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Likelihood based inference for semi-competing risks Heuchenne, Cédric ; Laurent, Stéphane ; et al in Communications in Statistics : Simulation & Computation (2014), 43(5), 1112-1132 Detailed reference viewed: 61 (7 ULg)Vershik’s intermediate level standardness criterion and the scale of an automorphism Laurent, Stéphane in Lecture Notes in Mathematics (2013) Vershik’s standardness criterion takes a particular form of combinatorial nature in the case of $r_n$-adic filtrations, which we call Vershik’s intermediate level criterion in this paper. This criterion ... [more ▼] Vershik’s standardness criterion takes a particular form of combinatorial nature in the case of $r_n$-adic filtrations, which we call Vershik’s intermediate level criterion in this paper. This criterion has been intensively used in the ergodic theory literature, but it is not easily applicable by probabilists because it is stated in a language proper to the theory of measurable partitions and has not been translated in probabilistic terms. We aim to provide an easily applicable probabilistic statement of this criterion. Finally, Vershik’s intermediate level criterion is illustrated by revisiting Vershik’s definition of the scale of an invertible measure-preserving transformation. [less ▲] Detailed reference viewed: 57 (17 ULg)Likelihood based inference for semi-competing risks Heuchenne, Cédric ; ; Laurent, Stéphane et al E-print/Working paper (2011) Detailed reference viewed: 32 (4 ULg)A Bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials Laurent, Stéphane ; in ESAIM: Probability and Statistics = Probabilité et statistique : P & S (2011) In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions and we are interested in performing statistical inference on the ratio of ... [more ▼] In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions and we are interested in performing statistical inference on the ratio of the two incidence rates, called the relative risk in vaccine efficacy trials, in which context x and y are the numbers of cases in the vaccine and the control groups respectively. In this paper we start by defining a natural semi-conjugate family of prior distributions for this model, allowing straightforward computation of the posterior inference. Following theory on reference priors, we define the reference prior for the partial immunity model when the relative risk is the parameter of interest. We also define a family of reference priors with partial information on the incidence rate of the unvaccinated population while remaining uninformative about the relative risk . We notice that these priors belong to the semi-conjugate family. We then demonstrate using numerical examples that Bayesian credible intervals enjoy attractive frequentist properties when using reference priors, a typical property of reference priors. [less ▲] Detailed reference viewed: 124 (26 ULg)Further comments on the representation problem for stationary processes Laurent, Stéphane in Statistics & Probability Letters (2010), 80 We comment on some points about the coding of stochastic processes by sequences of independent random variables. The most interesting question has to do with the standardness property of the filtration ... [more ▼] We comment on some points about the coding of stochastic processes by sequences of independent random variables. The most interesting question has to do with the standardness property of the filtration generated by the process, in the framework of Vershik's theory of filtrations. Non-standardness indicates the presence of long memory in a purely probabilistic sense. We aim to provide a short, non-technical presentation of Vershik's theory of filtrations. [less ▲] Detailed reference viewed: 115 (11 ULg)On standardness and I-cosiness Laurent, Stéphane in Séminaire de Probabilités (2010), XLIII The object of study of this work is the invariant characteristics of filtrations in discrete, negative time, pioneered by Vershik. We prove the equivalence between I-cosiness and standardness without ... [more ▼] The object of study of this work is the invariant characteristics of filtrations in discrete, negative time, pioneered by Vershik. We prove the equivalence between I-cosiness and standardness without using Vershik’s standardness criterion. The equivalence between I-cosiness and productness for homogeneous filtrations is further investigated by showing that the I-cosiness criterion is equivalent to Vershik’s first level criterion separately for each random variable. We also aim to derive the elementary properties of both these criteria, and to give a survey and some complements on the published and unpublished literature. [less ▲] Detailed reference viewed: 50 (9 ULg)On Vershikian and I-cosy random variables and filtrations Laurent, Stéphane in Teoriya Veroyatnostei i ee Primeneniya (2010), 55 We prove that the equivalence between Vershik’s standardness criterion and the I-cosiness criterion for a filtration in discrete, negative time, holds separately for each random variable. This gives a ... [more ▼] We prove that the equivalence between Vershik’s standardness criterion and the I-cosiness criterion for a filtration in discrete, negative time, holds separately for each random variable. This gives a strengthening and a more direct proof of the global equivalence between these two criteria. We also provide more elementary original propositions on Vershik’s standardness criterion, while emphasizing that similar statements for I-cosiness are sometimes not so obvious. [less ▲] Detailed reference viewed: 34 (8 ULg) |
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