Final project (MAS302L)

Final project.

Students need to have finished MAS201F before they start the final project.

Mathematics for Finance I (HAG122F)

The course will cover the main points of statistics and pricing in finance. Emphasis is placed on introducing students to the use of statistical and mathematical methods to analyze, price and obtain information about financial instruments. Emphasis is placed on real examples where students are trained to solve tasks similar to those they may have to solve in their jobs in the financial market.

In the statistical part of the course, ideas about continuous and sparse probability distributions, expected values, variance and standard deviation, confidence intervals, null hypotheses and linear regression analyses, both simple and multivariate, will be reviewed. The basic ideas of the Capital Asset Pricing Model (CAPM) will also be reviewed.

The pricing part of the course will deal with the pricing of futures contracts on shares, bonds and currency and interest rate swaps, the construction of interest rate curves, as well as the types and characteristics of options.

Mathematics for Finance II (HAG122M)

The course will cover the main points of statistics and pricing in finance. Emphasis is placed on introducing students to the use of numerical and mathematical methods to analyze, price and obtain information about financial instruments. Emphasis is placed on real examples where students are trained to solve tasks similar to those they may have to solve in the workplace.

The statistical part of the course will cover time series analysis. There, models such as auto regressive models (e. Auto regressive model, AR model) and models with moving averages (e. Moving-average model, MA model) will be introduced to play. Also the combination of ARMA, ARIMA and SARIMA models. Finally, conditional variance models or ARCH and GARCH models will be reviewed.

In the pricing section, we will cover binomial trees, Wiener processes, Ito's auxiliary theorem, the Black-Scoles-Merton model and the pricing of stock and currency options.

Computational Intelligence (IÐN102M)

Basic aspects of computational intelligence, which is the study of algorithms that improve automatically through experience.

Time Series Analysis (IÐN113F)

ARMAX and other similar time series models. Non-stationary time series. Correlation and spectral analysis. Parameter estimation, parametric and non-parametric approaches, Least Squares and Maximum Likelihood. Model validation methods. Models with time dependent parameters. Numerical methods for minimization. Outlier detection and interpolation. Introduction to nonlinear time series models. Discrete state space models. Discrete state space models. Extensive use of MATLAB, especially the System Identification Toolbox.

Epidemiology - a quantitative methodology (LÝÐ107F)

The course is an introduction to epidemiological research methods and causal inference. An overview is provided on measure of disease occurrence, measures of outcome (relative risks), and study design (experiments, intervention studies, cohort studies and case-control studies). Emphasis is on systematic errors and on methods to avoid such errors in planning (study design) and in data analyses. Students get training in reviewing epidemiological studies.

Biostatistics II (Clinical Prediction Models ) (LÝÐ301F)

This course is a continuation of Biostatistics I and constitutes a practical guide to statistical analyses of student's own research projects. The course covers the following topics. Estimation of relative risk/odds ratios and adjusted estimation of relative risk/odds ratios, correlation and simple linear regression, multiple linear regression and logistic regression. The course is based on lectures and practical sessions using R for statistical analyses.

R Programming (MAS102M)

Students will perform traditional statistical analysis on real data sets. Special focus will be on regression methods, including multiple regression analysis. Students will apply sophisticated methods of graphical representation and automatic reporting. Students will hand in a projects where they apply the above mentioned methods on real datasets in order to answer research questions

R for beginners (MAS103M)

The course focuses on statistical analysis using the R environment. It is assumed that students have basic knowledge of statistics and will learn how to apply statistical methods they know in R. Main topics are loading data, graphical representation, descriptive statistics and how to perform the most common hypothesis tests (t- test, chi-square test, etc.) in R. In addition, students will learn how to make reports using the knitr package.

The course is taught during a five week period. A teacher gives lectures and students work on a project in class.

Mixed Linear Models (MAS104M)

The course is about the theory and application of random effects, or linear mixed models, and related models for correlated response variables. The course will cover methods for continuous and approximately normally distributed variables. A statistical model for such data has to describe both the expected value and the covariance between observations. The theory extends the theory of general linear models. Special software is needed for such an analysis and the necessary packages are provided in R, STATA, and SAS. The application will be based on R but other programs will be introduced for comparison.
The course will be taught between beginning of September and end of November, meeting once a week. The teaching will be in a flipped class manner. All the material (both notes and lectures) are online (see below) and it is expected that students will have viewed the material before class. In class the theory will be discussed and then students are expected to work on the application on their own computer.

