Education

Degrees

  • PhD - June 2011 - Statistics and Applied Mathematics - University of California Santa Cruz
    Dissertation: Statistical Modeling for Dark Energy and the Associated Cosmological Constants
  • MS - May 2007 - Mathematics - San Jose State University
    Thesis: Investigation of Repeated Measures Linear Regression Methodologies
  • BS - May 2002 - Applied and Computational Mathematics (emphasis in Statistics) - San Jose State University


Interesting Courses (the links lead to special projects for the course)

  • Spatial statistics - modeling for data that are spatially referenced focused on geostatistic methods with Bayesian inference and Markov random fields
  • Stochastic processes- Markov processes, hidden Markov models, point processes, Gaussian process, and Brownian motion
    (project: Poisson Hidden Markov Model) {C}
  • Time series-ARMA models, Kalman filters, DLM, importance sampling, particle learning
    (project: Dynamic linear models (DLM), Kalman filtering, Sequential Monte Carlo)
  • Generalized Linear Models - statistical modeling and inference of GLMs including both classical and Bayesian inference
  • Bayesian non-parametrics-Dirichlet process priors and mixtures of DPs, Polya trees
    (project: Density Estimation with DP Mixture - blocked Gibbs sampler)
  • Bayesian Statistical Modeling - hierarchical modeling, regression and analysis of variance, multivariate regression models and mixture models. Computational simulation-based methods such as MCMC will be revised and used for parameter estimation and prediction (project: Multivariate Bayesian Regression)
  • Probability theory- introduction to measure theoretic probability
  • Decision theory-decision making under uncertainty from a Bayesian viewpoint- inference, hypotheses testing, classification and prediction, decision trees, loss functions  (project: Case study of breast cancer: decision trees
  • Special topics in MCMC- Kalman filters, importance sampling, HMM, reversible jump MCMC (RJMCMC)
    (project: RJMCMC) {C}
  • Regression analysis- linear and multiple regression, parameter estimation and interpretation, hypothesis testing, prediction, model diagnostics, model comparison and variable selection
  • Reliability Analysis
  • Partial differential equations - Existence and uniqueness of solutions of first order ordinary and partial differential equations. The classical theory of initial and boundary value problems for hyperbolic, parabolic and elliptic equations. Fourier series and transforms.
  • Multivariate Statistics
  • Other topics
    • Cluster Analysis
    • ODEs
    • Quadrature methods for numerical computing - Gauss-Chebyshev quadrature, trapazoid, Bayes quadrature
       

Computer Packages

  • Statistical Packages: R, S+, SPSS, JMP, Minitab
  • Other programming: Matlab, some Maple, and C++
  • Text Editors: Latex, Word, Excel, PowerPoint, Photoshop

 

Additional courses

  • Education: Teaching exceptional individuals
  • Education: Traditional and non-traditional assessment
  • American sign language (21 units)
  • Laboratory electronics for scientists
  • Cultural anthropolgy
  • Computer programming in C++