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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:[masked]-7.
- Monahan, John F. (2011). Numerical Methods of Statistics. English. 2nd Edition. Cambridge, UK: Cambridge University Press, pp. xiv + 428. isbn:
[masked]/hbk. doi:[masked]/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

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