General sample size analysis for probabilities of causation: a delta method approach
#probabilities of causation#probability of necessity and sufficiency#delta method#sample size#experimental data#observational data#statistical bounds#Judea Pearl#causal inference
📌 Key Takeaways
Probabilities of causation (PoCs) are crucial for decision making but are typically not point‑identifiable.
Prior research has provided bounds for PoCs using experimental and observational data, but has not addressed sample size requirements.
The authors propose a general sample‑size framework based on the delta method applicable when PoC bounds are finite minima or maxima of linear combinations of observed probabilities.
Simulation studies demonstrate that the derived sample‑size calculations yield stable estimation of the PoC bounds.
The work bridges statistical methodology (stat.ME) and artificial intelligence (cs.AI) research communities.
📖 Full Retelling
On 19 February 2026, Tianyuan Cheng, Ruirui Mao, Judea Pearl, and Ang Li published the methodology paper "General sample size analysis for probabilities of causation: a delta method approach" on arXiv (stat.ME) to address the lack of guidance on how many experimental and observational samples are needed to achieve a desired margin of error when estimating bounds on probabilities of causation such as the probability of necessity and sufficiency.
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Deep Analysis
Why It Matters
The paper provides a systematic way to determine how many samples are needed to estimate probabilities of causation within a desired precision, which is crucial for designing experiments and observational studies in fields such as medicine, economics, and AI safety.
Context & Background
Probabilities of causation are not point identifiable and usually bounded
Existing work provides bounds but not sample size guidance
The delta method offers a statistical tool for approximating variances of functions of random variables
What Happens Next
Researchers can apply the framework to plan future studies, ensuring adequate power to estimate causal probabilities. The methodology may also be extended to more complex causal models and integrated into software packages for causal inference.
Frequently Asked Questions
What is a probability of causation?
It is a measure that quantifies how likely an outcome would have occurred if a different action had been taken, such as the probability of necessity or sufficiency.
How does the delta method help with sample size?
It approximates the variance of a function of estimated probabilities, allowing calculation of how many observations are needed to achieve a target margin of error.
Can this approach be used in observational studies only?
No, it works for settings that combine experimental and observational data and can be applied to either or both.
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Original Source
-- Methodology arXiv:2602.17070 [Submitted on 19 Feb 2026] Title: General sample size analysis for probabilities of causation: a delta method approach Authors: Tianyuan Cheng , Ruirui Mao , Judea Pearl , Ang Li View a PDF of the paper titled General sample size analysis for probabilities of causation: a delta method approach, by Tianyuan Cheng and 3 other authors View PDF HTML Abstract: Probabilities of causation , such as the probability of necessity and sufficiency , are important tools for decision making but are generally not point identifiable. Existing work has derived bounds for these quantities using combinations of experimental and observational data. However, there is very limited research on sample size analysis, namely, how many experimental and observational samples are required to achieve a desired margin of error. In this paper, we propose a general sample size framework based on the delta method. Our approach applies to settings in which the target bounds of PoCs can be expressed as finite minima or maxima of linear combinations of experimental and observational probabilities. Through simulation studies, we demonstrate that the proposed sample size calculations lead to stable estimation of these bounds. Subjects: Methodology (stat.ME) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2602.17070 [stat.ME] (or arXiv:2602.17070v1 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2602.17070 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tianyuan Cheng [ view email ] [v1] Thu, 19 Feb 2026 04:25:36 UTC (2,061 KB) Full-text links: Access Paper: View a PDF of the paper titled General sample size analysis for probabilities of causation: a delta method approach, by Tianyuan Cheng and 3 other authors View PDF HTML TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2026-02 Change to browse by: cs cs.AI stat References & Citations NASA ADS Google Scholar Semantic Schola...
