TY - JOUR

T1 - Reference priors for natural exponential families having a simple quadratic variance function

AU - Consonni, Guido

AU - Veronese, Piero

AU - Gutiérrez-Peña, Eduardo

PY - 2004

Y1 - 2004

N2 - Reference analysis is one of the most successful general methods to derive noninformative
prior distributions. In practice, however, reference priors are often difficult to obtain.
Recently developed theory for conditionally reducible natural exponential families identifies
an attractive reparameterization which allows one, among other things, to construct an
enriched conjugate prior. In this paper, under the assumption that the variance function
is simple quadratic, the order-invariant group reference prior for the above parameter is
found. Furthermore, group reference priors for the mean- and natural parameter of the
families are obtained. A brief discussion of the frequentist coverage properties is
also presented. The theory is illustrated for the multinomial and negative-multinomial
family. Posterior computations are especially straightforward due to the fact that the
resulting reference distributions belong to the corresponding enriched conjugate family.
A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative
parameterizations.

AB - Reference analysis is one of the most successful general methods to derive noninformative
prior distributions. In practice, however, reference priors are often difficult to obtain.
Recently developed theory for conditionally reducible natural exponential families identifies
an attractive reparameterization which allows one, among other things, to construct an
enriched conjugate prior. In this paper, under the assumption that the variance function
is simple quadratic, the order-invariant group reference prior for the above parameter is
found. Furthermore, group reference priors for the mean- and natural parameter of the
families are obtained. A brief discussion of the frequentist coverage properties is
also presented. The theory is illustrated for the multinomial and negative-multinomial
family. Posterior computations are especially straightforward due to the fact that the
resulting reference distributions belong to the corresponding enriched conjugate family.
A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative
parameterizations.

KW - Natural exponential family

KW - Reference prior

KW - Natural exponential family

KW - Reference prior

UR - http://hdl.handle.net/10807/14762

UR - http://dx.medra.org/doi:10.1016/s0047-259x(03)00095-2

U2 - doi:10.1016/S0047-259X(03)00095-2

DO - doi:10.1016/S0047-259X(03)00095-2

M3 - Article

VL - 88

SP - 335

EP - 364

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -