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1991•Communication in Statistics- Theory and MethodsRequires access

Bayesian confidence estimation: an alternative approach

Julián de la Horra

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Abstract

From a Bayesian point of wiew, the estimation of an unknown parameter can be interpreted (in many situations) as the problem of fixing a partition of the parameter space (by means of small intervals I1,…Ik and choosing an interval Ij, from this partition, provided that sufficient information has been obtained. This idea is developed in a decision theory setting. If the Kolmogorov-Smirnov loss is used, it is proved that Ij is the best interval estimation if and only if its posterior probability is greater than or equal to 1/2

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What this paper is about

From a Bayesian point of wiew, the estimation of an unknown parameter can be interpreted (in many situations) as the problem of fixing a partition of the parameter space (by means of small intervals I1,…Ik and choosing an interval Ij, from this partition, provided that sufficient information has been obtained. This idea is developed in a decision theory setting. If the Kolmogorov-Smirnov loss is used, it is proved that Ij is the best interval estimation if and only if its posterior probability is greater than or equal to 1/2

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Available abstract

From a Bayesian point of wiew, the estimation of an unknown parameter can be interpreted (in many situations) as the problem of fixing a partition of the parameter space (by means of small intervals I1,…Ik and choosing an interval Ij, from this partition, provided that sufficient information has been obtained. This idea is developed in a decision theory setting. If the Kolmogorov-Smirnov loss is used, it is proved that Ij is the best interval estimation if and only if its posterior probability is greater than or equal to 1/2

Key concepts: Interval estimation, Point estimation, Mathematics, Partition (number theory), Credible interval, Bayesian probability, Confidence interval, Bayes estimator

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