Invariant conjugate analysis for exponential families

Pierre Druilhet (1) , Denys Pommeret (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 IML - Institut de mathématiques de Luminy

There are several ways to parameterize a distribution belonging to an exponential family, each one leading to a di erent Bayesian analysis of the data under standard conjugate priors. To overcome this problem, we propose a new class of conjugate priors which is invariant with respect to smooth reparameterization. This class of priors contains the Je reys prior as a special case, according to the value of the hyperparameters. Moreover, these conjugate distributions coincide with the posterior distributions resulting from a Je reys prior. Then these priors appear naturally when several datasets are analyzed sequentially and when the Je reys prior is chosen for the rst dataset. We apply our approach to inverse Gaussian models and propose full invariant analyses of three datasets.

Mots clés: sequential analysis.; Bayesian inference; conjugate prior; exponential family; inverse Gaussian distribution; Je ffreys prior; sequential analysis

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Pierre Druilhet, Denys Pommeret. Invariant conjugate analysis for exponential families. Bayesian Analysis, 2012, 7 (4), pp.903-916. ⟨10.1214/12-BA731⟩. ⟨hal-00803642⟩