## Probability and Statistics (AUC)

 Course code 900229SCI Credits 6 credit points Requirements Calculus (Linear Algebra highly recommended). Audience Amsterdam University College Lecturer Prof.dr. Mathisca de Gunst (Dept. of Mathematics, Faculty of Sciences, VUA). E-mail: degunst at cs.vu.nl Period Spring 2015, starts February 2. Hours Mondays 13.45-15.15, Thursdays 9.00-10.30. Location AUC 1.01-A Aim An introduction to probability and statistics: * Learn formal reasoning in terms of probability and gain intuition for randomness; * Get acquainted with statistical modeling and analysis; * Learn simple stochastic simulation schemes and statistical analysis tools in R. Form Lectures, problem sessions, a few computer labs. Description Many phenomena are subject to chance variation: economic time series, sampling of respondents in a survey (and subsequent lack of response), measurement error, survival after a medical treatment, physics of large systems, etc. Probability theory is the mathematical formalism to model such diverse phenomena. This course starts by introducing key concepts of probability theory: random variables and vectors, probability distributions and densities, independence and conditional probability, expectations, law of large numbers and central limit theorem. Probability models are the basis for statistical analysis. Whereas descriptive statistics is concerned with averages and numerical tables, statistical inference tries to answer scientific questions regarding financial series, earthquakes, the health effects of certain foods, etc. This is done by modelling data as the outcome of a chance experiment. Statistics next aims at inferring the probability model for this experiment from the data. Methods are developed, understood and investigated from this perspective. Drawing up a reliable model for the underlying chance experiment is not always easy, but once available this allows to make optimal decisions and quantify the remaining uncertainty and possibility for generalization. Key concepts discussed in this course are likelihood, estimation, testing, p-value, confidence regions, risk and power functions, Bayesian inference. The emphasis is on concepts, but well-known concrete methods as the t-test arise as examples. Literature Book: All of Statistics by Larry Wasserman, Springer Texts in Statistics, 2nd printing, 2010. Additional material will be available in Blackboard. Computer language The statistical package R can be downloaded from the R-project site www.r-project.org . It is free! Assessment Via take home assignments and exams. Schedule and other information Course manual and programme will be available in Blackboard.