NCSU : ST810 : Fall 2017

ST810 – Valid Probabilistic Inference  
Fall 2017   

Updated 09/19/2016

Instructor data

Name:   Ryan Martin
Office:   5238 SAS Hall
Phone:   919-515-1920
Email:   rgmarti3 AT ncsu.edu (best way to contact me)

Course data

Syllabus:   PDF file
Lecture:   T 3:00–5:45pm in SAS 5270
Office hrs: Wednesday 1–2pm, or by appointment.
Textbook:   R. Martin and C. Liu, Inferential Models, Chapman & Hall/CRC Press, 2015.
Software:   R is free to download at http://cran.r-project.org/

Announcements, etc

Please check this section occasionally for updates to the schedule or other information.

09/19: Here are the codes for the binomial IM example in class.

09/04: Sorry for the delay, but here is the description of the course project that I promised you. There are quite a few ideas of possible projects given there, but this certainly isn't exhaustive, so feel free to talk with me about any other ideas you might have. I'll say a few words about the project at the beginning of class on 09/05.

08/29: Here are the codes for the confidence distribution marginalization example in class.

08/17: I am going to assume that students are familiar with the basics of probability and statistical theory, as covered in ST521 and ST522 (now ST701 and ST702). More specifically, the ideas presented in my lecture notes here and especially here are the kinds of things I expect that you are familiar with. It's not necessary that you be familiar with the measure-theoretic stuff in the latter set of notes, but it wouldn't hurt. Some background with Bayesian methods and computational statistics (e.g., simulation, MCMC, optimization, etc) would also be helpful, though not required.

08/17: As described in the syllabus, pass/fail grades will be assigned based largely on a final course project. Details about the project, along with some suggested topics, will be given soon.

08/17: Welcome to ST810!


Course outline and supplements

  1. What is statistical inference?

    • On 8/22 I discussed some philosophical stuff concerning statistical inference. A key point in Fisher's line of reasoning was that the only way a conclusion could be made about a hypothesis was if a dichotomy could be established, namely, either the hypothesis is false OR it's true but a rare event occurred. Since "rare events won't happen," we are inclined to believe that the hypothesis is false. There really is nothing frequentist about this argument but, if one tries to operationalize it, then it turns into the all-to-familiar "reject if p-value is less than 0.05," which is not what Fisher had in mind. Anyway, I formulated this scenario when the above dichotomy can be reached through a particular validity condition. We will develop this further on 8/29, and make some connections to existing approaches.
    • A paper relevant to the discussion in the first two lectures is here. Eventually I will revise this paper to include some of the ideas presented in the first lecture.
  2. Existing approaches.

  3. Inferential models—the basics.

    • Chapter 1, 3, and 4 in the book.
      • High-level introduction
      • Fundamental principles—validity and efficiency
      • Three-step construction
      • Validity properties
      • Towards optimality
    • ...

  4. Some details on random sets.

    • Chapter 5 in the book.
    • ...

  5. Improved efficiency via dimension reduction.

    • Chapter 6: Combining information from independent sources via conditioning.
    • Chapter 7: Marginalization by ignoring nuisance directions.
    • ...

  6. Applications.

    • Chapter 8: Linear models
    • Chapter 9: Prediction
    • ...

  7. Extensions and open problems.

    • ...