Module Inhoud - Honneurs
Introduction to R (13074-723)
Objectives and content: This
module is an introduction to programming and data analysis within the R
open source environment. It is presented as a block course in the first
two weeks of the first semester and commences the week preceding
general commencement of classes. The viewpoint of this module as well as
of all modules where R plays a role is in agreement with the aim of the
R computer language: "R has a simple goal: To turn ideas into software, quickly and faithfully".
Biostatistics (10408-712)
Objectives and content: Biostatistics may be regarded as the study of the application of statistics to medicine. It covers medical terminology, the design of clinical trials, the collection and numerical analysis of data, the interpretation of the analyses and the drawing of conclusions. Particular emphasis is given to skills relevant to medical literature (the writing, as well as the understanding of writing by others) and statistical techniques and software that are widely used when doing medical research. It is not a mathematically strenuous course. It deals primarily with the philosophy and terminology of medical research, as well as the statistical techniques problems encountered in the medical field in particular. Topics that will be covered are: SAS, Clinical trials, Power and sample size analysis, Longitudinal data analysis, Handling missing data and Statistical genetics.
Multivariate Methods in Statistics A & B (10600-721 & 10601-751)
Objectives and content: The objective of the course is to teach students the practical application of multivariate analysis. Various multivariate methods are dealt with. Students learn when and where to apply these techniques. The consequences of the assumptions made on some of these techniques are also studied. The following topics are studied: Matrix algebra, Characterising and displaying multivariate data, The multivariate normal distribution, Inferences on one or two mean vectors, Multivariate analysis of variance, Inferences on the covariance matrix, Discriminant analysis, Classification analysis, Multivariate regression, Canonical correlation, Principal component analysis, Factor analysis and Cluster analysis. The R and SAS software are used in all the applications to datasets. The A module is a prerequisite for the B module.
Financial Mathematical Statistics (11164-732)
Objectives and Content: In
this module an introduction is given to Extreme Value Theory (EVT) and
its role in Financial Risk Management. EVT entails the study of extreme
events and for this theory has been developed to describe the behaviour
in the tails of distributions. The module will disduss the theory in a
conceptual fashion without proving the results. It will be shown how
this theory can be used to carry out inferences on the relevant
parameters of the underlying distribution. Both the classical approach
of block maxima based on the Fisher-Tippett Theorem and the more modern
threshold approach based on the Pickands-Balkema-de Haan Theorem will be
discussed and applied. Results for both independent and dependent data
will be covered.
Experimental Design (10440-713)
Objectives and content: This
module does not require advanced mathematics and is an option for both
statistics and mathematical statistics students. Focus is mainly on the
practical implementation of techniques together with computer packages
from consultancy perspective. Attention is given to modeling, design
matrices, least squares and diagnostics.
Data mining (58777-741)
Objectives and content: Data
mining is a relatively new discipline using techniques developed in
statistics, data base technology, pattern recognition, machine learning
and other related areas. It is concerned with the analysis of large
data bases in order to identify trends and patterns in the data, which
can be of value to the data base owners. Examples of applications of
data mining in practice are: credit assessment, fraud detection,
prediction of stock prices and marketing and sales forecasting. The
purpose of this module is to introduce students to the philosophy and
methodology of data mining, to study statistical and other techniques
that are applied in data mining, and to learn to apply data mining
software to practical problems.
Sampling Techniques (10705-742)
Objectives and content: The
design of a sample is one of the most important aspects of any survey:
no amount of statistical analysis can compensate for a badly-designed
sample. Therefore, the emphasis of this course is the scientific design
of samples, determination of sample sizes and is related to methods for
analysing the data from a survey. Contents include: Questionnaire
design, sampling techniques (simple random, stratified, systematic,
cluster, complex), proportional vs disproportional allocation for
stratified sampling, ratio and regression estimation, estimation of
means, totals proportions and their variances, weighting of survey data,
dealing with non-response.
Applied Time series Analysis (10748-722)
Objectives and content: This
module is a continuation of undergraduate time series analyses and
concentrates on more advanced forecasting techniques. Topics that are
covered include:
- The Box & Jenkins methodology of
tentative model identification, conditional and unconditional parameter
estimation and diagnostic methods for checking the fit of the series.
- ARIMA and Seasonal ARIMA-processes.
- Introduction
to Fourier Analysis, spectrum of a periodic time series, estimation of
the spectrum, periodogram analysis, smoothing of the spectrum.
- Case studies using STATISTICA, R and SAS.
- Forecasting with ARMA models and prediction intervals for forecasts.
- Transfer function models and intervention analysis.
