Math 475: Statistical Computation

Fall 2016

Fall 2016

Instructor:
Todd Kuffner (kuffner@math.wustl.edu)

Lecture: 4:00-5:30pm, Monday/Wednesday, Simon Hall, Room 018

Office Hours: Monday 8:00-9:00am, Tuesday 4:00-6:00pm; Cupples I Room 18 (basement).

Course Overview: This course provides students with an introduction to the foundations of modern computational statistics. Students will learn the basics of numerical analysis, random number generation, and computational tools for statistical inference, specifically Monte Carlo methods and the bootstrap. Students will be introduced to SAS during the first part of the course. Thereafter, students are welcome to use R or SAS (or both) for the relevant parts of homework assignments.

Prerequisite: It is assumed that students have taken a first course in multivariate-calculus-based-probability (including central limit theorems, laws of large numbers, transformations of variables), a first course in linear or matrix algebra, a course in statistics (including the principles of statistical inference, common estimation methods such as maximum likelihood), and have some familiarity with programming in either R or SAS.

Textbook: Both books are required. You may have electronic access through Washington University; log in to My Catalog on the library website and search for these books. Recommended readings for each lecture will consist of sections from these books.

Homework: There will be regular homework assignments. For the first part of the course, you may find example code and data from the The Little SAS book here: http://support.sas.com/publishing/authors/delwiche.html . Homework will be graded, but solutions will not be provided to students.

Homework grader: Yiqian Fang (yiqianfang@wustl.edu)

Blackboard: During the semester, homework assignments, homework and midterm exam grades and any other course-related announcements will be posted to Blackboard or sent by email using Blackboard.

Attendance: Attendance is required for all lectures. The student who misses a lecture is responsible for any assignments and/or announcements made.

Grades: 15% Homework, 20% Midterm 1, 20% Midterm 2, 45% Final

Exams: 2 in-class midterms and 1 final. The dates of the exams should not be considered fixed until the first day of class. What appears on Course Listings may be incorrect.

Homework: There will be weekly homework assignments. The lowest homework grade will be dropped. If you added the class late and missed the first homework, then that is the homework that will be dropped.

Final Course Grade: The letter grades for the course will be determined according to the following numerical grades on a 0-100 scale.

Other Course Policies: Students are encouraged to look at the Faculty of Arts & Sciences policies.

Lecture: 4:00-5:30pm, Monday/Wednesday, Simon Hall, Room 018

Office Hours: Monday 8:00-9:00am, Tuesday 4:00-6:00pm; Cupples I Room 18 (basement).

Course Overview: This course provides students with an introduction to the foundations of modern computational statistics. Students will learn the basics of numerical analysis, random number generation, and computational tools for statistical inference, specifically Monte Carlo methods and the bootstrap. Students will be introduced to SAS during the first part of the course. Thereafter, students are welcome to use R or SAS (or both) for the relevant parts of homework assignments.

Prerequisite: It is assumed that students have taken a first course in multivariate-calculus-based-probability (including central limit theorems, laws of large numbers, transformations of variables), a first course in linear or matrix algebra, a course in statistics (including the principles of statistical inference, common estimation methods such as maximum likelihood), and have some familiarity with programming in either R or SAS.

Textbook: Both books are required. You may have electronic access through Washington University; log in to My Catalog on the library website and search for these books. Recommended readings for each lecture will consist of sections from these books.

- The Little SAS Book: A Primer (5th edition, 2012) by Lora D. Delwiche and Susan J. Slaughter
- Computational Statistics (1st edition, 2009) by James E. Gentle errata

Homework: There will be regular homework assignments. For the first part of the course, you may find example code and data from the The Little SAS book here: http://support.sas.com/publishing/authors/delwiche.html . Homework will be graded, but solutions will not be provided to students.

Homework grader: Yiqian Fang (yiqianfang@wustl.edu)

Blackboard: During the semester, homework assignments, homework and midterm exam grades and any other course-related announcements will be posted to Blackboard or sent by email using Blackboard.

Attendance: Attendance is required for all lectures. The student who misses a lecture is responsible for any assignments and/or announcements made.

Grades: 15% Homework, 20% Midterm 1, 20% Midterm 2, 45% Final

Exams: 2 in-class midterms and 1 final. The dates of the exams should not be considered fixed until the first day of class. What appears on Course Listings may be incorrect.

Homework: There will be weekly homework assignments. The lowest homework grade will be dropped. If you added the class late and missed the first homework, then that is the homework that will be dropped.

Final Course Grade: The letter grades for the course will be determined according to the following numerical grades on a 0-100 scale.

A+ |
impress me (very rare) |
B+ |
[87, 90) |
C+ |
[77, 80) |
D+ |
[67, 70) |
F |
[0,60) |

A |
93+ |
B |
[83, 87) |
C |
[73, 77) |
D |
[63, 67) |
||

A- |
[90, 93) |
B- |
[80, 83) |
C- |
[70, 73) |
D- |
[60, 63) |

Other Course Policies: Students are encouraged to look at the Faculty of Arts & Sciences policies.

