Nonparametric perspectives on empirical Bayes
Abstract/Contents
- Abstract
- In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of when and why empirical Bayes point estimates accurately recover oracle Bayes behavior---in particular when the likelihood of the individual statistical problems is known and all problems are relevant to each other. In this thesis, we build upon advances in the theory of nonparametric statistics, machine learning, and computation to make three-fold contributions to the empirical Bayes literature: 1) We develop flexible and practical confidence intervals that provide asymptotic frequentist coverage of empirical Bayes estimands, such as the posterior mean or the local false sign rate. The coverage statements hold even when the estimands are only partially identified or when empirical Bayes point estimates converge very slowly. 2) We show that it is possible to achieve near-Bayes optimal mean squared error for the estimation of n effect sizes in the setting where both the prior and the per-problem likelihood are unknown. The requirement of our method is that we have access to replicated data, that is, each effect size of interest is estimated from K> 1 noisy observations. 3) We tackle the issue of relevance in empirical Bayes estimation of effect sizes. We propose a method that shrinks toward a per-problem location determined by a machine learning model prediction of the effect given side-information. We establish an extension to the classic result of James-Stein, whereby our proposed estimator dominates the sample mean for each problem under quadratic risk; even if the side-information contains no information about the true effects, or the machine learning model is arbitrarily miscalibrated. Taken together, these results broaden the applicability of empirical Bayes methods in areas such as genomics, and large scale experimentation, and demonstrate that it is fruitful to revisit traditional ideas in the empirical Bayes literature through a modern lens. The above results largely draw upon the following papers: Ignatiadis and Wager (2019, 2022) and Ignatiadis, Saha, Sun, and Muralidharan (2021).
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2022; ©2022 |
| Publication date | 2022; 2022 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Ignatiadis, Nikolaos |
|---|---|
| Degree supervisor | Wager, Stefan |
| Thesis advisor | Wager, Stefan |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Tibshirani, Robert |
| Degree committee member | Candès, Emmanuel J. (Emmanuel Jean) |
| Degree committee member | Tibshirani, Robert |
| Associated with | Stanford University, Department of Statistics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Nikolaos Ignatiadis. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2022. |
| Location | https://purl.stanford.edu/sy052fc9059 |
Access conditions
- Copyright
- © 2022 by Nikolaos Ignatiadis
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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