Statistical assumption | EPFL Graph Search

Êtes-vous un étudiant de l'EPFL à la recherche d'un projet de semestre?

Travaillez avec nous sur des projets en science des données et en visualisation, et déployez votre projet sous forme d'application sur GraphSearch.

Découvrez-en plus sur les applications Graph.

Statistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions. Here are some examples of statistical assumptions: Independence of observations from each other (this assumption is an especially common error). Independence of observational error from potential confounding effects. Exact or approximate normality of observations (or errors). Linearity of graded responses to quantitative stimuli, e.g., in linear regression. There are two approaches to statistical inference: model-based inference and design-based inference. Both approaches rely on some statistical model to represent the data-generating process. In the model-based approach, the model is taken to be initially unknown, and one of the goals is to select an appropriate model for inference. In the design-based approach, the model is taken to be known, and one of the goals is to ensure that the sample data are selected randomly enough for inference. Statistical assumptions can be put into two classes, depending upon which approach to inference is used. Model-based assumptions. These include the following three types: Distributional assumptions. Where a statistical model involves terms relating to random errors, assumptions may be made about the probability distribution of these errors. In some cases, the distributional assumption relates to the observations themselves. Structural assumptions. Statistical relationships between variables are often modelled by equating one variable to a function of another (or several others), plus a random error. Models often involve making a structural assumption about the form of the functional relationship, e.g. as in linear regression. This can be generalised to models involving relationships between underlying unobserved latent variables. Cross-variation assumptions.

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Concepts associés (8)

Cours associés (24)

Séances de cours associées (299)

MOOCs associés (5)

ENG-267: Estimation methods

Les étudiants traitent des observations entachées d'incertitude de manière rigoureuse. Ils maîtrisent les principales méthodes de compensation des mesures et d'estimation des paramètres. Ils appliquen

PHYS-467: Machine learning for physicists

Machine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practi

MATH-614: Foundations of causal inference

This seminar will provide a survey of the canonical literature in causal inference. At the end of this course, students will gain a broad understanding of the most important methodological concepts an

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Introduction

Learn the basics of plasma, one of the fundamental states of matter, and the different types of models used to describe it, including fluid and kinetic.

Plasma Physics: Applications

Learn about plasma applications from nuclear fusion powering the sun, to making integrated circuits, to generating electricity.

Statistical theory

The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures.

Statistical assumption

Model selection

Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. In the context of learning, this may be the selection of a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection.

Discute du prédicteur de Kalman à l'état d'équilibre, fournit des exemples et compare le filtrage de Luenberger et de Kalman.

Explore les méthodes de Taylor, les estimations ponctuelles, les méthodes de Monte Carlo et les incertitudes du génie civil.

Explore l'échelle et la renormalisation en mécanique statistique, en mettant l'accent sur les points critiques et les propriétés invariantes.