- Academic integrity: Students are expected to adhere to the University's policy on academic integrity.
- Auditing: There is an
option to audit, but this
still involves enrolling in the course. See the Faculty of Arts &
Sciences policy
on auditing.
Auditing students will still be expected to attend all
lectures and compete all required coursework and exams. A course grade
of 75 is required for a successful audit.

- Collaboration: Students are encouraged to discuss homework with one another, but each student must submit separate solutions, and these must be the original work of the student.
- Exam conflicts: Read the
University policy.
The exam dates for this course are posted before the semester begins,
and thus you are expected to be present at all exams.

- Late homework: Only by
prior arrangement. If a valid reason for an exception is not presented
at least 36
hours before a homework due date, then it will not be accepted late (a
zero will be given for that assignment).

- Missed exams: There are no make-up exams. For valid excused absences with midterm exams - such as medical, family, transportation and weather-related emergencies - the contribution of that midterm to the final course grade will be redistributed equally to the other midterm exam and final exam. Students missing both midterm exams and/or the final exam cannot earn a passing grade for the course.

Lecture 1: Overview Roles of estimation, simulation, and optimization in statistical inference Reading : CS 1.1-1.8 (review of prerequisite material); LSB 1.1-1.13 HW1 assigned |

Lecture 2: Computer Storage and Arithmetic Fixed-point and floating-point number systems; errors Reading: CS 2.1-2.3; LSB 2.1-2.21 |

Lecture 3: Algorithms and Programming I Numerical errors; algorithms and data Reading: CS 3.1-3.2; LSB 3.1-3.12 |

Lecture 4: Algorithms and Programming II Efficiency Reading: CS 3.3; LSB 4.1-4.24 HW3 assigned |

Lecture 5: Algorithms and Programming III Iterations and convergence; programming; computational feasibility Reading: CS 3.4-3.6; LSB 4.1-4.24 |

Lecture 6: Function Approximation Function approximation and smoothing; basis sets in function spaces Reading: CS 4.1-4.2 (see Ch. 10 for perspective) |

Lecture 7: Vector Spaces Review |

Lecture 8: Function Approximation II Review of Taylor series expansions for multi-variable functions; Inner products on function spaces; orthogonal polynomials; Applications of orthogonal polynomials (refinements of classical univariate central limit theorem with Edgeworth expansions in orthogonal Hermite polynomials) Reading: CS 4.3-4.4 (see Ch. 10 for perspective) HW3 due |

Lecture 9: Function Approximation III Splines Reading: CS 4.4 |

Lecture 10: Review for first Midterm Unconstrained descent methods in dense domains; unconstrained combinatorial and stochastic optimization |

Lecture 11:
Kernel methods Reading: CS 4.5 (see Ch. 10 for perspective); LSB 5.1-5.13 |

Midterm 1 during class on Monday 10th October Material: Lectures 1-10 |

Lecture 12: Introduction to integral approximation Why must we approximate integrals? Liouville's theorem; Risch algorithm; statistical examples; overview of approximation methods Reference: see slides |

Lecture 13: Gaussian Quadrature Reference: CS Ch. 4 |

Lecture 14: Basics of Bayesian Computational Statistics Motivating uses of integral approximation in statistical inference; common setting of MCMC Reference: slides |

Lecture 15: Saddlepoint and Laplace Approximation Deterministic integral approximation methods; Bayesian logistic regression example Reference: slides |

Lecture 16: Random Variable Generation; Monte Carlo Integration Quantile transform method; rejection sampling; importance sampling Reference: CS Ch. 7, 11 and Appendix A |

Lecture 17: More on RNG; Intro to MCMC Types of pseudo-random number generators; basics of Markov chain theory Reference: CS Ch. 7, 11 and Appendix A |

Lecture 18: More Markov chain theory; Metropolis-Hastings and Gibbs Independent and random walk Metropolis-Hastings; optimal scaling and convergence diagnostics Reference: CS Ch. 11 and slides |

Midterm 2 during class on Wednesday 9th November Material: Lectures 11-17 |

Lecture 19: MCMC Examples Metropolis-Hastings and Gibbs examples; convergence diagnostics (Gelman-Rubin); writing R functions for MCMC Reference: see Blackboard articles |

Lecture 20: Introduction to Bootstrap Nonparametric bootstrap; bias estimation and standard error estimation; jackknife Reference: CS Ch. 12 and 13 |

Lecture 21: Bootstrap Confidence Intervals Normal, percentile and bootstrap t intervals; BCa intervals; implementation in R Reference: CS Ch. 12 and 13 |

Lecture 22: Cross-Validation and Permutation Tests Rference: CS Ch. 12 and 13 |

Lecture 23: Current Research in Computational Statistics Reference: slides |

Last day of fall semester classes is 12/09 |

Final Exam is Friday 12/16, 6:00-8:00pm (see your exam schedule for the room) |