A Conversation with Jim Pitman
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چکیده
منابع مشابه
Poisson - Kingman Partitions ∗ Jim Pitman
This paper presents some general formulas for random partitions of a finite set derived by Kingman’s model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the ...
متن کاملRegenerative Tree Growth: Binary Self-similar Continuum Random Trees and Poisson–dirichlet Compositions1 by Jim Pitman
We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford’s sequence of alpha model trees in the continuum tree which we identified in a previous article as a distributional scaling limit of Ford’s trees. In general, the Markov branching trees induced by the t...
متن کاملON THE DISTRIBUTION OF RANKED HEIGHTS OF EXCURSIONS OF A BROWNIAN BRIDGE1 By Jim Pitman and Marc Yor
The distribution of the sequence of ranked maximum and minimum values attained during excursions of a standard Brownian bridge Bbr t 0 ≤ t ≤ 1 is described. The height Mbr+ j of the jth highest maximum over a positive excursion of the bridge has the same distribution as Mbr+ 1 /j, where the distribution of Mbr+ 1 = sup0≤t≤1 Bbr t is given by Lévy’s formula P Mbr+ 1 > x = e−2x 2 . The probabilit...
متن کاملOn Pitman Closeness of Pitman Estimators
Pitman estimators of location are unbiased, translation-equivariant and possess some optimality properties under quadratic loss. Similar optimality properties of Pitman estimators are studied with respect to the measure of Pitman closeness of estimators.
متن کاملContinuum Tree Asymptotics of Discrete Fragmentations and Applications to Phylogenetic Models by Bénédicte Haas, Grégory Miermont, Jim Pitman
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous’s beta-splitting models and Ford’s alpha models for phylogenetic trees. This confirms in a strong way that the whole trees grow at the same speed as the ...
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ژورنال
عنوان ژورنال: Statistical Science
سال: 2018
ISSN: 0883-4237
DOI: 10.1214/18-sts656