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With Paul Trowbridge (Center for Advanced Digital Applications @ NYU)
Saturday, July 19, 2014 at 10:00 AM   $2490   AlleyNYC, 500 7th Ave, 17th Fl

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Instructor: Paul Trowbridge

Date: July 19th, 26th, August 2nd, 9th, 16th

Time: 10:00-5:00pm

Our Venue: 500 7th Ave, 17th floor, New York, NY

(close to Times Square, between 37th and 38th street)

alley_resize300_225 image-1


This course introduces statistical computing and statistical modeling with C++. All of the computational work will be programmed in C++, however, we will link our compiled code into R functions. This will give students experience coding statistical models in a compiled language, and by linking compiled code into R functions, end users will have the familiar R interface to work with and use the code. All the statistical and numerical methods are introduced using relevant contemporary examples. Each week students will have homework assignments based on contemporary applications in order to practice and develop the skills introduced in that week's session, by analyzing real datasets and coding the analysis in C++. Students will also complete a course project of their choosing. Students will identify a topic or problem of interest to them, and apply the skills and concepts taught to address the topic. Students are encouraged to be creative with their course project and the instructor will provide valuable feedback as students work complete their projects.

After completing the course, students will have a solid understanding of core statistical modeling methods, those most commonly encountered in applied work, as well as learning how to code these models from scratch.

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 Edi-
tion. 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.


Week 1: Introduction to C and C++

Introduction to the Course

Creating R packages

- 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:

Laplace method and Quadrature

- Numerical Integration

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
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