This course provides a comprehensive introduction to computational techniques essential for modern statistical analysis and machine learning. Topics include Monte Carlo methods, large-scale matrix computations, numerical optimization, machine learning algorithms, and GPU parallel computing. Emphasis is placed on efficiency, scalability, and practical implementation for solving statistical problems.
Athena Title
Statistical Computing I
Prerequisite
(STAT 4510 or STAT 6510 or STAT 6810) and STAT 6420 and STAT 8330
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Student learning Outcomes
By the end of this course, students will be able to apply Monte Carlo simulation techniques, including random number generation, variance reduction, and importance sampling, to statistical inference problems.
By the end of this course, students will be able to implement numerical integration and differentiation methods, including Gaussian quadrature, finite difference approximations, and Monte Carlo techniques in statistical applications.
By the end of this course, students will be able to analyze large-scale matrix computations, including factorization methods and iterative solvers, to optimize performance in statistical applications.
By the end of this course, students will be able to evaluate majorization-minimization, Newton-Raphson-based, and Monte Carlo optimization techniques for parameter estimation in statistical models.
By the end of this course, students will be able to utilize GPU parallel computing frameworks (CUDA, OpenCL) to accelerate matrix operations, Monte Carlo simulations, and machine learning algorithms.
By the end of this course, students will be able to communicate computational findings effectively through written reports and visualizations using Open Science tools such as Jupyter or Quarto.
Topical Outline
Monte Carlo Methods: Monte Carlo simulation; Properties of random number generators (uniform, normal, and other distributions); Pseudo-random vs. quasi-random number generation; Markov chain Monte Carlo methods (Metropolis-Hastings and Gibbs Sampler)
Numerical Integration and Differentiation: Trapezoidal, Simpson’s, and Romberg rules; Gaussian quadrature methods; Monte Carlo methods with variance reduction techniques and importance sampling; Finite difference approximations for numerical differentiation
Matrix Computations: Matrix factorization techniques (LU, QR, Cholesky); Eigenvalue and singular value decomposition methods; Efficient storage and manipulation of large matrices
Optimization Methods: Majorization-minimization (MM) methods; Newton’s method for optimization; Quasi-Newton methods and their advantages; Monte Carlo (genetic, evolutionary) optimization methods
GPU Parallel Computing: Introduction to parallel computing concepts; GPU architecture and programming models (CUDA, OpenCL); Parallelization of matrix operations and Monte Carlo simulations; Implementation of machine learning algorithms on GPUs; Performance benchmarks and comparisons with CPU-based computation; Practical applications in high-performance statistical computing
Institutional Competencies Learning Outcomes
Analytical Thinking
The ability to reason, interpret, analyze, and solve problems from a wide array of authentic contexts.
