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Research School

This tutorial will be a beginner’s introduction to Bayesian statistical modelling and analysis. Simple models and computational tools will be described, followed by a discussion about implementing these approaches in practice. A range of case studies will be presented and possible solutions proposed, followed by an open discussion about other ways that these problems could be tackled.

62C10 ; 62F15 ; 62P12 ; 62P10

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Research talks;Probability and Statistics

I shall classify current approaches to multiple inferences according to goals, and discuss the basic approaches being used. I shall then highlight a few challenges that await our attention : some are simple inequalities, others arise in particular applications.

62J15 ; 62P10

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- vii; 277 p.
ISBN 978-1-4704-2321-6

Contemporary mathematics , 0685

Localisation : Collection 1er étage

géométrie algébrique # algèbre commutative # théorie des groupes # représentation de groupes # analyse fonctionnelle # géométrie discrète et convexe # polytope # polyhèdre # analyse numérique # théorie des jeux

00B20 ; 13P25 ; 20C30 ; 46N30 ; 51D20 ; 52B05 ; 62-07 ; 62P10 ; 65C60 ; 91B12

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- viii; 198 p.
ISBN 978-1-4614-4132-8

Fields institute communications , 0063

Localisation : Collection 1er étage

optimisation # informatique biomédicale # imagerie biomédicale # programmation

92-06 ; 92C55 ; 62P10 ; 68U99 ; 90C90 ; 00B25

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ISBN 978-90-277-2397-0

The university of western ontario series in philosophy of science , 0038

Localisation : Colloque 1er étage (LOND)

analyse discriminante de groupe multiple # analyse multivariée # biostatistique # cancer # cancérologie # corrélation intraclasse # dérivation échantillon large # effet d'amas # erreur de moindre carrée # estimateur # estimation de rapport impair # estimation de vraissemblance maximum # exploration des grandes bases de données médicales # expérimentation toxicologique # génération de somme # modèle de probabilité de Poisson généralisée # méthode d'estimation pour évaluation parabolique symétrique # méthode de régression # processus du mécanisme des chances # qualité de vie # ramification de statistique # repression logistique multinomiale # récolte des expériences # statistique # table de contingence # traitement de données en biostatistique # épidémiologie # évaluation d'ensemble de réponse # évaluation du mécanisme des chances analyse discriminante de groupe multiple # analyse multivariée # biostatistique # cancer # cancérologie # corrélation intraclasse # dérivation échantillon large # effet d'amas # erreur de moindre carrée # estimateur # estimation de rapport impair # estimation de vraissemblance maximum # exploration des grandes bases de données médicales # expérimentation toxicologique # génération de somme # modèle de probabilité de Poisson généralisée # méthode ...

15542 ; 62Hxx ; 62P10 ; 92B10 ; 92B15

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- 386 p.
ISBN 978-0-8218-5087-9

Contemporary mathematics , 0080

Localisation : Collection 1er étage

biométrie # processus ponctuel # processus stochastique # série temporelle

60G44 ; 60G55 ; 60G57 ; 62M10 ; 62P10

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ISBN 978-0-520-02188-4

Localisation : Colloque 1er étage (BERK)

DNA # RNA # probabilité # statistique mathématique # séquence d'amino-acide # théorie # théorie de l'évolution darwiniènne # étude de population # évolution

62-06 ; 62Lxx ; 62P10 ; 62P15

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ISBN 978-0-520-02187-7

Localisation : Colloque 1er étage (BERK)

biologie et santé # biostatistique # carcinogénèse # phénomène cellulaire # probabilité # processus de branchement # procédure séquentielle # psychologie # statistique mathématique # épreuve clinique # étude des populations # étude observationnelle

62-06 ; 62Lxx ; 62P10 ; 62P15

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Localisation : Colloque 1er étage (BERK)

biologie et santé # cognition # diagnostic médical # démographie # expérimentation # hasard et vie # phénomènre cellulaire carcinogénèse # probabilité # statistique mathématique # théorie de la décision # traitement de l'information # écologie # épidémiologie génétique

62-06 ; 62P10 ; 92C60 ; 92D40 ; 94Axx

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Localisation : Colloque 1er étage (TALL)

biométrie # classe de distribution de Lie # classification # comparaison de population # estimation de fiabilité de système # mesure de similarité # modèle linéaire # méthode # processus stochastique # prédiction # rangement sélection # risque de compétition # test de durée de vie # théorie statistique

