Statistics

This course explains the theory of probability and some of the statistical methods based upon it. The course begins with the basic ideas of probability theory: events, probabilities, random variables and the notion of independence. It continues with the two crucial principles: the law of large numbers and the central limit theorem. Using these, the course covers the fundamental concepts of statistical inference (estimation and hypothesis testing), and illustrates these concepts using the most important statistical models.

Today's world relies much on the accumulation, presentation, and interpretation of large quantities of information. Statistics is a tool that enables us to organize our data in an efficient manner, and provides us with methods that help us understand the relationships that occur in our data and our increasingly complex world. This course draws on examples from multiple disciplines, such as political science, economics, medical sciences, and biology to demonstrate how to search for and evaluate patterns in large amounts of data, as well as to interpret what these patterns tell us about the world. The material in this course covers data display, statistical inference, regression and experimental design. The course primarily focuses on developing substantive and precise understanding of the various quantitative research designs and corresponding statistical methods. Students develop individual projects, applying their knowledge to real-world problems using elementary computer programming in the R statistical programming package. This course is designed to be accessible for students at all levels of mathematical skill. The focus is on developing conceptual understanding of statistics without heavy reliance on rigorous mathematical background. The knowledge obtained from this course should provide solid background for students who wish to continue their statistical education with more advanced courses as well as prepare students to perform their own statistical analyses in their coursework and beyond. Upon completion the course aims to provide the students with the following skills: apply scientific research process, including theory formulation and hypothesis testing; critically analyze various types of data and learn to select most appropriate elementary statistical technique to answer their research question; use statistical programming to enter data, generate descriptive statistics and graphs, and estimate basic statistical models; communicate and present statistical results to a variety of audiences – academic experts and policy-makers.

This course provides students with tools for handling high-dimensional statistical problems. The course contains models and methods with practical applications, mainly for spatial statistics and image analysis. Of special importance are the Bayesian aspects, since they form the foundation for many modern spatial statistical and image analysis methods. The course emphasizes methods with applications in climate, environmental statistics, and remote sensing. The following topics are covered: Bayesian methods for stochastic modelling, classification, and reconstruction; random fields, Gaussian random fields, Kriging, Markov fields, Gaussian Markov random fields, non-Gaussian observationer; covariance functions, multivariate techniques; simulation methods for stochastic inference (Gibbs sampling); applications in climate, environmental statistics, remote sensing, and spatial statistics.

The discipline of statistics is concerned with situations in which uncertainty and variability play an essential role and forms an important descriptive and analytical tool in many practical problems. Against a background of motivating problems, this course develops relevant probability models for the description of such uncertainty and variability. Topics: sample spaces; operations of events; probability and probability laws; conditional probability; independence; discrete random variables; cumulative distribution function; probability mass function; Bernoulli, binomial, geometric, and Poisson distributions; continuous random variables; probability density function; exponential, gamma, and normal distributions; functions of a random variable; joint distributions; marginal distributions; independent random variables; functions of jointly distributed random variables; expected value; variance and standard deviation; covariance and correlation.

This course covers statistical analysis and modelling methods that are commonly used in the finance industry. Major topics include statistical properties of returns, regression analysis with applications to single and multi-factor pricing models, multivariate analysis with applications in Markowitz's portfolio management, modelling and estimation of volatilities, calculation of value-at-risk, nonparametric methods with applications to option pricing and interest rate markets.

This course introduces the fundamental principles and methods of demography. The role of demographic data in describing the health status of a population, spotting trend and making projection will be highlighted. Topics include sources and interpretation of demographic data, rates, proportions and ratios, standardization, complete and abridged life tables, estimation and projection of fertility, mortality and migration, Interrelations among demographic variables, population dynamics, demographic models.

Analysis of scientific data and experiments: Design of experiments and ethical research. Data modelling and management. Exploratory data analysis. Randomness and probability. Statistical analysis including linear regression, analysis of variance, logistic regression, categorical data analysis, and non-parametric methods.