Machine Learning (REI505M)

An overview of some of the main concepts, techniques and algorithms in machine learning. Supervised learning and unsupervised learning. Data preprocessing and data visualization. Model evaluation and model selection. Linear regression, nearest neighbors, support vector machines, decision trees and ensemble methods. Deep learning. Cluster analysis and the k-means algorithm. The students implement simple algorithms in Python and learn how to use specialized software packages. At the end of the course the students work on a practical machine learning project.

Computing and Calculus for Applied Statistics (STÆ012F)

Univariate calculus (basic algebra, functi ons, polynomials, logarithms and exponenti al functi ons, conti nuity and limits, diff erenti ati on, local extrema andintegrati on).
Linear algebra (vectors, matrices, linear projecti ons with matrices, matrix inverses and determinants).
Programming in R (arithmeti c, functi ons and organizing R code).
Multi variate calculus (Jacobian, Hessian and double integrals).
The approach will be to address each mathemati cs topic using a mix of (a) basic theory (in the form of concepts rather than proofs), (b) computerprogramming using R to visualize the theory, and (c) examples exclusively from stati stics. Formal lectures are not planned, but students will be able toseek assistance with their weekly assignments.
The goal of the course is to cover the calculus, linear algebra and computer programming concepts most commonly needed in stati sti cs. A student who has completed this course should have the mathematical basis for statistics courses currently taught at the MSc level by the mathematics department(and thus also for all stati sti cs courses taught by other departments).

Students will author examples and multiple-choice questi ons, and their submissions will be graded by their peers.

The material is openly available at https://open-educati on-hub.github.io/ccas/.

Mathematics N (STÆ108G)

Course description: The fundamental concepts of calculus will be discussed. Subjects: Limits and continuous functions. Differentiable functions, rules for derivatives, derivatives of higher order, antiderivatives. Applications of differential calculus: Extremal value problems, linear approximation. The main functions in calculus: logarithms, exponential functions and trigonometric functions. The mean value theorem. Integration: The definite integral and rules of integration. The fundamental theorem of calculus. Techniques of integration, improper integrals. Series and sequences. Ordinary differential equations. Vectors and matrix calculations.

Theory of linear models (STÆ310M)

Simple and multiple linear regression, analysis of variance and covariance, inference, variances and covariances of estimators, influence and diagnostic analyses using residual and influence measures, simultaneous inference. General linear models as projections with ANOVA as special case, simultaneous inference of estimable functions. R is used in assignments. Solutions to assignments are returned in LaTeX and PDF format.

In addition selected topics will be visited, e.g. generalized linear models (GLMs), nonlinear regression and/or random/mixed effects models and/or bootstrap methods etc.

Students will present solutions to individually assigned
projects/exercises, each of which is handed in earlier through a web-page.

This course is taught in semesters of even-numbered years.

Theoretical Statistics (STÆ313M)

Likelihood, Sufficient Statistic, Sufficiency Principle, Nuisance Parameter, Conditioning Principle, Invariance Principle, Likelihood Theory. Hypothesis Testing, Simple and Composite Hypothesis, The Neyman-Pearson Lemma, Power, UMP-Test, Invariant Tests. Permutation Tests, Rank Tests. Interval Estimation, Confidence Interval, Confidence, Confidence Region. Point Estimation, Bias, Mean Square Error. Assignments are returned using LaTeX and consitute 20% of the final grade.

Stochastic Processes (STÆ415M)

Introduction to stochastic processes with main emphasis on Markov chains.

Subject matter: Hitting time, classification of states, irreducibility, period, recurrence (positive and null), transience, regeneration, coupling, stationarity, time-reversibility, coupling from the past, branching processes, queues, martingales, Brownian motion.

Statistics Seminar (STÆ311M)

Selected topics in statistics. The seminar can be taken more than once for credit. Each student will give at least one presentation during the semester. Participation in all lectures is mandatory. Spring and fall semester when participation is sufficient.

Bayesian Data Analysis (STÆ529M)

Goal: To train students in applying methods of Bayesian statistics for analysis of data. Topics: Theory of Bayesian inference, prior distributions, data distributions and posterior distributions. Bayesian inference  for parameters of univariate and multivariate distributions: binomial; normal; Poisson; exponential; multivariate normal; multinomial. Model checking and model comparison: Bayesian p-values; deviance information criterion (DIC). Bayesian computation: Markov chain Monte Carlo (MCMC) methods; the Gibbs sampler; the Metropolis-Hastings algorithm; convergence diagnostistics. Linear models: normal linear models; hierarchical linear models; generalized linear models. Emphasis on data analysis using software, e.g. Matlab and R.

