Some Open Problems in Probability that are Relevant to Applied Statistics (my talk this Wed noon at the Columbia statistics department student seminar)

2026-02-10 · Source: Statistical Modeling, Causal Inference, and Social Science · Field: Science & Research — Mathematics & Computational Sciences, Social Sciences & Behavioral Studies, Research Methodology & Innovation · Depth: Advanced, quick

Summary

Andrew Gelman from Columbia University's Departments of Statistics and Political Science will present "Some Open Problems in Probability that are Relevant to Applied Statistics" on Wednesday, February 11, at noon in room 1025 of the Social Work Building. The talk will explore how probability theory extends beyond traditional fixed-model asymptotics to address challenges in models of growing complexity. Gelman plans to discuss several specific open problems, including piranha theorems, incoherent Gibbs sampling, the martingale property of probability forecasts, predictively consistent priors, and infill or sprawl asymptotics. This presentation aims to highlight how solving these theoretical probability issues can lead to more accurate models and improved predictions and inferences in real-world statistical applications.

Key takeaway

For AI Scientists and statisticians developing complex models, understanding these open problems in probability is critical. Focusing on areas like incoherent Gibbs sampling or infill/sprawl asymptotics can lead to more robust and accurate predictive models. Your work could directly benefit from engaging with these theoretical challenges to enhance real-world statistical inference.

Key insights

Open problems in probability theory are crucial for advancing statistical practice and improving real-world predictions.

Principles

• Probability theory extends beyond fixed-model asymptotics.
• Growing model complexity introduces new theoretical challenges.

In practice

• Explore piranha theorems for large effects in small datasets.
• Investigate predictively consistent priors for model accuracy.

Topics

• Applied Statistics
• Probability Theory
• Statistical Asymptotics
• Bayesian Priors
• Gibbs Sampling

Best for: AI Scientist, AI Researcher, Research Scientist, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by Statistical Modeling, Causal Inference, and Social Science.