DS6310

Theory II: Inference & Prediction - Spring 2026

Course information


Course materials

Additional resources


Topics

  1. Foundations of inference
    • Sampling distributions
    • Point estimation, interval estimation, and hypothesis testing
    • Optimality criteria
  2. Likelihood methods
    • Parametric models and exponential families
    • Information
    • Maximum likelihood
  3. Asymptotic evaluations
    • Consistency
    • Delta method
    • Asymptotic properties of MLEs
  4. Bootstrapping and resampling methods
    • The jackknife estimate of standard error
    • Non-parametric bootstrap
    • Parametric bootstrap
  5. Prediction
    • Estimates of predictive accuracy
    • Shrinkage and ridge regression
    • Contemporary ideas in prediction (if time allows)

Schedule

Jan 13 2026: Course overview + the terminology of inference

Jan 15 2026: Sample sizes tending toward infinity

Jan 20 2026: Beyond the CLT, analyzing estimators

Jan 22 2026: Bias and variance

Jan 27 2026: Bounds for optimal estimation, information

Jan 29 2026: Data reduction, sufficiency

Feb 05 2026: TBD

Feb 12 2026: TBD

Feb 19 2026: TBD

Feb 26 2026: Midterm exam

Mar 03-05 2026: Spring recess (no class)

Mar 12 2026: TBD

Mar 19 2026: TBD

Mar 26 2026: TBD

Apr 02 2026: TBD

Apr 09 2026: TBD

Apr 28 2026: Final review

May 04 2026: Final exam (2:00 - 5:00 pm, location TBD)


Grades

Final grades will be computed using the following weighting:

Grading scale:

Note that a B- is the lowest satisfactory grade for graduate credit.

Course Policies

Submitting Homework

Homework will be accepted through the Assignments page on Canvas. Submissions will be in PDF format. You may hand-write and scan problem solutions, or you may use a typesetting software like LaTeX, Markdown, etc. Some homework assignments will involve using code to produce graphical or numerical outputs and will require the use of software. Please compile all materials in a single PDF for submission and make sure that whatever you have written can be clearly read by the grader.

Grades for (on-time) homework will be made visible to students no later than one week after the assignment due date. Grades for late work (see below) will become available as time permits.

Late Work Policy

The expectation in this course is that all assignments will be submitted on time. Submitting your work on time respects the efforts of your instructor and teaching assistant, and it ensures that you are prepared to learn subsequent material.

Assignments turned in after the due date incur a 10% penalty per late day. For example, an assignment due at 9:30 am on Tuesday that is submitted to Canvas at 3:00 pm on Thursday will incur a 30% penalty. If the assignment would have received a 95% had it been returned on time, then the late grade is 65%. Note that weekend days count towards the late penalty.

I will not accept work that is late by more than one week past its due date.

To provide flexibility for weeks in which life circumstances do not permit the completion of your coursework, your lowest homework grade will be dropped.

Class Attendance

Attendance in this class is mandatory. If you need to miss a class for any reason, please email me in advance. You are responsible for keeping up with the lecture material, but I am happy to work with you during office hours or by appointment to brush up on things you may have missed.

Extenuating Circumstances

Students are expected to communicate with me as soon as possible regarding extenuating circumstances and how their participation in the course, including attendance and assignment submissions, may be affected by them.

Academic Integrity

I encourage collaboration among students to complete homework assignments. The purpose of collaborating is to help yourself and your classmates learn the material more effectively.

Do not cheat. Cheating circumventes the learning process and deprives you of the chance to gain expertise in your discipline. It also puts you in a position to fail the in-class exams, for which you will not be able to use resources outside of your own problem solving ability

I ask that you:

  1. Do not copy text or code from classmates, the internet, or AI systems. Write your own solutions and understand them.
  2. Do not send text or code to classmates or post your solutions in a place where everyone can access them. If you are collaborating with others, you are working together to arrive at a solution.
  3. Try to solve each problem before resorting to outside help. Even if you do not ultimately arrive at a solution completely on your own, starting the solution process by yourself is crucial to learning.

If an action you are considering is not covered by one of these specific asks, please use your own sense of right and wrong to determine whether it constitutes cheating.

University Support and Policies


Homework explications

Definition and goal

An explication is a detailed explanation. The goal of homework explications is to give students the opportunity to explain, in detail, their reasoning as they work towards the solution of a homework problem. Explications are intended to encourage real-time logical thinking and argument based upon the principles learned in class and in readings.

How will explications be implemented?

For each homework that is assigned, two students will be asked to give an explication. Explications will take place during the class period coinciding with the assignment due date (typically this will be a Thursday). Specifically,

  1. At the start of class time, the instructor will choose a homework problem from the week’s assignment and ask one of the students to present their solution to the problem to the class on the whiteboard (if an element of the solution involves a simulation, the student may use a laptop as well).

  2. A Q&A and discussion will follow, in which members of the class and/or the instructor may ask clarifying questions of the presenting student. Subjects of relevance to lecture material will be elucidated.

  3. Steps 1. and 2. will be repeated for the second student, but a different problem will be chosen. The two explications combined should take around 25-30 minutes of class time.

How will explications be graded?

Your grade will be determined by the instructor based on a combination of

  1. The quality of your solution.
  2. The clarity of your reasoning.
  3. Your ability to justify your solution choices based on things we have learned in class and in readings.

Note that the correctness of your solution is not a criterion. Yes, correct solutions may tend to be higher quality, but an incorrect solution could still be high quality if the steps taken along the way are coherent and generally sensible.

Additional notes for explicators