Statistical Modeling and Computation with C/C++

Introduction:

This course introduces statistical computing and statistical modeling in C and C++. All of the computational “work” will programmed in C/C++, however, we will link our compiled code into R functions. This will give students experience coding statistical models in a high level language, and by linking compiled code into R functions, end users will have the familar R interface to work with and use the code.

Recommended Textbook

• Eddelbuettel, Dirk (2013). Seamless R and C++ Integration with Rcpp. New
  York: Springer. isbn: 978-1-4614-6867-7.
• Monahan, John F. (2011). Numerical Methods of Statistics. English. 2nd Edition. Cambridge, UK: Cambridge University Press, pp. xiv + 428. isbn:
  0-521-79168-5/hbk. doi: 10.1017/CBO9780511812231.
• Press, W. H. et al. (2007). Numerical Recipes: the Art of Scientific Computing.
  3rd Edition. Cambridge, UK: Cambridge University Press.

Syllabus:

Week 1: Introduction & Linear Models

Introduction to C and C++

• Introduction to the .C and .Call interfaces in R
• Review of Probability for Statistical Modeling

Statistical Model:

• Linear regression
• Non-parametric regression via splines

Numerical/Computational Method:

• Solving linear systems
• Computing matrix inverse
• Least square fit

Week 2: Maximum Likelihood Estimation and Non-Linear Models

Statistical Model:

• Generalized linear models
• Non-linear regression models

Numerical/Computational Method:

• Numerical Differentiation
• Non-linear Optimization
• Fisher Scoring algorithm

Week 3: Numerical Integration and Generalized Linear Mixed Models

Statistical Model:

• Generalized linear mixed models

Numerical/Computational Method:

• Numerical Differentiation
• Laplace method
• Quadrature

Week 4: Monte Carlo Methods; Hypothesis testing and Goodness-of-fit

Statistical Model:

• Network analysis; testing hypotheses about network characteristics
• Evaluating Goodness-of-fit when Chi-Square assumptions are violated

Numerical/Computational Method:

• Monte Carlo Integration

Week 5: Markov Chain Monte Carlo:

Part I

Statistical Model:

• Gaussian Copula models
• Discrete Choice models with random coefficients

Numerical/Computational Method:

• Markov chains
• Gibbs sampler
• Metropolis-Hastings algorithm

Part II

Statistical Model:

• Statistical Genetics
• Spatial Epidemiology

Numerical/Computational Method:

• Markov Chain Monte Carlo maximum likelihood estimation