Courses relevant for statisticians in spe

and a few words on topics and supervisors for Master theses

Autumn 2020 semester

For the year 3 student

• TMA4265 Stokastiske prosesser Important models for multivariate random variables: Markov chains, Poisson processes, birth-and-death processes in continuous time, Brownian motion and Gaussian processes. Approaches for stochastic simulation of random variables.

For the year 4/5 students

• TMA4285 Time series models Autoregressive and moving average based models for stationary and non-stationary time series. Parameter estimation. Model identification. Forecasting. ARCH and GARCH models for volatility. State space models (linear dynamic models) and the Kalman filter. [Gunnar Taraldsen]

• TMA4295 Statistical inference. Transformations and moments of random variables. Families of distributions. Inequalities and convergence theorems. Sufficient statistics. Frequentist and Bayesian estimators. Methods of constructing point estimators, interval estimators and hypothesis tests, and optimality of these. Asymptotic properties of estimators and hypothesis tests. [John Tyssedal]

• TMA4315 Generalized linear models. Univariate exponential family. Multiple linear regression. Logistic regression. Poisson regression. General formulation for generalised linear models with canonical link. Likelihood-based inference with score function and expected Fisher information. Deviance. AIC. Wald and likelihood-ratio test. Linear mixed effects models with random components of general structure. Random intercept and random slope. Generalised linear mixed effects models. Strong emphasis on programming in R. Possible extensions: quasi-likelihood, over-dispersion, models for multinomial data, analysis of contingency tables, quantile regression. [Jarle Tufto]

• MA8704 Probability Theory and Asymptotic Techniques PhD course, given every autumn. The course gives a broad introduction to classical probability theory and asymptotic techniques towards applications in statistics. Together with course MA8701 General statistical methods it provides a theoretical basis for PhD students in statistics. The contents include basic probability theory, convergence of sequences of random variables, characteristic functions, classical limit theorems, asymptotic properties of statistical methods. Requires TMA4295. [Bo Lindqvist]

Spring 2021 semester

For the 3rd year student

• TMA4267 Linear statistical models Multiple linear regression. Analysis of variance. Experimental design. Multivariate normal distribution. Multiple testing.

For the 4th year student

statistics courses

• TMA4250 Spatial statistics. Parameter estimation, simulation and applications of Gaussian random fields, point fields and discrete Markov random fields. Examples from image analysis, and environmental and natural resource applications. [Henning Omre]

• TMA4268 Statistical learning Statistical learning refers to a vast set of tools for understanding data. Central is the bias-variance trade-off. The course covers methods for regression (simple and multiple, regularized lasso and ridge, principal components, nonlinear) and classification (linear and quadratic discriminant analysis, k-nearest neighbour, logistic regression, ROC, AUC), and tree-based methods (classification and regression trees, bagging, random forest), support-vector-machines, unsupervised methods (clustering, dimensionality reduction) and neural networks. Compulsory exercises use R. Focus is both on theory and on implementation in R, and understanding of statistical analyses. [NN]

• TMA4275 Lifetime analysis. Basic concepts in lifetime modelling. Censored observations. Nonparametric estimation and graphical plotting for lifetime data (Kaplan-Meier, Nelson-plot). Estimation and testing in parametric lifetime distributions. Analysis of lifetimes with covariates (Cox-regression, accelerated lifetime testing). Modelling and analysis of recurrent events. Nonhomogeneous Poisson-processes. Nelson-Aalen estimators. [Bo Lindqvist]

• TMA4300 Computational statistics. Classical and Markov chain methods for stochastic simulation. Hierarchical Bayesian models and inference in these. The expectation maximisation (EM) algorithm. Bootstrapping. [Sara Martino]

mathematics courses

• TMA4180 Optimization 1. First and second order necessary and sufficient (Karush-Kuhn-Tucker) optimality conditions for unconstrained and constrained optimization problems in finite-dimensional vector spaces. Basics of convex analysis and Lagrangian duality theory and their application to optimization problems and algorithms. An overview of modern optimization techniques and algorithms for smooth problems (including line-search/trust-region, quasi-Newton, interior point and active set methods, SQP and augmented Lagrangian approaches). Basic derivative-free and non-smooth optimization methods.

