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Estimating a product of means: Bayesian analysis with reference priors. (English) Zbl 0682.62018

Suppose that we observe \(X\sim N(\alpha,1)\) and, independently, \(y\sim N(\beta,1)\), and are concerned with inference (mainly estimation and confidence statements) about the product of means \(\theta =\alpha \beta\). This problem arises, most obviously, in situations of determining area based on measurements of length and width. It also arises in other practical contexts, however. Approximately independent samples can be obtained for each mean. Noninformative prior Bayesian approaches to the problem are considered, in particular the reference prior approach of the second author [J. R. Stat. Soc., Ser. B 41, 113-147 (1979; Zbl 0428.62004)]. An appropriate reference prior for the problem is developed, and relatively easily implementable formulas for posterior moments (e.g., the posterior mean and variance) and credible sets are derived. Comparisons with alternative noninformative priors and with classical procedures are also given.

MSC:

62F15 Bayesian inference
62F10 Point estimation

Citations:

Zbl 0428.62004
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