Mathematical Statistics 2

Course
2023-2024

a basic understanding of introductory statistical concepts and some familiarity with R as taught in Inleiding Mathematische Statistiek.

Description

An overview about each of the four topics topic presented in this course is given here below

Survival analysis (Prof. Dr. M. Fiocco)

This area of statistics deals with time to event data, whose analysis is complicated not only by
the dynamic nature of events occurring in time but also by censoring where some events are not
observed directly but it is only known that they fall in some interval or range. Different types of
censored and truncated data, non-parametric methods to estimate the survival function and
regression models to study the effect of risk factors on survival outcomes will be discussed.
Special aspects such as time-dependent covariates and stratification will be introduced.

Longitudinal data analysis (Dr. M. Signorelli)

Longitudinal data are data collected through a series of observations of the same subjects over time (“repeated measurements”). Repeated measurements from the same subject are typically correlated, so the analysis of longitudinal data cannot rely on traditional methods that assume independent and identically-distributed observations. Instead, it requires more flexible models that can account for the existing correlation between repeated measurements. Generalized linear mixed models (GLMMs) are extensions of the linear regression model that make it possible to account for such correlation. After introducing the theory behind linear and generalized linear mixed models, we will discuss how such models can be estimated, and how to use them to test statistical hypotheses and to compute predictions.

Non parametric Bayesian methods (Dr. V. Masarotto).

The goal of the three lessons is to give an introduction to nonparametric Bayes thinking, with some practically motivated examples. The course will provide additional and complementary knowledge with respects to concepts of Bayesian statistics and classic non-parametric estimation. We will explore what it means to think “non-parametrically” within a Bayesian paradigm, and then move into introducing some canonical classes of models, covering simple approaches to posterior computation within such models. We will conclude with some basic estimations using the R software environment.

Online learning (Dr. D. van den Hoeven)

Online learning is a general framework that can be applied in various settings such as for example recommendation systems, auctions, games, traffic routing, statistical learning, and advertising. In online learning we work in an interactive environment. In each interaction with the environment we make a prediction, suffer the loss associated with that prediction, obtain feedback, and use that feedback to adjust our prediction for the next interaction with the environment. We will discuss various ideas and algorithms from online learning, including bandit feedback and the exponential weights algorithm.

Course objectives

The overall aim of the course is to introduce students to four different areas of statistics. By the
end of the course, students are expected to have a basic understanding of the topics discussed
and to be able to use existing software to apply the methods covered during the course.

Timetable

The schedule of the course can be found on MyTimeTable.

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Mode of instruction

Weekly 2 × 45 min of lecture in class, and 2 × 45 min of practical sessions with exercises. Laptop with the statistical package R (http://www.r-project.org) already installed is required for each practical section.

Assessment method

Four individually written reports (20% each), and a presentation (20%) on a selected topic. The presentations will be held individually or in pairs, depending on the group size. The reports are regarded as practical assignments, and can not be retaken. The presentation can be retaken.

Lecture material provided in class.

Registration

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