Tosta

In this part of the course we will first consider further aspects of statistical analysis for RCTs. Next we consider numerical methods for generalized linear mixed models and give an introduction to Markov random fields.

Some data sets and R-code used in the course.

  1. Slides with some further remarks on causal inference. Slides on analysing RCTs with baseline adjustment and mixed models. Tutorial on using prognostic scores in RCTs.
  2. We continue with slides from last time.
  3. Slides on missing data in RCTs.
  4. Slides. Videos tosta_logistic1-4 at youtube.
  5. Slides. Note on Laplace approximation. Practical exercise on Laplace approximation. Some extra material on Monte Carlo methods.
  6. Slides on Markov random fields I. Additional reading: Chapter on conditional auto regressions (beware, their notation differs a bit from mine).
  7. Slides on Markov random fields II. We continue with Markov random fields.
  8. Selfstudy on Markov random fields and Bayesian image analysis.

Additional reading material: page 1-23 in Markov random fields and their applications by Kindermann and Snell.

Exam exam is oral without preparation. Duration 20 minutes including assessment. Prepare 15 minutes presentation on blackboard for each of the questions below. The curriculum for the course and exam consists of the lecture slides including the exercises given in the slides, the material referenced by Emilie in the book by Schuler, and Appendix A in the tutorial article.

Exam questions:

  1. Causal inference and randomized trials
  2. Influence functions for asymptotically linear estimators
  3. Construction of asymptotically linear and efficient estimators using influence functions
  4. Missing data and randomized trials
  5. Computation of the likelihood function for GLMMs: Laplace approximation and numerical quadrature
  6. Markov random fields: the Hammersley-Clifford theorem
  7. Markov random fields: Brooks factorization and Gaussian Markov random fields
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