A statistical diptych: Admissible inferences -- recurrence of symmetric Markov chains

DOI10.1214/aos/1176348764zbMath0767.62002OpenAlexW2023377965MaRDI QIDQ1206701

Publication date: 1 April 1993

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176348764

zbMATH Keywords

predictive distributions risk function improper prior distribution prediction problem marginal measure almost admissibility estimating a bounded measurable function formal Bayes rules formal posterior distribution quadratically regular decision problems recurrence of symmetric Markov chains

Mathematics Subject Classification ID

Bayesian problems; characterization of Bayes procedures (62C10) Continuous-time Markov processes on discrete state spaces (60J27) Admissibility in statistical decision theory (62C15) General considerations in statistical decision theory (62C05)

Related Items (19)

A conversation with Larry Brown ⋮ Stability of the tail Markov chain and the evaluation of improper priors for an exponential rate parameter ⋮ Admissibility in quadratically regular problems and recurrence of symmetric Markov chains: Why the connection? ⋮ Bayes and robust Bayes prediction with an application to a rainfall prediction problem ⋮ Distributional inference ⋮ Evaluating default priors with a generalization of Eaton's Markov chain ⋮ Larry Brown's contributions to parametric inference, decision theory and foundations: a survey ⋮ Larry Brown's work on admissibility ⋮ Gibbs sampling, exponential families and orthogonal polynomials ⋮ Admissible predictive density estimation ⋮ When is Eaton's Markov chain irreducible? ⋮ Estimation, prediction and the Stein phenomenon under divergence loss ⋮ Evaluation of formal posterior distributions via Markov chain arguments ⋮ Integral priors for Bayesian model selection: how they operate from simple to complex cases ⋮ Bayes, E-Bayes and robust Bayes prediction of a future observation under precautionary prediction loss functions with applications ⋮ Eaton's Markov chain, its conjugate partner and \(\mathcal P\)-admissibility ⋮ Bayes and robust Bayes predictions in a subfamily of scale parameters under a precautionary loss function ⋮ Integral equation solutions as prior distributions for Bayesian model selection ⋮ Conditions for recurrence and transience of a Markov chain on \(\mathbb Z^ +\) and estimation of a geometric success probability.

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