course at the medicine/health faculty

• KLMED8005 Analysis of repeated measurements
• SMED8002 Epidemiology 2
• NEVR3004 Neural networks (in the brain)

computer science courses

• TDT4100 Objektorientert programmering.
• TDT4145 Datamodellering og databasesystemer. Requires TDT4100.
• TDT4300 Data warehouse and data mining. Requires TDT4145
• TDT4173 Machine learning and case-based reasoning (Big overlap with TMA4268 in topics, but maybe not in philosophy.)
• IT3030 Deep learning (new): The course is a follow-up to TDT4173 Machine Learning. It gives thorough coverage of deep learning. The course covers both mathematical and computational foundation for deep learning, practical applications such as processing of images, text, and other modalities. In addition, deep reinforcement learning will be discussed. Modern software frameworks for deep learning will be introduced.

For the 5th year student

• MA8702 Advanced Computer Intensive Statistical Methods Phd course with selected topics relevant for computational statistics. The course will give a theoretical and methodological introduction and discussion of computational intensive statistical methods, but assumes also good computational skills. Topics to be discussed are a selection of the following; theory and methods for Markov chain Monte Carlo, Hidden Markov chains, Gaussian Markov random fields, mixtures, non-parametric methods and regression, splines, bootstrapping, classification and graphical models, latent Gaussian models and their approximate Bayesian inference. Relative weighting of the various topics will vary according to need.

Master thesis

Deadline for choosing topic and supervisor is around January 15, 2020. You need to rank 3 different supervisors (with problems). NB: not one supervisor and three problems.

Groups of problems and or fields

In statistics the following subgroups are defined:

• Biostatistics (applications from medicine, genomikk, biology, ecology, population genetics)
• Computational statistics (space-time models, Monte Carlo methods, INLA, point processes)
• Industrial statistics (design of experiments, life time models, process control)
• Spatial statistics (space-time models)
• Statistical inference (GLM, LMM, GLMM, multiple testing, testing, distributions, nonparametrics)
• Statistical learning (ensamble methods, unsupervised learning, neural networks, boosting)
• Statistics and finance (models for risk, allocation of capital, interest, derivates)

Supervisors

• Erlend Aune (Statistical learning: active learning, neural networks, dataanalysis). Based in Oslo, 20% position, will come to Trondheim ca 1 each month, additional supervision on Skype.
• Øyvind Bakke (Statistical inference, population dynamics, statistical problems with a strong mathematical component)
• Benjamin Dunn (Neuroscience, Industrial statistics). New 01.01.2019!
• Jo Eidsvik (Computational, AI, statistical learning, value of information)
• Geir-Arne Fuglstad (Computational, INLA, biostatistics). New 01.01.2019!
• Mette Langaas(Biostatistics, statistical learning and inference)
• Bo Lindqvist (Statistical inference, statistical learning, survival, reliability, industrial)
• Jacob Laading (Statistical finance) Based in Bergen, 20% postion, gives “emnemoduler” in finance in the autumn, comes to Trondheim ca 1 every month.
• Sara Martino (Computational, INLA, energy)
• Thiago G. Martins (Statistical learning, recurrent networks, time series, reinforcement learning). 20% position, based in Trondheim.
• Stefanie Muff Stefanie will join us as an Associate Professor in the autumn of 2019. Her interests include measurement error models, and statistical models in ecology.
• Bob O’Hara (Computational, ecology)
• Henning Omre (Spatial, geostatistics, seismic inversion)
• Andrea Riebler(Computational, biostatistics)
• Ingelin Steinsland (Population genetics, computational, climate). Pro-dean of research at IE.
• Gunnar Taraldsen (Mathematical analysis, theoretical statistics, statistical learning and neural networks)
• Håkon Tjelmeland (Computational, MCMC, Bayesian inferencs, genomics)
• Jarle Tufto (Computational, quantitative genetics, probabilistic quizzes, selection in populations)
• John Tyssedal (Industrial statistics, design of experiments)
• Nikolai Ushakov (Statistical inference, theoretical statistics)

For a full overview see: https://wiki.math.ntnu.no/student/indmat/oppgavekatalog