• ECTS

    4 credits

  • Component

    Faculty of Science

Description

Many phenomena are only incompletely or indirectly observed, which complicates their analysis. Their statistical modeling must then include unobserved variables, called latent variables, which are linked in one way or another to the observed variables. This course introduces the various ways of introducing latent variables into a model, depending on their type (qualitative or quantitative), and of estimating the parameters of the model.

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Objectives

Train in statistical modeling in the presence of unobserved or indirectly observed variables.

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Necessary pre-requisites

Multivariate data analysis course (PCA & CA). Multivariate analysis course. Inferential statistics course.

 

 

Recommended prerequisites: Very good knowledge of matrix algebra, vector derivation and constrained optimization.

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Syllabus

Introduction.

Situations and typology of latent variables: continuous / nominal; random / non-random.

I - Non-random LV models

  1. Nominal VL: clustering models

    a) Gaussian model.

    b) Multinomial model.

  2. Continuous LVs: component models

    a) PCA model.

    b) PCAVI model.

    c) PLS model.

    d) Multi-block explanatory models: THEME and SCGLR.

II - Random LV models

  1. The EM algorithm

  2. Nominal LV: mixing models

    a) Gaussian mixture.

    b) Multinomial mixture: latent class analysis.

  3. VL Continuous: factor models

    a) Factor model for 1 block.

    b) Structural equation models.

  4. Hidden Markov chain models

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Additional information

 

Hourly volumes:

            CM : 21

            TD:

            TP: 

            Terrain:

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