- Multiple regression with ARMA errors, cointegration of non-stationary time series.
- Conditional heteroscedastic time series models, ARCH and GARCH.
Applied Stochastic simulation (65269-746)
Objectives and content: In this module the student learns to understand and apply the underlying mathematical principles behind stochastic simulation. Statistical theory is applied to practical problems which are modelled on computer. To achieve this, the student revises probability theory, including conditional probability and independence, discrete and continuous distributions, probability integral transformation, and Bayes' theorem. Pseudorandom number generation is studied to simulate stochastic problems. These pseudorandom numbers are used to evaluate integrals, and to generate discrete and continuous random variables. It is also important to do a statistical analysis of simulated data using point and interval estimates of the mean and variance, as well as bootstrap techniques. Input data for simulation models are analysed with the chi-squared and Kolmogorov-Smirnoff goodness-of-fit tests. The student finally develops practical simulation models of discrete-event, dynamic stochastic processes using a dedicated simulation software package.
Capita Selecta in Statistics A & B (11920-725 & 11921-755)
Objectives and content: Selected and specialised topics to be followed in Applied Statistics. Content varies from year to year when offered.
Module Inhoud - Magister
Bootstrap and other Resampling techniques A & B (10694-811 & 10695-841)
Objectives and content: Traditional
procedures of statistical inference in many cases are true only
asymptotically or under strict assumptions for small samples. For many
problems it is impossible to find solutions analytically. Re-sampling
techniques are computer intensive methods using repeated re-sampling
from the original sample in order to obtain solutions for inferential
statistical problems. The aim of this module is to introduce the
student to the bootstrap and related computer intensive methods enabling
him/her to use correctly these methods with confidence in practice. The A module is a prerequisite for the A module.
Applied Statistical Learning Theory
Objectives and content: The outcomes of these modules can be summarised as follows:
- The students should develop a holistic view of the subject of statistics, gaining an appreciation of the general principles underlying many (seemingly unrelated) statistical methods.
- The students should develop an awareness of the size, complexity and diversity of data sets which one encounters in practice.
- The students should develop an appreciation of the challenges and problems posed to a statistician wishing to analyse a data set, especially the problem referred to as the "curse of dimensionality" in high-dimensional problems.
- The students must gain knowledge of the various approaches to the "curse of dimensionality" problem and the manner in which these approaches compromise between underlying assumptions and sample size requirements.
- The students must understand the important role played by more traditional, established statistical procedures such as multiple regression analysis, logistic regression analysis and linear discriminant analysis in modern data mining.
- The students should become sensitive to and appreciative of the valuable contributions made to the development of data mining procedures in areas such as computer science and machine learning.
- The students should be granted the opportunity to enhance their programming skills through writing appropriate programs to solve various data analysis problems.
Regarding the content of the modules, statistical learning theory is a collective noun for a variety of techniques that can be used to identify, describe and model important patterns and trends in data sets. The topics which are studied in these modules include techniques that are well established in traditional statistics, namely regression analysis, discriminant analysis, spline models and smoothing splines, as well as more recently developed approaches such as regression and classification trees, additive models, bagging, boosting (also from a functional gradient descent point of view), neural networks, random forests and support vector machines.
Advanced Sampling Techniques (10523-818)
Objectives and content: In
practice, complex sampling techniques are usually applied to design
sample surveys. Furthermore, nonresponse and skewness generally
manifest in sampling surveys that need to be addressed scientifically.
This course covers both theoretical and practical aspects regarding
sampling and include the following: two-stage cluster sampling; design
and estimation of complex sample surveys; design effects; dealing with
nonresponse and missing data; weighting of surveys; inferential
statistics for complex survey data.
Multi-dimensional Scaling A & B (10597-822 & 11910-852)
Objectives and content: Multi-dimensional
scaling (MDS) consists of various techniques from the field of
multivariate statistical analysis. MDS focuses on dimension reduction
and graphical displays of multi-dimensional data. This module introduces
the theory and practical implementation of classical metrical scaling,
non-metrical scaling, various forms of Procrustes analysis, unfolding
techniques, individual differences models, as well as m-mode n-way
models. Biplot methodology is emphasised. MDS techniques for both
quantitative and qualitative data are considered. Correspondence
analysis, multiple correspondence analysis, homogeneity analysis,
analysis of distance as well as non-linear principal component analysis
and canonical variate analysis are also discussed. The A module is a prerequisite for the B module.
Advanced Statistics A & B (10521-821 & 10522-851)
Objectives and content: Selected and specialised topics to be followed in Applied Statistics. Content varies from year to year when offered.