arXiv 14 Jan 2026 · Econometrics
arXiv:2601.09888 · PDF · DOI · OpenAlex · Extracted main text
We establish concentration rates for estimation of treatment effects in experiments that incorporate prior sources of information -- such as past pilots, related studies, or expert assessments -- whose external validity is uncertain. Each source is modeled as a Gaussian prior with its own mean and precision, and sources are combined using Bayesian model averaging (BMA), allowing data from the new experiment to update posterior weights. To capture empirically relevant settings in which prior studies may be as informative as the current experiment, we introduce a nonstandard asymptotic framework in which prior precisions grow with the experiment's sample size. In this regime, posterior weights are governed by an external-validity index that depends jointly on a source's bias and information content: biased sources are exponentially downweighted, while unbiased sources dominate. When at least one source is unbiased, our procedure concentrates on the unbiased set and achieves faster convergence than relying on new data alone. When all sources are biased, including a deliberately conservative (diffuse) prior guarantees robustness and recovers the standard convergence rate.
appendix boundary found by appendix_command · 53% of the source is main text. Read the extracted text to check this.
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 | Wasserman, Larry (2000) Bayesian Model Selection and Model Averaging | 0.585 | 3 | 1 | 100% |
| 2 | Kass, Robert E. and Raftery, Adrian E (1995) Bayes Factors | 0.511 | 2 | 1 | 100% |
| 3 | Steel, Mark F. J (2020) Model Averaging and Its Use in Economics | 0.511 | 2 | 1 | 100% |
| 4 | Fernandez, Carmen and Ley, Eduardo and Steel, Mark (2001) Model uncertainty in cross-country growth regressions | 0.405 | 1 | 1 | 100% |
| 5 | Fernández, Carmen and Ley, Eduardo and Steel, Mark F. J (2001) Model Uncertainty in Cross-Country Growth Regressions | 0.405 | 1 | 1 | 100% |
| 6 | Jennifer A. Hoeting and David Madigan and Adrian E. Raftery and Chri… (1999) Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors | 0.405 | 1 | 1 | 100% |
| 7 | Valen E. Johnson and David Rossell (2012) Bayesian Model Selection in High-Dimensional Settings | 0.405 | 1 | 1 | 100% |
| 8 | Kaufmann, Emilie and Korda, Nathaniel and Munos, Rémi (2012) Thompson Sampling: An Asymptotically Optimal Finite-Time Analysis | 0.405 | 1 | 1 | 100% |
| 9 | Cheng Li and Wenxin Jiang (2016) On oracle property and asymptotic validity of Bayesian generalized method of moments | 0.405 | 1 | 1 | 100% |
| 10 | Liang, Feng and Paulo, Rui and Molina, Germán and Clyde, Merlise A.… (2008) Mixtures of $g$ Priors for Bayesian Variable Selection | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 18 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | 0.5 in Using Prior Studies to Design Experiments: An Empirical Bayes Approach | 0.405 | 1 | 1 |
| 2 | Quasi-Bayesian Hierarchical Models | 0.405 | 1 | 1 |