Courses

Please find below the list of courses. Click on a course to have the details.

Course 1: Survival Analysis

Course 2: Time series

Course 3: Introduction to spatial points processes and simulation-based inference

Course 4: Extreme values statistics

Course 5: Spatially correlated survival data

Course 6: Programming and simulations with R / Statistics with R

Course 7: Empirical processes and censored data

Course 1: Survival Analysis

Prof. Philippe Saint-Pierre, Université de Toulouse, France

Survival analysis consists in studying the delays before the occurrence of an event of interest (death, healing, etc.). The aim of this course is to present the main models of analysis of life time data. We introduce the context as well as the notion of censorsing that makes the specifity of survival data. Non-parametric approaches (Nelson-Aalen, Kaplan-Meier) and parametric approach (maximum likelihood) will be considered for the estimation of the cumulative risk or the survival function. The effect of covariates on survival will be studied through the Cox semi-parametric model. We will be also interested in the comparison of the survival functions in order to identify significant differences. Finally, multi-state models that generalize the survival models will be discussed. These methods will be implemented with the R software.

Course 2: Time series

Prof. Jean-Marc Bardet, Université Paris 1, France

Based on examples of climate or environmental data treated with R software, we will remind some key points of time series: 

1. Theoretical definitions of processes, stationarity and its applications
2. Parametric and non-parametric estimation of trend and seasonality
3. Common examples of time series: ARIMA, GARCH, long memory, ...
4. Parametric and semi-parametric estimators and tests for stationary time series
5. Model selection for time series
6. Prediction for times series

Course 3: Introduction to spatial points processes and simulation-based inference

Prof. Jesper Møller, Department of Mathematical Sciences, Aalborg University

A spatial point process is a  mathematical model for randomly distributed points in two or higher dimensional space, e.g. the  locations of restaurants in a city, trees in a forest, cases of a disease in a country or galaxies in the  Universe. The model may be extended to include information about covariates such as soil  conditions in case of trees and random "marks" such as "types of points" (e.g. different types of  restaurants or species of trees), "size of associated object" (e.g. the diameter of a tree at breastheight) or "direction of associated object" (e.g. the direction from the center of a brain cell to its  apex). The course covers the following topics of spatial point pattern analysis.

1. Introduction to  spatial point pattern analysis.
2. Poisson processes.
3. Functional summary statistics.
4. Cox  processes.
5. Markov point processes.
6. Simulation.
7. Inference procedures.

Handout: Handout_Moller_CIMPA_Togo_2018.pdf

Course 4: Extreme values statistics

Prof. Aliou Diop, Université Gaston Berger, Senegal

Taking into account extreme events (precipitation, raw, waves of heat, exceptional course of action, abnormal loads, etc..) is often very important in the statistical modelling of risk. It is the behavior in tail of distribution which is then essential and not the central portion behavior as in usual statistics. Extreme Value Theory provides a rigorous probabilistic mathematical basis on which it is possible to build statistical models that allow to predict the intensity and frequency of these extreme events. 

Domains of application: risk management, finance/insurance, hydrology, reliability.

This course will address the following topics:

1. Asymptotic behavior of the largest value in a sample.
2. Domain of attraction of the Frechet, Weibull and Gumbel distributions. Generalized Pareto Distribution. Regular varying functions.
3. Estimation of the parameters of the Generalized Pareto distribution. Hill Estimator. Application to the estimation of extreme quantiles. Illustration with simulated datasets and real data.
4. Introduction to extreme value statistics in presence of censoring.

Course 5: Spatially correlated survival data

Prof. Sophie Dabo-Niang, Université de Lille 3, France

Spatial statistics includes any (statistical) techniques which study phenomenons observed on spatial sets. Such phenomenons appear in a variety of fields including survival analysis.  Survival data are encountered in various settings such as biomedical, reliability, actuarial science, sociology, public health to name a few, and are part of a class of data called survival or failure time data. Parametric, semi and non-parametric, and regressions type survival models have been the subject of intense research in past decades. The models developed are mainly based on the assumption that units involved are independent of each others. That  assumption of independent units may be violated in many situations especially in biomedical studies, epidemiology, and others.

In this course, we consider the situation where the units, located at some geographical areas are monitored for the occurrence of some event such as: disease, epidemic, tornadoes, cancer etc.. There exists nuisance parameters such as: environmental factors, social and physical environments, population density, weather conditions out of control of the investigators that can have substantial impact on the occurrence of events for a pair of units via their  spatial coordinates. Correct inference on the association of the main covariates with the event-specific survival times relies on careful consideration of underlying spatial correlations especially in region-wide disease studies in epidemiology. The development of parametric,  semiparametric and nonparametric survival models that accounts for spatial correlation is therefore of considerable importance. The main driver of this course is to introduce statistical models for spatially correlated survival data.

Cours 6: Programming and simulations with R / Statistics with R

Prof. Jean-François Dupuy, INSA de Rennes
Dr. Simplice Dossou-Gbete, Associate Professor, Université de Pau, France

This course will address the following themes:

• Introduction to programmation with  R,
• Vvectors, arrays, matrices, data frame , lists,
• Data manipulation  (data input and output),
• statistical tests,
• linear models,
• ANOVA,
• Principal Components Analysis, Correspondence factor analysis, Multiple Correspondence Analysis,  Automatic classification,
• Life data analysis.

Cours 7: Empirical processes & censored data

Prof. Kossi Gneyou, Université de Lomé, Togo

This course will address the following themes:

• Empirical processes,
• Uniform Law of Large Numbers, Uniform Central Limit Theorem,
• Entropy,
• VC Classes,
• Kaplan-Meier product-limit process
• Non-parametric estimators of hazard rate and regression
• Conditional case.