Ellis Scharfenaker, Duncan K. Foley
arXiv 5 Sep 2025 · Statistics — Methodology
arXiv:2509.05520 · PDF · DOI · OpenAlex · Extracted main text
A central challenge in statistical inference is the presence of confounding variables that may distort observed associations between treatment and outcome. Conventional "causal" methods, grounded in assumptions such as ignorability, exclude the possibility of unobserved confounders, leading to posterior inferences that overstate certainty. We develop a Bayesian framework that relaxes these assumptions by introducing entropy-favoring priors over hypothesis spaces that explicitly allow for latent confounding variables and partial information. Using the case of Simpson's paradox, we demonstrate how this approach produces logically consistent posterior distributions that widen credibly intervals in the presence of potential confounding. Our method provides a generalizable, information-theoretic foundation for more robust predictive inference in observational sciences.
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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 | Golan, A (2018) Foundations of Info-Metrics: Modeling, Inference and Imperfect Information | 0.737 | 3 | 2 | 100% |
| 2 | de Finetti, B (1974) Theory of Probability: A Critical Introductory Treatment | 0.737 | 3 | 2 | 100% |
| 3 | Foley, D. K. and E. Scharfenaker (2025) Bayesian inference and the principle of maximum entropy self | 0.644 | 2 | 2 | 100% |
| 4 | Jaynes, E. T (1983) Papers on Probability, Statistics, and Statistical Physics | 0.644 | 2 | 2 | 100% |
| 5 | Beni, G. and X. Liu (1994) A least biased fuzzy clustering method | 0.405 | 1 | 1 | 100% |
| 6 | Chau, T (2001) Marginal maximum entropy partitioning yields asymptotically consistent probability density functions | 0.405 | 1 | 1 | 100% |
| 7 | Cover, T. M. and J. A. Thomas (2006) Elements of Information Theory\/ (2 ed.) | 0.405 | 1 | 1 | 100% |
| 8 | Flashner-Abramson, E., S. Vasudevan, I. Adejumobi, A. Sonnenblick, a… (2019) Decoding cancer heterogeneity: studying patient-specific signaling signatures towards personalized cancer therapy | 0.405 | 1 | 1 | 100% |
| 9 | Fujino, A., N. Ueda, and K. Saito (2008) Semisupervised learning for a hybrid generative/discriminative classifier based on the maximum entropy principle | 0.405 | 1 | 1 | 100% |
| 10 | Gupta, M., R. Gray, and R. Olshen (2006) Nonparametric supervised learning by linear interpolation with maximum entropy | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 38 scored citations.