Computational Biostatistics

(2 Credits)

Biostatisticians face many numerical challenges, including simulation, integration, smoothing, and optimization. This course covers the statistical computing methods needed for PhD level biostatistics, with a focus on simulation, Monte Carlo methods for planning studies, and numerical optimization, and it aims to provide the computational tools necessary for biostatistical research and practice, beginning with the basics of reproducible coding. The class will start with rigor and reproducibility, go on to random number generation and sampling from arbitrary distributions, to Monte Carlo integration, to study design with power analysis and sample size calculation, to resampling methods including permutation tests, the bootstrap, the jackknife, and cross-validation, to Markov chain Monte Carlo for Bayesian inference, and to numerical optimization and its use in maximum likelihood estimation and variational inference. Core algorithms for statistical inference and statistical learning are introduced and illustrated alongside these methods. Because simulation and resampling quickly exceed what a personal machine can deliver, the course also covers high performance computing: all coding is done in R, and every coding assignment is run on BigPurple, the NYU Grossman School of Medicine cluster, so that students become comfortable loading software modules, writing and submitting job scripts, monitoring jobs, and retrieving results. Through the class, students will learn the motivation, concepts, technical details, and software implementation of these methods, and will gain experience writing and troubleshooting code on applied problems and coding simulations in order to plan studies and assess the performance of inferential methods.