Scale Parameters: A Bayesian Treatment
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1981 · Volume 43 · Issue 3
DOI: 10.1111/j.2517-6161.1981.tb01680.x
Abstract
A definition of a scale parameter ϕ is given which includes the usual definition of a scale parameter in the exponential family. Some suggestions for the estimation of ϕ and approximations to the marginal posterior distribution of θ, a vector-valued parameter of primary interest, are made. In particular, the possibility of a χ2approximation to the posterior distribution of ϕ, leading to h.p.d. regions for θ based on theFdistribution, is explored. Two examples are discussed, where observations are from a normal and gamma distribution.
Keywords
scale parameters, bayesian inference, posterior approximations
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