Intrinsic Bayesian inference on a Poisson rate and on the ratio of two Poisson rates

Stéphane Laurent (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Our purpose is to explore the intrinsic Bayesian inference on the rate of a Poisson distribution and on the ratio of the rates of two independent Poisson distributions, with the natural conjugate family of priors in the first case and the semi-conjugate family of priors defined by Laurent & Legrand (2011) in the second case. Intrinsic Bayesian inference is derived from the Bayesian decision theory framework based on the intrinsic discrepancy loss function. We cover in particular the case of some objective Bayesian procedures suggested by Bernardo when considering reference priors.

Mots clés: Intrinsic Discrepancy; Hypothesis testing; Reference prior; Intrinsic loss

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

Stéphane Laurent. Intrinsic Bayesian inference on a Poisson rate and on the ratio of two Poisson rates. Journal of Statistical Planning and Inference, 2012, doi:10.1016/j.jspi.2012.02.040. ⟨10.1016/j.jspi.2012.02.040⟩. ⟨hal-00505234v3⟩