11 results on '"Hoscheit, Patrick"'
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2. Fluctuations for the number of records on subtrees of the Continuum Random Tree
- Author
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Hoscheit, Patrick
- Subjects
Mathematics - Probability - Abstract
We study the asymptotic behavior af the number of cuts $X(T_n)$ needed to isolate the root in a rooted binary random tree $T_n$ with $n$ leaves. We focus on the case of subtrees of the Continuum Random Tree generated by uniform sampling of leaves. We elaborate on a recent result by Abraham and Delmas, who showed that $X(T_n)/\sqrt{2n}$ converges a.s. towards a Rayleigh-distributed random variable $\Theta$, which gives a continuous analog to an earlier result by Janson on conditioned, finite-variance Galton-Watson trees. We prove a convergence in distribution of $n^{-1/4}(X(T_n)-\sqrt{2n}\Theta)$ towards a random mixture of Gaussian variables. The proofs use martingale limit theory for random processes defined on the CRT, related to the theory of records of Poisson point processes.
- Published
- 2012
3. Exit times for an increasing L\'evy tree-valued process
- Author
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Abraham, Romain, Delmas, Jean-François, and Hoscheit, Patrick
- Subjects
Mathematics - Probability - Abstract
We give an explicit construction of the increasing tree-valued process introduced by Abraham and Delmas using a random point process of trees and a grafting procedure. This random point process will be used in companion papers to study record processes on L\'evy trees. We use the Poissonian structure of the jumps of the increasing tree-valued process to describe its behavior at the first time the tree grows higher than a given height. We also give the joint distribution of this exit time and the ascension time which corresponds to the first infinite jump of the tree-valued process.
- Published
- 2012
4. A note on Gromov-Hausdorff-Prokhorov distance between (locally) compact measure spaces
- Author
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Abraham, Romain, Delmas, Jean-Francois, and Hoscheit, Patrick
- Subjects
Mathematics - Metric Geometry ,Mathematics - Probability - Abstract
We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a locally finite measure. We prove that this space with the extended Gromov-Hausdorff-Prokhorov metric is a Polish space. This generalization is needed to define L\'evy trees, which are (possibly unbounded) random real trees endowed with a locally finite measure.
- Published
- 2012
- Full Text
- View/download PDF
5. Additional file 1 of Dynamic centrality measures for cattle trade networks
- Author
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Hoscheit, Patrick, Éric Anthony, and Vergu, Elisabeta
- Abstract
Additional file 1. Supplementary information regarding precise definitions of static centralities (Section S1), variance in the simulated outbreak sizes (Section S2), the relative weight of markets and assembly centres in highly ranked nodes (Section S3), the impact of using different yearly datasets to compute centralities (Section S4), the impact of varying epidemic parameters (Section S5), and the impact of varying random walk parameters to approximate TempoRank measures (Section S6).
- Published
- 2021
- Full Text
- View/download PDF
6. Λ-coalescents as priors in phylodynamical analysis
- Author
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Hoscheit, Patrick, Vaughan, Tim, Pybus, Oliver, Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), Department of Zoology [Oxford], Wildlife Conservation Research Unit [Oxford], University of Oxford [Oxford]-University of Oxford [Oxford], and Hoscheit, Patrick
- Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,[MATH.MATH-PR] Mathematics [math]/Probability [math.PR] ,[SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie ,[SDV.BID.EVO]Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE] ,[SDV.BID.EVO] Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE] ,[SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie ,ComputingMilieux_MISCELLANEOUS - Abstract
International audience
- Published
- 2019
7. The multifurcating skyline plot
- Author
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Hoscheit, Patrick, Pybus, Oliver G., Mathématiques et Informatique Appliquées du Génome à l'Environnement [Jouy-En-Josas] (MaIAGE), Institut National de la Recherche Agronomique (INRA), Departement of Zoology, University of Oxford, University of Oxford, European Project: 614725,EC:FP7:ERC,ERC-2013-CoG,PATHPHYLODYN(2014), European Project: 267196, and University of Oxford [Oxford]
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MESH: phylodynamics ,MESH: phylogenetics ,[SDV]Life Sciences [q-bio] ,Bayesian probability ,computer.software_genre ,01 natural sciences ,Microbiology ,Plot (graphics) ,Coalescent theory ,010104 statistics & probability ,03 medical and health sciences ,Virology ,MESH: maximum likelihood ,Statistics ,Quantitative Biology::Populations and Evolution ,[INFO]Computer Science [cs] ,MESH: coalescent ,maximum likelihood ,0101 mathematics ,[MATH]Mathematics [math] ,030304 developmental biology ,Mathematics ,Skyline ,0303 health sciences ,Degree (graph theory) ,Phylogenetic tree ,030306 microbiology ,MESH: multifurcating ,Estimator ,coalescent ,phylodynamics ,3. Good health ,phylogenetics ,Piecewise ,multifurcating ,Data mining ,Erratum ,Algorithm ,computer ,Smoothing ,Research Article ,Count data - Abstract
A variety of methods based on coalescent theory have been developed to infer demographic history from gene sequences sampled from natural populations. The “skyline plot” and related approaches are commonly employed as exible prior distributions for phylogenetic trees in the Bayesian analysis of pathogen gene sequences. In this work we extend the classic and generalised skyline plot methods to phylogenies that contain one or more multifurcations (i.e.hard polytomies). We use the theory of Λ-coalescents (specifically, Beta(2α,α)-coalescents) to develop the “multifurcating skyline plot”, which estimates a piecewise constant function of effective population size through time, conditional on a time-scaled multifurcating phylogeny. We implement a smoothing procedure and extend the method to serially-sampled (heterochronous) data, but we do not address here the problem of estimating trees with multifurcations from gene sequence alignments. We validate our estimator on simulated data using maximum likelihood and find that parameters of the Beta(2α,α)-coalescent process can be estimated accurately. Lastly we apply the multifurcating skyline plot to a molecular clock phylogeny of 1,610 Ebola virus sequences from the 2014-2016 West African outbreak. We artificially collapse short branches in this empirical phylogeny in order to mimic different levels of multifurcation and show that variance in the reproductive success of the pathogen through time can be estimated by combining the skyline plot with epidemiological case count data.