Data Base Theory and Practice (TÖL303G)

Databases and database management systems. Physical data organization. Data modelling using the Entity-Relationship model and the Relational model. Relational algebra and calculus.  The SQL query language. Design theory for relational data bases, functional dependencies, decomposition of relational schemes, normal forms. Query optimization. Concurrency control techniques and crash recovery. Database security and authorization. Data warehousing.

Introduction to deep neural networks (TÖL506M)

In this course we cover deep neural networks and methods related to them. We study networks and methods for image, sound and text analysis. The focus will be on applications and students will present either a project or a recent paper in this field.

Probability and Statistics (MAS201F)

Basic concepts in probability and statistics based on univariate calculus. 

Topics: 
Sample space, events, probability, equal probability, independent events, conditional probability, Bayes rule, random variables, distribution, density, joint distribution, independent random variables, condistional distribution, mean, variance, covariance, correlation, law of large numbers, Bernoulli, binomial, Poisson, uniform, exponential and normal random variables. Central limit theorem. Poisson process. Random sample, statistics, the distribution of the sample mean and the sample variance. Point estimate, maximum likelihood estimator, mean square error, bias. Interval estimates and hypotheses testing form normal, binomial and exponential samples. Simple linear regression. Goodness of fit tests, test of independence.

Final project (MAS302L)

Final project.

Students need to have finished MAS201F before they start the final project.

Statistical Consulting (MAS201M)

Participants in the course will obtain training in practical statistics as used when providing general statistical counselling. The participants will be introduced to actual statistical projects by assisting students in various departments within the university. The participants will report on the projects in class, discuss options for solving the projects and subsequently assist the students with analyses using R and interpretation of results.

Applied data analysis (MAS202M)

The course focuses on statistical analysis using the R environment. It is assumed that students have basic knowledge of statistics and the statistical software R. Students will learn to apply a broad range of statistical methods in R (such as classification methods, resampling methods, linear model selection and tree-based methods). The course on 12 weeks and will be on "flipped" form. This means that no lectures will be given but students will read some material and watch videos before attending classes. Students will then work on assignments during the classes.

Mathematics for Physicists II (EÐL408G)

Python tools related to data analysis and manipulation of graphs. Differential equations and their use in the description of physical systems. Partial differential equations and boundary value problems. Special functions and their relation to important problems in physics. We will emphasize applications and problem solving.

Survey research methods (FÉL089F)

The purpose of this course is to provide students with understanding on how to plan and conduct survey research. The course will address most common sampling design and different type of survey research (phone, face-to-face, internet, mail etc.). The basic measurement theories will be used to explore fundamental concepts of survey research, such as validity, reliability, question wording and contextual effect. The use of factor analysis and item analysis will be used to evaluate the quality of measurement instruments.  The course emphasizes students’ active learning by planning survey research and analyzing survey data.

This course is taught every other year.

Regression methods 2: Analysis of ordinal and nominal dependent variables. (FOM006F)

In the course we cover regression methods where the dependent variable is dichotomous (binary logistic regression) ordinal (ordinal regression) or multinomial. The courses emphasize application in social sciences. Students should have completed FOM401M Regression 1 that addresses assumptions and application of linear regression.  In this course we start with review of basic descriptive statistics and inferential statistics for categorical and ordinal variables. Bivariate and multivariate cross tables, percent, probabilities, ratios, odds ratios, and proportions, measures of association and chi-square test of independence.  Then we address in some details binary logistics regression with emphasize of interpreting regression coefficients. The binary logistic regression method is then extended to ordinal regression.  Then we extend the binary logistic regression method to multinomial regression. We address methods to work with different and complex sample design with and without sample weights. We will address multilevel regression methods. We will both use SPSS and R statistical packages.

Econometrics III (HAG606G)

Modern econometrics methods, in particular time-series methods and methods concerning duration data. Univariate and multivariate models for discrete and continuous-time models. Relation to some risk-management concepts are introduced. Students do their own projects and present them. Emphasis is on data from financial markets. Some preliminiary knowledge of statistics/econometrics as well as experience of working with data in computers is useful.

