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## Submitted APPROXIMATION OF IMPROPER PRIOR BY VAGUE

### Citations

5201 |
Convergence of Probability Measures
- Billingsley
- 1999
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Citation Context ...arrowly to Π ∈Mb then {Πn}n∈N converges vaguely to Π. Proposition B.13. If {Πn}n∈N and Π are probability measures, then vague and narrow convergences of {Πn}n∈N to Π are equivalent. Proposition B.14 (=-=Billingsley, 1986-=-). Let {Πn}n∈N be a sequence of probabilities and Π be a probability. If lim n→∞Fn(x) = F (x) for each x at which F is continuous, where Fn, resp F , is the distribution function of Πn, resp Π, then {... |

962 | Theory of Point Estimation - Lehmann, Casella - 1998 |

274 |
Information and Exponential Families in Statistical Theory.
- Barndorff-Nielsen
- 1978
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Citation Context ...s an open set in Rp, p ≥ 1, such that f(x|θ) is a well defined pdf. We assume that φ(θ) and Iθ(θ) are continuous. These conditions are satisfied if t(X) is not concentrated on an hyperplane a.s. (see =-=Barndorff-Nielsen, 1978-=-). Druilhet and Pommeret (2012) proposed a class of conjugate priors that aims to approximate the Jeffreys prior and that is invariant w.r.t. smooth reparameterization. The notion of approximation was... |

203 | Reference posterior distributions for bayesian inference. - Bernardo - 1979 |

124 |
Natural exponential families with quadratic variance functions: statistical theory
- Morris
- 1983
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Citation Context ... is a proper prior and there is no general result to characterize this property such as in Diaconis and Ylvisaker (1979) for usual conjugate priors. In the case of quadratic exponential families (see =-=Morris, 1983-=-), JCPs and usual conjugate priors coincide and correspond to ha l-0 08 80 19 4,sv er sio ns1s- 5sN ovs2 01 3 16 C. BIOCHE AND P. DRUILHET Normal, Gamma or Beta distribution which are examined through... |

114 |
Elements de mathematique. Topologie generale.
- Bourbaki
- 1971
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Citation Context ...ace, α0Π0(f) = Π′0(f). So, the graph of ∼, G, is closed. The result follows from Bourbaki (1971, section I.55). APPENDIX B: REMINDERS ON TOPOLOGY B.1. Some definitions and properties. Definition B.1 (=-=Bourbaki, 1971-=-, p76). A Hausdorff space is a topological space in which two distinct points have disjoint neighbourhoods. Lemma B.2 (Malliavin, 1982, chapter 2.2). For a locally compact Hausdorff space that is seco... |

88 | Conjugate priors for exponential families, - Diaconis, Ylvisaker - 1979 |

39 | The formal definition of reference priors.
- Berger, Bernardo, et al.
- 2009
(Show Context)
Citation Context ...improper priors, i.e. measures with infinite mass. When no prior information is available, several approaches such as flat priors (Laplace, 1812), Jeffreys’ priors (Jeffreys, 1946), reference priors (=-=Berger et al, 2009-=-) or Haar’s measures (Eaton, 1989) often lead to improper priors. However, the use of improper prior may cause some problems such as improper posterior priors or undesirable behaviour in hypothesis te... |

38 |
Group Invariant Applications in Statistics.
- Eaton
- 1989
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Citation Context ...nite mass. When no prior information is available, several approaches such as flat priors (Laplace, 1812), Jeffreys’ priors (Jeffreys, 1946), reference priors (Berger et al, 2009) or Haar’s measures (=-=Eaton, 1989-=-) often lead to improper priors. However, the use of improper prior may cause some problems such as improper posterior priors or undesirable behaviour in hypothesis testing. So, many authors prefer to... |

12 | Statistical decision theory and Bayesian - Berger - 1985 |

7 | The bayesian - Robert - 2001 |

5 | Locally uniform prior distributions - Hartigan - 1996 |

4 |
Intégration et probabilités. Analyse de Fourier et analyse spectrale
- Malliavin
- 1982
(Show Context)
Citation Context ... ON TOPOLOGY B.1. Some definitions and properties. Definition B.1 (Bourbaki, 1971, p76). A Hausdorff space is a topological space in which two distinct points have disjoint neighbourhoods. Lemma B.2 (=-=Malliavin, 1982-=-, chapter 2.2). For a locally compact Hausdorff space that is second countable E, there exists a sequence of compact sets {Kn}n∈N such that E = ⋃ n∈N Kn and Kn ⊂ K̊n+1 where K̊n is the interior of Kn.... |

2 | Invariant conjugate analysis for exponential families - Druilhet, Pommeret - 2012 |

2 | Coherent and continuous - Lane, Sudderth - 1983 |

1 | 41 113–147. ha l-0 4, v er sio n - 5 N ov 30 - B - 1968 |

1 | A Bayesian choice between Poisson, binomial and negative binomial models - Dauxois, Druilhet, et al. - 2006 |