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- 2019
8. A note on Gromov-Hausdorff-Prokhorov distance between (locally) compact measure spaces
- Author
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Abraham, Romain, Delmas, Jean-Francois, Hoscheit, Patrick, Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO), Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), and École des Ponts ParisTech (ENPC)
- Subjects
Probability (math.PR) ,boundedly finite measure ,Metric Geometry (math.MG) ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Mathematics - Metric Geometry ,51F99, 05C05, 05C80, 60D05 ,FOS: Mathematics ,Gromov-Hausdorff ,Levy tree ,Mathematics::Metric Geometry ,Prokhorov metric ,[MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG] ,Mathematics - Probability ,length space - Abstract
International audience; We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a locally finite measure. We prove that this space with the extended Gromov-Hausdorff-Prokhorov metric is a Polish space. This generalization is needed to define Lévy trees, which are (possibly unbounded) random real trees endowed with a locally finite measure.
- Published
- 2013
9. Processus à valeurs dans les arbres aléatoires continus
- Author
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Hoscheit, Patrick and STAR, ABES
- Subjects
CRT ,Gromov-Hausdorff-Prokhorov ,[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM] ,Probabilités ,Galton-Watson ,Probability ,Trees ,Arbres - Abstract
In this thesis, we study continuum tree-valued processes. First, we define an abstract framework for these processes, by constructing a metric on the space of locally compact, complete R-trees, endowed with a locally finite Borel measure. This topology, called Gromov-Hausdorff-Prokhorov topology, allows for the definition of tree-valued Markov processes. We then give a new construction of the pruning process of Abraham-Delmas-Voisin, which is an example of a Lévy tree-valued process. Our construction reveals a new genealogical structure of Lévy trees. Furthermore, it is a path wise construction, which describes the transitions of the process explicitly. We apply this description to the study of certain stopping times, such as the first moment the process crosses a given height. We describe the process at that time through a new spinal decomposition. Finally, we focus on the Aldous-Pitman fragmentation of Aldous's Brownian tree. Following Abraham and Delmas, we study the effect of the fragmentation on discrete subtrees of the Brownian tree. The number of cuts needed to isolate the root, suitably renormalized, converges towards a Rayleigh-distributed random variable; we prove a Central Limit Theorem describing the fluctuations around this limit, Cette thèse est consacrée à l'étude de certains processus aléatoires à valeurs dans les arbres continus. Nous définissons d'abord un cadre conceptuel pour cette étude, en construisant une topologie polonaise sur l'espace des R-arbres localement compacts, complets et munis d'une mesure borélienne localement finie. Cette topologie, dite de Gromov-Hausdorff-Prokhorov, permet alors la définition de processus de Markov à valeurs arbre. Nous donnons ensuite une nouvelle construction du processus d'élagage d'Abraham-Delmas-Voisin, qui est un exemple de processus qui prend ses valeurs dans les arbres de Lévy. Notre construction, qui dévoile une nouvelle structure généalogique des arbres de Lévy, est trajectorielle, et permet d'identifier explicitement les transitions du processus d'élagage. Nous appliquons cette description à l'étude de certains temps d'arrêt, comme le premier temps auquel le processus franchit une hauteur donnée. Nous décrivons le processus à cet instant grâce à une nouvelle décomposition de type spinal. Enfin, nous nous intéressons à la fragmentation d'Aldous-Pitman de l'arbre brownien d'Aldous. En particulier, nous étudions, à la suite d'Abraham et Delmas, l'effet de cette fragmentation sur les sous-arbres discrets de l'arbre brownien. Le nombre de coupures nécessaires avant d'isoler la racine, convenablement renormalisé, converge vers une variable aléatoire de Rayleigh ; nous donnons un théorème central limite qui précise les fluctuations autour de cette limite
- Published
- 2012
10. A note on the Gromov-Hausdorff-Prokhorov distance between (locally) compact metric measure spaces
- Author
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Abraham, Romain, primary, Delmas, Jean-François, additional, and Hoscheit, Patrick, additional
- Published
- 2013
- Full Text
- View/download PDF
11. Erratum: The multifurcating skyline plot.
- Author
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Hoscheit P and Pybus OG
- Abstract
[This corrects the article DOI: 10.1093/ve/vez031.].
- Published
- 2019
- Full Text
- View/download PDF
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