M2 - Statistics and Data Science (SSD) - BIOSTATS

This course presents some of the classical and modern methods for constructing non-parametric density or regression estimators. Both theoretical and practical aspects are covered

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This course introduces the general framework of linear models in which we seek to express a response variable as a function of a linear combination of predictors. By assuming both a specific relationship between the mean response and the predictors (link function), as well as a specific distribution of the random variation of the response around its mean, it is possible to represent binary data (e.g. presence/absence, mortality/survival) or count data (e.g. number of individuals, number of species). Thanks to this general framework, non-normally distributed variables can be modeled. In particular, the use and interpretation of logistic, binomial and Poisson regression models will be detailed.

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TD courses in English for students in the "M2 Statistics and Data Science" program, who are aiming for professional autonomy in English.

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This course provides an introduction to parametric Bayesian statistics. After a presentation of the Bayesian paradigm, the cases of point and ensemble estimation will be considered, followed by the methodology of Bayesian model selection. Binomial, Gaussian and linear models will serve as illustrations for the previous topics.

For complex models, the problems of model estimation and selection in the Bayesian context require the use of advanced integral approximation tools. The second part of the course will therefore focus on Monte Carlo methods and Markov Chain Monte Carlo algorithms.

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The size of statistical data is constantly increasing, and so is the richness of the description of statistical units. However, classical linear statistical modeling becomes invalid in high dimensions, i.e. when the number of variables exceeds the number of statistical units. This course presents the most common techniques used to regularize linear models in high dimension.

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This course deals with the machine learning framework from a statistical point of view.
We will focus mainly on the supervised framework (regression and classification) and introduce some elements of the unsupervised framework through partitioning methods (clustering).
In addition to modeling and theoretical aspects, the course will also cover some elements of optimization and implementation (sklearn, pytorch, etc.) of the methods introduced.

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The lifespan of an individual in biostatistics, or of a component in reliability analysis, is a quantity whose statistical analysis differs from the usual data. On the one hand, it leads to the consideration of quantities such as the hazard function, the residual mean life time, etc., which are of less interest in other fields of statistics. On the other hand, it often involves a censoring mechanism, as the data are observed incompletely due to the length of the experiments in relation to the time we want to allocate to them.

The aim of this module is to present the basics of survival analysis. The rationale and main mechanisms of data censoring are discussed. Two main types of statistical approach are presented: the parametric approach, which, despite its limitations, is often favored by users because "the parameters speak for themselves", and the non-parametric approach, which supports and complements parametric analyses, giving them greater flexibility and depth when data are plentiful. The module also presents various models (Cox model, accelerated failure rate, etc.) linking survival to explanatory factors, enabling us to determine which factors may have an impact on survival. This information is particularly useful in a health context, as it can be used to personalize survival projections for an individual.

These methods will be implemented using R software.

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Complementary courses open up more specialized areas of statistics and stochastic modeling. Their content may change from year to year. Topics may include
- biological sequence analysis: probabilistic models of biological sequence evolution, phylogeny inference, hidden Markov models for pattern detection, graphical models and inference of gene regulation networks
- population dynamics: birth and death processes (definitions, properties, asymptotic behavior, parameter estimation, simulation), deterministic, stochastic or hybrid approximations
- biomedical statistics: Introduction to clinical research data, regulatory and methodological aspects, Likelihood function and applications to biomedical data, Reminders on survival data, competitive risk models, U-statistic-based testing, Models for fertility data analysis, Medical diagnosis and ROC curves as an application of a U-statistic, Meta-analyses.
- Extreme-value statistics and environmental applications:Univariate and multivariate extreme-value theory: law of maxima and high threshold violations for random variables and vectors, extreme dependencies, estimation of extreme quantiles, risk studies. Applications to environmental data: rainfall, wave heights, temperatures, etc.
- spatial statistics: Introduction to the fundamentals of spatial prediction and applications. In order to cover a wide range of spatial statistics, this course can be divided into two parts: point processes and geostatistics.
- linear mixed models : Extension of linear models to linear mixed models. Estimation of both fixed-effect and variance parameters within these models. Implementation on various practical cases. Random effects in generalized linear models.

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Complementary courses open up more specialized areas of statistics and stochastic modeling. Their content may change from year to year. Topics may include
- biological sequence analysis: probabilistic models of biological sequence evolution, phylogeny inference, hidden Markov models for pattern detection, graphical models and inference of gene regulation networks
- population dynamics: birth and death processes (definitions, properties, asymptotic behavior, parameter estimation, simulation), deterministic, stochastic or hybrid approximations
- biomedical statistics: Introduction to clinical research data, regulatory and methodological aspects, Likelihood function and applications to biomedical data, Reminders on survival data, competitive risk models, U-statistic-based testing, Models for fertility data analysis, Medical diagnosis and ROC curves as an application of a U-statistic, Meta-analyses.
- Extreme-value statistics and environmental applications:Univariate and multivariate extreme-value theory: law of maxima and high threshold violations for random variables and vectors, extreme dependencies, estimation of extreme quantiles, risk studies. Applications to environmental data: rainfall, wave heights, temperatures, etc.
- spatial statistics: Introduction to the fundamentals of spatial prediction and applications. In order to cover a wide range of spatial statistics, this course can be divided into two parts: point processes and geostatistics.
- linear mixed models : Extension of linear models to linear mixed models. Estimation of both fixed-effect and variance parameters within these models. Implementation on various practical cases. Random effects in generalized linear models.

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4 to 6-month internship in a company, EPIC or research laboratory, supervised by a researcher, teacher-researcher or research engineer.

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Many phenomena are only incompletely or indirectly observed, which complicates their analysis. Their statistical modeling must therefore include unobserved variables, known as 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 model parameters.

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