Flora C. Shi, Martin J. Wainwright, Stephen Bates
arXiv 24 Oct 2025 · cs.GT
arXiv:2510.21178 · PDF · DOI · OpenAlex · Extracted main text
We study hypothesis testing over a heterogeneous population of strategic agents with private information. Any single test applied uniformly across the population yields statistical error that is sub-optimal relative to the performance of an oracle given access to the private information. We show how it is possible to design menus of statistical contracts that pair type-optimal tests with payoff structures, inducing agents to self-select according to their private information. This separating menu elicits agent types and enables the principal to match the oracle performance even without a priori knowledge of the agent type. Our main result fully characterizes the collection of all separating menus that are instance-adaptive, matching oracle performance for an arbitrary population of heterogeneous agents. We identify designs where information elicitation is essentially costless, requiring negligible additional expense relative to a single-test benchmark, while improving statistical performance. Our work establishes a connection between proper scoring rules and menu design, showing how the structure of the hypothesis test constrains the elicitable information. Numerical examples illustrate the geometry of separating menus and the improvements they deliver in error trade-offs. Overall, our results connect statistical decision theory with mechanism design, demonstrating how heterogeneity and strategic participation can be harnessed to improve efficiency in hypothesis testing.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Shi, Flora C, Bates, Stephen, Wainwright, Martin J (2024) Sharp Results for Hypothesis Testing with Risk-Sensitive Agents self | 0.644 | 3 | 2 | 67% |
| 2 | Bolton, Patrick, Dewatripont, Mathias (2004) Contract Theory | 0.644 | 2 | 2 | 100% |
| 3 | Gneiting, Tilmann, Raftery, Adrian E (2007) Strictly proper scoring rules, prediction, and estimation | 0.644 | 2 | 2 | 100% |
| 4 | Laffont, Jean-Jacques, Martimort, David (2001) The Theory of Incentives: The Principal-Agent Model | 0.644 | 2 | 2 | 100% |
| 5 | McCarthy, John (1956) Measures of the value of information | 0.644 | 2 | 2 | 100% |
| 6 | Savage, Leonard J (1971) Elicitation of personal probabilities and expectations | 0.644 | 2 | 2 | 100% |
| 7 | Bates, Stephen, Jordan, Michael I., Sklar, Michael, Soloff, Jake A (2022) Principal-Agent Hypothesis Testing self | 0.511 | 2 | 1 | 100% |
| 8 | Bates, Stephen, Jordan, Michael I., Sklar, Michael, Soloff, Jake A (2023) Incentive-Theoretic Bayesian Inference for Collaborative Science self | 0.511 | 2 | 1 | 100% |
| 9 | Hossain, Safwan, Chen, Yatong, Chen, Yiling (2025) Strategic Hypothesis Testing | 0.511 | 2 | 1 | 100% |
| 10 | Jagadeesan, Ravi, Viviano, Davide (2025) Publication Design with Incentives in Mind | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 36 scored citations.