Showing papers by "Bo Henry Lindqvist published in 2017"
TL;DR: A new approach for statistical modeling of failures and the corresponding statistical inference when there is both an observable and unobservable heterogeneity between such systems.
19 citations
TL;DR: The conditional fiducial model is not unique in general, but in a restricted class of models it is uniquely determined by the sampling distribution of the data as mentioned in this paper, which depends in particular not on the choice of a data generating model.
11 citations
TL;DR: In this article, a recent theory which includes improper distributions, and which is related to Renyi's theory of conditional probability spaces, is discussed, and several examples from statistical practice with improper distributions are discussed in light of the given theoretical results.
8 citations
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TL;DR: In this paper, a general concept of conditional expectation in Renyi spaces is introduced, where improper priors are allowed and the resulting posterior can also be improper, and the paradoxes are investigated.
Abstract: In 1933 Kolmogorov constructed a general theory that defines the modern concept of conditional expectation. In 1955 Renyi fomulated a new axiomatic theory for probability motivated by the need to include unbounded measures. We introduce a general concept of conditional expectation in Renyi spaces. In this theory improper priors are allowed, and the resulting posterior can also be improper.
In 1965 Lindley published his classic text on Bayesian statistics using the theory of Renyi, but retracted this idea in 1973 due to the appearance of marginalization paradoxes presented by Dawid, Stone, and Zidek. The paradoxes are investigated, and the seemingly conflicting results are explained. The theory of Renyi can hence be used as an axiomatic basis for statistics that allows use of unbounded priors.
Keywords: Haldane's prior; Poisson intensity; Marginalization paradox; Measure theory; conditional probability space; axioms for statistics; conditioning on a sigma field; improper prior
7 citations
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TL;DR: This short note analyses an example introduced by Seidenfeld (1992) where the fiducial distribution is restricted to a string.
Abstract: The fiducial argument of Fisher (1973) has been described as his biggest blunder, but the recent review of Hannig et al. (2016) demonstrates the current and increasing interest in this brilliant idea. This short note analyses an example introduced by Seidenfeld (1992) where the fiducial distribution is restricted to a string.
Keywords and phrases: Bayesian and fiducial inference, Restrictions on parameters, Uncertainty quantification, Epistemic probability, Statistics on a manifold.
2 citations