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Scale parameters: a Bayesian treatment

Sweeting, TJ; (1981) Scale parameters: a Bayesian treatment. Journal of the Royal Statistical Society. Series B , 43 (3) 333 - 338.

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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 χ<sup>2</sup> approximation to the posterior distribution of φ, leading to h.p.d. regions for θ based on the F distribution, is explored. Two examples are discussed, where observations are from a normal and gamma distribution.

Title:Scale parameters: a Bayesian treatment
Keywords:Scale parameters, Bayesian inference, Posterior approximations
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

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