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American University

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Selected work

Representative Papers

Constructing and extending $n$ = 1 Bayesian confidence intervals for location parameters in location-scale families

Jul 27, 2026

This study addresses the long-standing challenge of constructing nontrivial, efficient confidence intervals for the location parameter of a location-scale family when only a single observation is available. The authors propose two Bayesian approaches: first, deriving priors that yield asymptotically efficient intervals at high confidence levels; second, integrating classical t-intervals with prior information to form an enhanced t-interval based on Bayes factor testing. The work establishes, for the first time, a systematic Bayesian mechanism for generating single-sample confidence intervals and demonstrates an equivalence between Bayesian credible intervals and frequentist confidence intervals. The methodology extends to any continuous symmetric location-scale family. Theoretical results show that the proposed intervals are asymptotically efficient when \( n = 1 \), and for \( n \geq 2 \), the enhanced t-interval achieves smaller expected squared width over parts of the parameter space, with practical utility validated on interstellar object velocity data.

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Recent publications

Latest Papers

Constructing and extending $n$ = 1 Bayesian confidence intervals for location parameters in location-scale families

Jul 27, 2026

This study addresses the long-standing challenge of constructing nontrivial, efficient confidence intervals for the location parameter of a location-scale family when only a single observation is available. The authors propose two Bayesian approaches: first, deriving priors that yield asymptotically efficient intervals at high confidence levels; second, integrating classical t-intervals with prior information to form an enhanced t-interval based on Bayes factor testing. The work establishes, for the first time, a systematic Bayesian mechanism for generating single-sample confidence intervals and demonstrates an equivalence between Bayesian credible intervals and frequentist confidence intervals. The methodology extends to any continuous symmetric location-scale family. Theoretical results show that the proposed intervals are asymptotically efficient when \( n = 1 \), and for \( n \geq 2 \), the enhanced t-interval achieves smaller expected squared width over parts of the parameter space, with practical utility validated on interstellar object velocity data.

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