Abstract
Summary A parameter μ is to be estimated from an unbiased, unit-variance measurement x. The prior distribution is symmetrical about zero with unknown scale parameter σ. It is claimed that the observation x gives information about σ which is contained in the likelihood distribution p(dx|σ). An estimator μ̂ = γx is found, based on the posterior distribution of μ conditional on the most probable value of σ. For a prior distribution of arbitrary shape, γ is zero when x2 ≤ 1 and approaches 1 – x–2 when x2 ≥ 1. A minimum mean-square estimator is found based on an estimate of the prior variance. This gives the same result, independently of the shape of the prior distribution, as the previous estimator for a normal prior.
Keywords
MathematicsStatisticsEstimatorPrior probabilityBias of an estimatorMinimum-variance unbiased estimatorDistribution (mathematics)Variance (accounting)Scale parameterShape parameterNormal distributionScale (ratio)Posterior predictive distributionTrimmed estimatorBayesian linear regressionMathematical analysisPhysicsBayesian probabilityBayesian inference
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Publication Info
- Year
- 1965
- Type
- article
- Volume
- 27
- Issue
- 1
- Pages
- 17-27
- Citations
- 4
- Access
- Closed
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Cite This
M. Clutton-Brock
(1965).
Using the Observations to Estimate the Prior Distribution.
Journal of the Royal Statistical Society Series B (Statistical Methodology)
, 27
(1)
, 17-27.
https://doi.org/10.1111/j.2517-6161.1965.tb00582.x
Identifiers
- DOI
- 10.1111/j.2517-6161.1965.tb00582.x