Statistique (indicateur)

Résumé

Une statistique est, au premier abord, le résultat d'une suite d'opérations appliquées à un ensemble de nombres appelé échantillon. D'une façon générale, c'est le résultat de l'application d'une méthode statistique à un ensemble de données. Dans le calcul de la moyenne arithmétique, par exemple, l'algorithme consiste à calculer la somme de toutes les valeurs des données et à diviser par le nombre de données. La moyenne est ainsi une statistique. Pour être complet dans la description de l'utilisation d'une statistique, il faut décrire à la fois la procédure et l'ensemble de données. De façon formelle, et bien que cela soit rarement utilisé, une statistique est une variable aléatoire d'un type particulier. C'est en effet une fonction d'un vecteur composée de plusieurs observations d'une loi. Cela permet entre autres d'étendre aux statistiques un certain nombre de résultats sur les variables aléatoires, entre autres le caractère indépendant de deux statistiques ou calculer des densités

Source officielle

https://fr.wikipedia.org/wiki/Statistique_(indicateur)

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Publications associées (47)

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Concepts associés (39)

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Cours associés (41)

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This course presents an introduction to statistical mechanics geared towards materials scientists. The concepts of macroscopic thermodynamics will be related to a microscopic picture and a statistical interpretation. Lectures and exercises will be complemented with hands-on simulation projects.

This course provides an introduction to experimental statistics, including use of population statistics to characterize experimental results, use of comparison statistics and hypothesis testing to evaluate validity of experiments, and design, application, and analysis of multifactorial experiments

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Séances de cours associées (105)

Séances de cours associées

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Statistical Analysis of Chao’s Immune System Simulation

Eric Winnington

Modeling the immune system (IS) means putting together a set of assumptions about its components (cells and organs) and their interactions. Simulations of a model show joint behavior of the components, which for complex realistic models is often impossible to find analytically. Simulations allow us to experiment on how initial concentrations and properties of the immune cells and viruses impact the IS behavior, and gain better quantitative and qualitative insight into how the IS works and why different behavior patterns occur. A simulation, once it has been created, must be reviewed both statistically and analytically as well as validated from the biological point of view. We analyzed Chao’s immune system simulation [1][2] from a statistical and analytical point. We explicited both the Markov chain which was simulated and the underlying process on which Chao’s stage-structured approach was built. Furthermore, we established a test protocol for timestep validation which Chao’s simulator passed. We evaluated Chao’s simulator’s dependence on the random number generator, which was shown to be negligible. Finally, we evaluated the simulator output and our major result is the discovery of a secondary response to a primary infection, an occurrence is not shown in Chao’s dissertation. A tertiary response to the infection is never possible due to the size of the secondary response caused by memory cells.

2005

Chargement

Domain adaptation is a major challenge for future remote sensing applications. Both financial and temporal constraints of data acquisition lead to the developing of new techniques able to use knowledge from alternative sources. Different approaches have been developed by considering the statistical properties of images or by modifying already existing classifiers. We propose a intermediary approach of these two kinds of methods by using a manifold alignment technique constrained by similarity between two images. The two images are mapped in a high dimensional latent space which maximizes the proximity of similar elements, thus allowing classification of the images suffering from label scarcity by using the knowledge of the other image. Such a classification offers improvement compared to various used processes.

2012

Chargement

To cope with a variety of clinical applications, research in medical image processing has led to a large spectrum of segmentation techniques that extract anatomical structures from volumetric data acquired with 3D imaging modalities. Despite continuing advances in mathematical models for automatic segmentation, many medical practitioners still rely on 2D manual delineation, due to the lack of intuitive semi-automatic tools in 3D. In this thesis, we propose a methodology and associated numerical schemes enabling the development of 3D image segmentation tools that are reliable, fast and interactive. These properties are key factors for clinical acceptance. Our approach derives from the framework of variational methods: segmentation is obtained by solving an optimization problem that translates the expected properties of target objects in mathematical terms. Such variational methods involve three essential components that constitute our main research axes: an objective criterion, a shape representation and an optional set of constraints. As objective criterion, we propose a unified formulation that extends existing homogeneity measures in order to model the spatial variations of statistical properties that are frequently encountered in medical images, without compromising efficiency. Within this formulation, we explore several shape representations based on implicit surfaces with the objective to cover a broad range of typical anatomical structures. Firstly, to model tubular shapes in vascular imaging, we introduce convolution surfaces in the variational context of image segmentation. Secondly, compact shapes such as lesions are described with a new representation that generalizes Radial Basis Functions with non-Euclidean distances, which enables the design of basis functions that naturally align with salient image features. Finally, we estimate geometric non-rigid deformations of prior templates to recover structures that have a predictable shape such as whole organs. Interactivity is ensured by restricting admissible solutions with additional constraints. Translating user input into constraints on the sign of the implicit representation at prescribed points in the image leads us to consider inequality-constrained optimization.

EPFL2011

Chargement

EPFL2011