62N05 ; 62P10

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Research talks

The term ‘Public Access Defibrillation’ (PAD) is referred to programs based on the placement of Automated External Defibrillators (AED) in key locations along cities’ territory together with the development of a training plan for users (first responders). PAD programs are considered necessary since time for intervention in cases of sudden cardiac arrest outside of a medical environment (out-of-hospital cardiocirculatory arrest, OHCA) is strongly limited: survival potential decreases from a 67% baseline by 7 to 10% for each minute of delay in first defibrillation. However, it is widely recognized that current PAD performance is largely below its full potential. We provide a Bayesian spatio-temporal statistical model for predidicting OHCAs. Then we construct a risk map for Ticino, adjusted for demographic covariates, that explains and forecasts the spatial distribution of OHCAs, their temporal dynamics, and how the spatial distribution changes over time. The objective is twofold: to efficiently estimate, in each area of interest, the occurrence intensity of the OHCA event and to suggest a new optimized distribution of AEDs that accounts for population exposure to the geographic risk of OHCA occurrence and that includes both displacement of current devices and installation of new ones. The term ‘Public Access Defibrillation’ (PAD) is referred to programs based on the placement of Automated External Defibrillators (AED) in key locations along cities’ territory together with the development of a training plan for users (first responders). PAD programs are considered necessary since time for intervention in cases of sudden cardiac arrest outside of a medical environment (out-of-hospital cardiocirculatory arrest, OHCA) is strongly ...

62F15 ; 62P10 ; 62H11 ; 91B30

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Research talks

In many health studies, interest often lies in assessing health effects on a large set of outcomes or specific outcome subtypes, which may be sparsely observed, even in big data settings. For example, while the overall prevalence of birth defects is not low, the vast heterogeneity in types of congenital malformations leads to challenges in estimation for sparse groups. However, lumping small groups together to facilitate estimation is often controversial and may have limited scientific support.
There is a very rich literature proposing Bayesian approaches for clustering starting with a prior probability distribution on partitions. Most approaches assume exchangeability, leading to simple representations in terms of Exchangeable Partition Probability Functions (EPPF). Gibbs-type priors encompass a broad class of such cases, including Dirichlet and Pitman-Yor processes. Even though there have been some proposals to relax the exchangeability assumption, allowing covariate-dependence and partial exchangeability, limited consideration has been given on how to include concrete prior knowledge on the partition. We wish to cluster birth defects into groups to facilitate estimation, and we have prior knowledge of an initial clustering provided by experts. As a general approach for including such prior knowledge, we propose a Centered Partition (CP) process that modifies the EPPF to favor partitions close to an initial one. Some properties of the CP prior are described, a general algorithm for posterior computation is developed, and we illustrate the methodology through simulation examples and an application to the motivating epidemiology study of birth defects.
In many health studies, interest often lies in assessing health effects on a large set of outcomes or specific outcome subtypes, which may be sparsely observed, even in big data settings. For example, while the overall prevalence of birth defects is not low, the vast heterogeneity in types of congenital malformations leads to challenges in estimation for sparse groups. However, lumping small groups together to facilitate estimation is often ...

62F15 ; 62H30 ; 60G09 ; 60G57 ; 62G05 ; 62P10

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Research talks;Computer Science;Mathematics in Science and Technology;Probability and Statistics

Many data can be represented as rankings or permutations, raising the question of developing machine learning models on the symmetric group. When the number of items in the permutations gets large, manipulating permutations can quickly become computationally intractable. I will discuss two computationally efficient embeddings of the symmetric groups in Euclidean spaces leading to fast machine learning algorithms, and illustrate their relevance on biological applications and image classification. Many data can be represented as rankings or permutations, raising the question of developing machine learning models on the symmetric group. When the number of items in the permutations gets large, manipulating permutations can quickly become computationally intractable. I will discuss two computationally efficient embeddings of the symmetric groups in Euclidean spaces leading to fast machine learning algorithms, and illustrate their relevance ...

62H30 ; 62P10 ; 68T05

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Research talks;Mathematics in Science and Technology;Probability and Statistics

Geneticists have always been aware that, when looking for signal across the entire genome, one has to be very careful to avoid false discoveries. Contemporary studies often involve a very large number of traits, increasing the challenges of "looking every-where". I will discuss novel approaches that allow an adaptive exploration of the data, while guaranteeing reproducible results.

62F15 ; 62J15 ; 62P10 ; 92D10

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Research School;Mathematics in Science and Technology;Probability and Statistics

Dans une première partie, je présenterai différentes problématiques liées à des statistiques d'occurrences de mots dans des génomes et décortiquerai plus en détail la question de savoir comment détecter si un mot a une fréquence d'apparition significativement anormale dans une séquence. Dans une deuxième partie, je présenterai différentes extensions pour tenir compte du fait qu'un motif d'ADN fonctionnel n'est pas toujours un " mot ", mais qu'il peut avoir une structure plus complexe qui nécessite le développement de nouvelles méthodes statistiques. Dans une première partie, je présenterai différentes problématiques liées à des statistiques d'occurrences de mots dans des génomes et décortiquerai plus en détail la question de savoir comment détecter si un mot a une fréquence d'apparition significativement anormale dans une séquence. Dans une deuxième partie, je présenterai différentes extensions pour tenir compte du fait qu'un motif d'ADN fonctionnel n'est pas toujours un " mot ", mais qu'il ...

