Topics in adaptive inference
Abstract/Contents
- Abstract
- The recent rapid expansion in data collection has presented the field of statistics with an inexhaustible array of exciting new applications and problem settings not directly covered by classical methods or theory. In more complex problems, we must choose an appropriate computational algorithm, statistical model, or scientific question that is well-tuned to the sampling distribution we are presented with. Thus the payoff from using methods that adapt to the data set at hand is high. This work details several such methods. Chapter 2, essentially a reproduction of Fithian and Hastie (2014), describes an adaptive subsampling strategy for computationally efficient inference on massive data sets. Using a modified case-control sampling algorithm, we ``compress'' a large data set into a much smaller subsample, enriching for the most informative observations. Our algorithm enables potentially much faster analysis, at a provably small cost to statistical performance. Most statistical inference procedures are formally invalid if they are preceded by ``data snooping.'' However, in most real data problems it is hard to specify a reliable model a priori. Chapter 3, essentially a reproduction of Fithian, Sun, and Taylor (2014), discusses methods for carrying out valid inference after adaptive model selection, correcting for selection by conditioning on the model selected. Chapter 4 is as-yet unpublished work and gives further examples of selective inference applied to specific problems. First, I discuss the problem of ``rank verification'' --- testing, for example, whether the candidate who receives the most votes in a random survey is actually leading in the population from which the survey was taken. Second, I discuss an exact nonparametric selective inference procedure for use when a the data fail a goodness-of-fit test for some set of parametric assumptions.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Fithian, William |
|---|---|
| Associated with | Stanford University, Department of Statistics. |
| Primary advisor | Hastie, Trevor |
| Thesis advisor | Hastie, Trevor |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Taylor, Jonathan E |
| Thesis advisor | Tibshirani, Robert |
| Advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Advisor | Taylor, Jonathan E |
| Advisor | Tibshirani, Robert |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | William Fithian. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by William Shannon Fithian
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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