Operations Research (IÐN401G)

This course will introduce the student to decision and optimization models in operations research. On completing the course the student will be able to formulate, analyze, and solve mathematical models, which represent real-world problems, and critically interpret their results. The course will cover linear programming and the simplex algorithm, as well as related analytical topics. It will also introduce special types of mathematical models, including transportation, assignment, network, and integer programming models. The student will become familiar with a modeling language for linear programming.

Business Intelligence (IÐN610M)

Business intelligence are the strategies and technologies companies use to collect, interpret and utilize data for decision support. This course goes beyond reports and dashboards and demonstrates how artificial intelligence can help us gain insights and recommend action. The course is comprised of five learning modules: 1.) regression and classification where data is segmented accoring to predetermined labels. 2.)  semi- and un-labelled data where items are grouped based on similarity measures. 3.) Process mining. 4.) Natural language processing, and 5.) Data ethics. Within each learning module students prepare for class and work in teams on a business problem, followed by an individual assessment.

Biostatistics III (Survival analysis) (LÝÐ079F)

The course covers methods for analysis of cohort studies using methods for time to event or survival analysis. It is based on the course Biostat III – Survival analysis for epidemiologists in R at the Karolinska Institutet: See (https://biostat3.net/index.html): "Topics covered include methods for estimating patient survival (life table and Kaplan-Meier methods), comparing survival between patient subgroups (log-rank test), and modelling survival (primarily Poisson regression, Cox proportional hazards model and flexible parametric models). The course addresses the concept of 'time' as a potential confounder or effect modifier and approaches to defining 'time' (e.g., time since entry, attained age, calendar time). The course will emphasise the basic concepts of statistical modelling in epidemiology, such as controlling for confounding and assessing effect modification." 

The AI lifecycle (REI603M)

In this course, we study the AI lifecycle, i.e. the productionisation of AI methods.
We explore the following parts of the lifecycle:
- Data collection and preparation
- Feature engineering
- Model training
- Model evaluation
- Model deployment
- Model serving
- Model monitoring
- Model maintenance
Three large projects will be handed out during the semester where students compete to solve AI problems.

Random Effects Models (STÆ004F)

The focus of this course is on Bayesian latent Gaussian models (BLGMs) which are a class of Bayesian hierarchical models and applications of these models. The main topics are three types of BLGMs: (i) Bayesian Gaussian—Gaussian models, (ii) BLGMs with a univariate link function, and (iii) BLGMs with a multivariate link function, as well as prior densities for BLGMs and posterior computation for BLGMs. In the first part of the course, the basics of these models is covered and homework assignments will be given on these topics. In the second part of the course, the focus is on a project, in which data are analyzed using BLGMs. Each student can contribute data that she or he wishes to analyze. The material in the course is based on a theoretical background. However, the focus on data analysis is strong, and computation and programming play a large role in the course. Thus, the course will be useful to students in their future projects involving data analysis.

Linear regression models, the multiple normal distribution, hierarchical models, fixed and random effect models, restricted maximum likelihood estimation, best linear unbiased estimators, Bayesian inference, statistical decision theory, Markov chains,  Monte Carlo integration, importance sampling, Markov chain Monte Carlo, Gibbs sampling, the Metropolis-Hastings algorithm.

Mathematics for Physicists I (STÆ211G)

Python tools related to data analysis and plotting. Mathematical concepts such as vectors, matrices, differential operators in three dimensions, coordinate transformations, partial differential equations and Fourier series and their relation to undergraduate courses in physics and engineering. We will emphasize applications and problem solving.

Introduction to Measure-Theoretic Probability (STÆ418M)

Probability based on measure-theory.

Subject matter: Probability, extension theorems, independence, expectation. The Borel-Cantelli theorem and the Kolmogorov 0-1 law. Inequalities and the weak and strong laws of large numbers. Convergence pointwise, in probability, with probability one, in distribtution, and in total variation. Coupling methods. The central limit theorem. Conditional probability and expectation.

Seminar on Machine Learning (TÖL028M)

In this course, students familiarize themselves with a particular topic in artificial intelligence (e.g. computer vision, natural language processing, data processing, generative modeling or other topics) by studying relevant academic literature and preparing a talk on this topic for their classmates.

Students can choose from a selection of topics provided by the teacher, or propose a topic that they are interested in on their own.

Besides learning about the subject matter of the talks, the goal of the course is to practice presentation skills.

The course starts on June 8th and will finish on August 17th.