1 / 10

Discussion of Profs. Robins’ and M  ller’s Papers

Discussion of Profs. Robins’ and M  ller’s Papers. S.A. Murphy ENAR 2003. Insert Slides commenting on Robins’ Paper. Connection Between Papers. Both are decision problems in which multiple decisions must be made: “Multi-stage Decisions”.

lydie
Download Presentation

Discussion of Profs. Robins’ and M  ller’s Papers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Discussion of Profs. Robins’ and Mller’s Papers S.A. Murphy ENAR 2003

  2. Insert Slides commenting on Robins’ Paper

  3. Connection Between Papers Both are decision problems in which multiple decisions must be made: “Multi-stage Decisions”

  4. Collect information: L1 (Robins) or y1 (Mller) • Choose a treatment (or decision) based on this info a1 (or d1) • Collect more information: L2 (or y2) • Choose an treatment based on info to date  a2 (or d2) • And so on….. until time K (or T) • GOAL: Choose a1, a2,…. to maximize • E[u(a1,…aK,L1,….LK+1;)]

  5. Information Used to Achieve Goal • Robins: Random Sample of Observations: • L1, A1, L2, A2, …., AK, LK+1 • (A’s are randomized treatments)

  6. Information Used to Achieve Goal • Mller: Known multivariate distribution of • L1, L2, …., LK+1 • indexed by decisions, a1, a2, …., aK and  • + prior for .

  7. A Commonality • The information at time t: • L1, L2, …., Lt • is high dimensional; both authors must use summary statistics, a.k.a. “Feature Extraction” • Open problem: Best methods for Feature Extraction in multi-stage decision problems

  8. Delayed Effects of Decisions • Treatment decision influences Lt and other unobserved individual characteristics: • Robins’ setting: known Lt and other unobserved characteristics may interact with next treatment effect. • Mller’s setting: Optimal decision depends on latent . Lt is used to update the distribution of .

  9. Computational Development • Robins’ and Murphy’s methods: undeveloped with unknown computational issues. • Mller’s, Bayesians, Reinforcement Learning methods: well developed with sophisticated understanding of computational issues.

  10. Interesting Philosophical Note • Statistical analysis should be conducted as if it is a confirmatory trial • versus • Statistical analysis should be conducted as if this trial is part of a sequence of trials with a confirmatory study to follow. • Sequential Experimentation

More Related