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With Paul Trowbridge (Center for Advanced Digital Applications @ NYU)
Saturday, July 19, 2014 at 10:00 AM    Cost: $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 & 38th street)

alley_resize300_225 image-1


This course introduces statistical computing & 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, & by linking compiled code into R functions, end users will have the familiar R interface to work with & use the code. All the statistical & numerical methods are introduced using relevant contemporary examples. Each week students will have homework assignments based on contemporary applications in order to practice & develop the skills introduced in that week's session, by analyzing real datasets & 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, & apply the skills & concepts taught to address the topic. Students are encouraged to be creative with their course project & 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 & 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 & C++

Introduction to the Course

Creating R packages

- Introduction to the .C & .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 & 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 & Generalized Linear Mixed Models

Statistical Model:

- Generalized linear mixed models

Numerical/Computational Method:

Laplace method & Quadrature

- Numerical Integration

Week 4: Monte Carlo Methods; Hypothesis testing & 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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