92C40 ; 62P10 ; 60J20 ; 92C42

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Research talks;Probability and Statistics

Faced with data containing a large number of inter-related explanatory variables, finding ways to investigate complex multi-factorial effects is an important statistical task. This is particularly relevant for epidemiological study designs where large numbers of covariates are typically collected in an attempt to capture complex interactions between host characteristics and risk factors. A related task, which is of great interest in stratified medicine, is to use multi-omics data to discover subgroups of patients with distinct molecular phenotypes and clinical outcomes, thus providing the potential to target treatments more precisely. Flexible clustering is a natural way to tackle such problems. It can be used in an unsupervised or a semi-supervised manner by adding a link between the clustering structure and outcomes and performing joint modelling. In this case, the clustering structure is used to help predict the outcome. This latter approach, known as profile regression, has been implemented recently using a Bayesian non parametric DP modelling framework, which specifies a joint clustering model for covariates and outcome, with an additional variable selection step to uncover the variables driving the clustering (Papathomas et al, 2012). In this talk, two related issues will be discussed. Firstly, we will focus on categorical covariates, a common situation in epidemiological studies, and examine the relation between: (i) dependence structures highlighted by Bayesian partitioning of the covariate space incorporating variable selection; and (ii) log linear modelling with interaction terms, a traditional approach to model dependence. We will show how the clustering approach can be employed to assist log-linear model determination, a challenging task as the model space becomes quickly very large (Papathomas and Richardson, 2015). Secondly, we will discuss clustering as a tool for integrating information from multiple datasets, with a view to discover useful structure for prediction. In this context several related issues arise. It is clear that each dataset may carry a different amount of information for the predictive task. Methods for learning how to reweight each data type for this task will therefore be presented. In the context of multi-omics datasets, the efficiency of different methods for performing integrative clustering will also be discussed, contrasting joint modelling and stepwise approaches. This will be illustrated by analysis of genomics cancer datasets.
Joint work with Michael Papathomas and Paul Kirk.
Faced with data containing a large number of inter-related explanatory variables, finding ways to investigate complex multi-factorial effects is an important statistical task. This is particularly relevant for epidemiological study designs where large numbers of covariates are typically collected in an attempt to capture complex interactions between host characteristics and risk factors. A related task, which is of great interest in stratified ...

62F15 ; 62P10

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Research talks;Mathematics in Science and Technology;Probability and Statistics

We analyse patterns of genetic variability of populations in the presence of a large seed bank with the help of a new coalescent structure called seed bank coalescent. This ancestral process appears naturally as scaling limit of the genealogy of large populations that sustain seed banks, if the seed bank size and individual dormancy times are of the same order as the active population. Mutations appear as Poisson process on the active lineages, and potentially at reduced rate also on the dormant lineages. The presence of ‘dormant’ lineages leads to qualitatively altered times to the most recent common ancestor and non-classical patterns of genetic diversity. To illustrate this we provide a Wright-Fisher model with seed bank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seed bank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Commonly employed distance statistics, in the presence and absence of a seed bank, are compared. The effect of a seed bank on the expected site-frequency spectrum is also investigated. Our results indicate that the presence of a large seed bank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect the presence of a large seed bank in genetic data. Joint work with Bjarki Eldon, Adrián González Casanova, Noemi Kurt, Maite Wilke-Berenguer We analyse patterns of genetic variability of populations in the presence of a large seed bank with the help of a new coalescent structure called seed bank coalescent. This ancestral process appears naturally as scaling limit of the genealogy of large populations that sustain seed banks, if the seed bank size and individual dormancy times are of the same order as the active population. Mutations appear as Poisson process on the active lineages, ...

92D10 ; 60K35 ; 62P10

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- xv; 552 p.
ISBN 978-1-4822-4819-7

Chapman & Hall / CRC biostatistics series

Localisation : Ouvrage RdC (BROE)

analyse de variance à mesure répétée # inférence bayésienne # biostatistiques # code WinBUGS # régression bayésienne # modèle linéaire

62F15 ; 62J05 ; 62J10 ; 62P10 ; 92B15

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- xiii; 391 p.
ISBN 978-1-4822-0642-5

Monographs and research notes in mathematics

Localisation : Ouvrage RdC (BANK)

incertitude # propagation d'incertitudes # problème inverse # données agrégées # chaîne de Markov à temps continu # système stochastique # système déterministe

00A71 ; 62-02 ; 62-07 ; 60H10 ; 60H25 ; 60J27 ; 62K05 ; 62P10 ; 92-01

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- x; 228 p.
ISBN 978-0-521-51766-9

Localisation : Ouvrage RdC (POLD)

92-00 ; 92C55 ; 92C20 ; 94A08 ; 94A12 ; 62-07 ; 62P10

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