Abstract
The log-normal distribution is a popular model in biostatistics and
other fields of statistics. Bayesian inference on the mean and median of the distribution
is problematic because, for many popular choices of the prior for the
variance (on the log-scale) parameter, the posterior distribution has no finite moments,
leading to Bayes estimators with infinite expected loss for the most common
choices of the loss function. We propose a generalized inverse Gaussian prior for the
variance parameter, that leads to a log-generalized hyperbolic posterior, for which
it is easy to calculate quantiles and moments, provided that they exist. We derive
the constraints on the prior parameters that yield finite posterior moments of order
r. We investigate the choice of prior parameters leading to Bayes estimators
with optimal frequentist mean square error. For the estimation of the lognormal
mean we show, using simulation, that the Bayes estimator under quadratic loss
compares favorably in terms of frequentist mean square error to known estimators.
Lingua originale | English |
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pagine (da-a) | 975-996 |
Numero di pagine | 21 |
Rivista | Bayesian Analysis |
Volume | 2012 |
DOI | |
Stato di pubblicazione | Pubblicato - 2012 |
Keywords
- Bayes estimators
- Bessel functions
- generalized hyperbolic distribution
- generalized inverse gamma distribution