Sequential Hypothesis Testing

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Sequential hypothesis testing studies how to accept or reject claims as data arrive, so experiments can stop once evidence is sufficient instead of using a fixed sample size. Classical sequential probability ratio tests are joined by martingale and e-value methods, including testing by betting, which can preserve error guarantees under adaptive sampling and optional stopping. These tools support applications such as online change detection, fairness and model audits, clinical or A/B experiments, and evaluation of AI systems and agents. A central challenge is balancing reliable anytime-valid error control with fast detection and low data costs, especially when assumptions, data distributions, or evaluator quality may change.

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63 papers15 papers in the last four weeks, up 150% on the four weeks before. 0.1% of all new papers.

Asymptotically Optimal Sequential Testing with Markovian Data
Feb 19, 2026Alhad Sethi, Kavali Sofia Sagar, Shubhada Agrawal +2Sequential Hypothesis Testing Markov Models
Indian Institute of Science, Bangalore · Indian Institute of Technology, Hyderabad · Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 – CRIStAL
On Cost-Aware Designs for Sequential Hypothesis Testing
Dec 22, 2025George Vershinin, Asaf Cohen, Omer GurewitzSequential Hypothesis Testing
The School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Israel
SGM: A Statistical Godel Machine for Risk-Controlled Recursive Self-Modification
Oct 11, 2025Xuening Wu, Shenqin Yin, Yanlan Kang +4Automated Machine Learning Self-Improving Agents
Fudan University · University of California, San Diego · Tongji University

Feb 19, 2026J/K move · Enter open · S save

Asymptotically Optimal Sequential Testing with Markovian Data

Alhad Sethi, Kavali Sofia Sagar, Shubhada Agrawal, Debabrota Basu+1

Indian Institute of Science, Bangalore · Indian Institute of Technology, Hyderabad · Univ. Lille, Inria, CNRS, Centrale Lille, UMR 9189 – CRIStAL

Sequential Hypothesis Testing Markov Models

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We study one-sided and

α

-correct sequential hypothesis testing for data generated by an ergodic, finite-state Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set

P

of stochastic matrices, and the alternative corresponds to a disjoint set

Q

. We establish a non-asymptotic instance-dependent lower bound on the expected stopping time of any valid sequential test under the alternative, which is asymptotically tight. Our novel analysis improves the existing lower bounds, which are either asymptotic or provably sub-optimal in this setting. Our lower bound incorporates both the stationary distribution and the transition structure induced by the unknown Markov chain. We further propose an optimal test whose expected stopping time matches this lower bound asymptotically as

α\to 0

. We illustrate the usefulness of our framework through applications to sequential detection of model misspecification in Markov Chain Monte Carlo and to testing structural properties, such as the linearity of transition dynamics, in Markov decision processes. Our findings yield a sharp and general characterization of optimal sequential testing procedures under Markovian dependence.

Latest papers

Asymptotically Optimal Sequential Testing with Markovian Data

On Cost-Aware Designs for Sequential Hypothesis Testing

SGM: A Statistical Godel Machine for Risk-Controlled Recursive Self-Modification