details two common apporaches, propensity score analysis and instrumental variable analysis, for drawing such conclusions. A copy can be found here.
- "Bootstrapping a Spatial Point Process", Math 289B - Topics in Statistics (The Bootstrap), 3/11/09
- A summary of a paper by Loh and Stein of the same name. The authors develop a new bootstrap technique which relaxes the assumption that the data from the point process is stationary. A copy can be found here.
- "The Smallest Eigenvalue of a Large Dimensional Wishart Matrix", Math 287B - Multivariate Analysis, 3/6/09
- A summary of a paper by Jack Silverstein of the same name which uses Gersgorin's Circle Theorem to show asymptotic results about the distribution of smallest (and largest) eigenvalues of a Wishart matrix. A copy can be found here.
- "Variability of Starting vs. Ending Positions of Indy 500 Races from 1911-2007", Math 111A - Mathematical Modeling, 12/3/07
- An application of non-parametric statistics to analyze the variability of Indy 500 races. The data suggests that over time, variability has decreased. A copy can be found here.
- "A Brief Introduction to Combinatorial Game Theory", MathZoom Summer Camp 2007, 8/15/07
- A summary of the main ideas of combinatorial game theory, including examples of games and the result that all impartial games are essentially Nim. A copy can be found here.
- "Consistency of the Jackknife and the Bootstrap", Math 289A - Topics in Statistics (The Bootstrap), 6/1/07
- An overview of the jackknife and bootstrap method as well as outlines of the proofs for the consistency of both methods. A copy can be found here.
- "Robust Regression", Math 282B - Applied Statistics, 5/30/07
- A summary of regression methods which are not sensitive to outliers in the data. A copy can be found here.
- "Planting the (Intellectual) Need From Which Learning Grows", UCSD Mathematics Undegraduate Honors Thesis, 6/8/06
- Working with Dr. Guershon Harel, I examined ways to foster intellectual need in First Year Calculus students. A copy can be found here.
- "Perfect Numbers and Mersenne Primes", Math 104C - Number Theory, 5/22/06
- A discussion of the sum of divisors function, its relation to perfect numbers, and Euclid's statement about the correspondence between perfect numbers and Mersenne primes. Also included are six properties of perfect numbers. A copy can be found here.
- "Application of DNR in Mathematics and Various Instructional Settings", 19th Annual UCSD Undegraduate Research Conference, 5/20/06
- An early talk of my work with Dr. Guershon Harel on teaching methods. See the above link for the final text.
- "An Application of Group Theory: Diffie-Hellman Key Exchange and Public Key Cryptography", Math 100C - Modern Algebra, 4/26/06
- This talk summarized the motivation for the Diffie-Hellman Key Exchange, the protocol itself and the mathematics behind it, the impracticality of a brute force approach, and some of the vulnerabilities of the protocol. A copy can be found here.
|