Lecture

Gaussian Conditional Model and Properties

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In course

EE-209: Elements of statistics for data science

Théorie de l'estimation: estimateurs du maximum de vraisemblance, information de Fisher, inégalité de Cramer-Rao, intervalles de confiance. Tests d'hypothèses: cadre de Neyman-Pearson: test du rapport de vraisemblance, tests paramétriques et non-parmétriq ...

Description

This lecture covers the Gaussian conditional model for linear regression, the properties of the model if the data is Gaussian, and the paradox of Simpson illustrated with the example of kidney stone treatment comparison. It also discusses the normal equations, linear vs affine regression, and the maximum likelihood estimation principle.

Instructor

Florent Gérard Krzakala

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

Bayesian linear regression

Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often labelled ) conditional on observed values of the regressors (usually ).

Segmented regression

Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.

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