Lecture

Algebraic statistics: tables and networks

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers algebraic statistics, contingency tables, and networks, focusing on the Fienberg advantage. It discusses networked data, testing model goodness of fit, log-linear models for contingency tables, and algorithmic and theoretical considerations. The lecture explores the geometry and algebra of log-linear models, Markov bases, and the application of algebraic statistics in testing for reciprocation effect. It also delves into stochastic blockmodels, latent variants, and the mixture of log-linear models. The lecture concludes with discussions on structural considerations, model equivalences, and the application of algebraic statistics in connectome data.

Official source

Related concepts (32)

Contingency table

In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering, and scientific research. They provide a basic picture of the interrelation between two variables and can help find interactions between them.

Generalized linear model

In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.

Linear probability model

In statistics, a linear probability model (LPM) is a special case of a binary regression model. Here the dependent variable for each observation takes values which are either 0 or 1. The probability of observing a 0 or 1 in any one case is treated as depending on one or more explanatory variables. For the "linear probability model", this relationship is a particularly simple one, and allows the model to be fitted by linear regression.

Goodness of fit

The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test).

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Related lectures (64)

Binary Covariate Impact: 2x2 Contingency Tables

Explores the impact of a binary covariate on binary responses using 2x2 tables.

Categorical Data Analysis: Poisson GLM

Explores Poisson GLM for analyzing count data in categorical analysis, focusing on contingency tables and Bayesian inference.

Linear Regression: Estimation and Testing

Explores linear regression estimation, hypothesis testing, and practical applications in statistics.

Estimation of Theoretical Frequencies

Covers the estimation of theoretical frequencies and independence testing between two characteristics, with examples for practical application.

Weighted Least Squares Estimation: IRLS Algorithm