Statistics

This course provides an overview of practical aspects of statistical analysis techniques for social science. The objective is to develop an intuitive understanding of statistical analysis from a practical angle. The course consists of classroom lectures and self-study of PC skills. Application examples used in each class will differ depending on the instructor. The course develops the ability to numerically analyze political and/or economic data, to interpret estimation results, and to suggest policy proposals based on the results.

This advanced course in probability introduces various probability models used in physical sciences, life sciences, and economics. It serves as an introduction to stochastic modeling and stochastic processes. The course covers discrete time processes including Markov chains, random walks, continuous time processes (such as Poisson processes), birth-death processes, and queuing systems.

This course aims at providing basic knowledge of programming and conducting statistical analysis with software. Different computing tools, such as R, SAS, C, and C++ are introduced throughout the course for computation and demonstration purposes. The course covers programming with emphasis on data storage, data retrieval, data manipulation, data transformation, descriptive analysis, sorting, files merging, file updating, random sampling and data reporting.

The course presents the fundamental statistical methods for extreme value analysis, discusses examples of applications regarding floods, storm damage, human life expectancy, and corrosion, provide practical use of the models, and points to some open problems and possible developments. Extreme value theory concerns mathematical modelling of random extreme events. Recent development has introduced mathematical models for extreme values and statistical methods for them. Extreme values are of interest in economics, safety and reliability, insurance mathematics, hydrology, meteorology, environmental sciences, and oceanography, as well as branches in statistics such as sequential analysis and robust statistics. The theory is used for flood monitoring, construction of oil rigs, and calculation of insurance premiums for re-insurance of storm damage. Often extreme values can lead to very large consequences, both financial and in the loss of life and property. At the same time the experience of really extreme events is always very limited. Extreme value statistics is therefore forced to difficult and uncertain extrapolations, but is, none the less, necessary in order to use available experience in order to solve important problems.

This course covers basic econometrics. It requires at least a basic course in probability theory and statistical inference as a prerequisite since all the major concepts, methods, and models build upon probability theory and statistical inference. The course focuses mainly on the theory and applications of single and multiple linear regression analysis. Great emphasis is put on the estimation, inference, and interpretation of the multiple linear regression model and its extensions. The course also covers the assumptions of OLS, why they are needed and how to detect and deal with violations of these assumptions. The following topics are covered: general information about econometric models and their application within economic planning; linear-regression models with one or several explanatory variables; nonlinear models; estimation and hypothesis testing; Gauss-Markovs Nonlinear theorem; heteroscedasticity and autocorrelation; multicollinearity; measurement errors; instrumental variables; dummy variables; models with a dichotomous variable as dependent variable: LPM - and the Logit-model; simultaneous equation models: the simultanity bias, identification; the two-stage least square method.

In this course, students learn how to understand, analyze, and resolve complex problems using a range of quantitative techniques. Emphasis is placed on the importance of understanding the science and techniqies behind these ideas in engaging with the modern world. Students tackle estimation problems, learn coding with Python, and explore statistics and game theory.

This course provides an overview of the use of statistical methods in biological sciences. It examines how questions in biology can be answered quantitatively using statistics. The course looks at descriptive, associative, and comparitive statistical methodologies and analyzes key concepts of statistical sampling and experimental design in biology.

This course covers the principles of data mining, exploratory analysis and visualization, as well as predictive modeling for complex data sets. It introduces modern tools for regression and classification for high-dimensional or ultra-high dimensional data from the perspective of statistical decision theory and makes comparison to traditional methods. The course explores statistical principles, computational issues, and hands-on data analysis on high noise, observational data.