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Master's programme in mathematical statistics

For more detailed course information regarding our Master's programme 2009-2011 see Master's programme 2009-2011 study order
For more detailed course information regarding our Master's programme 2010-2012 see Master's programme 2010-2012 study order

Courses Academic Year 2009/10

Matstat introductory and intermediate level

Course	Code		CRED	Autumn	Spring
Mathematical statistics, basic course	MASA01		15
Mathematical statistics	MASB02		7.5
Mathematical statistics	MASB03		9
Biostatistics, basic course  (given 3 times)	MASB11		7.5
Probability theory	MASC01		7.5
Inference theory	MASC02		7.5
Markov processes	MASC03		6
Stationary stochastic processes	MASC04		7.5
Design of Experiments	MASC05		7.5

Matstat advanced

Course	Code		CRED	Autumn	Spring
Biostatistics	BINP12		7.5
Monte Carlo methods for stochastic inference	MASM11		7.5
Non-linear Time Series Analysis	MASM12		7.5
Statistical image analysis	MASM13		7.5
The Mathematical Basis for Probability Theory	MASM14		7.5
Statistical Modelling of Extreme Values	MASM15		7.5
Time series analysis	MASM17		7.5
Valuation of Derivative Assets	MASM19		9
Survival analysis	MASM21		7.5

Matstat master's and bachelor's thesis

Course	Code		CRED	Autumn	Spring
Degree Project for a Bachelor of Science in Mathematical Statistics	MASK01		15
Degree Project for Master of Science in Mathematical Statistics	MASM01		30
Degree Project for a Bachelor of Science in Mathematical Statistics	MASX01		15
Master's degree project	MASY01		30

Course descriptions

Introductory and intermediate level courses

MASA01: Mathematical statistics, basic course, 15 ECTS CREDITS

Period: Autumn term, halftime whole term

Pre-requisites: 45 ECTS credits in mathematics

Literature: S.E. Alm och T. Britton: Stokastik, 2008.

Teaching language: Swedish

Course-description:

MASB02: Mathematical statistics, 7.5 ECTS CREDITS

Period: Autumn term, halttime 1st half

Pre-requisites:

Literature: Olbjer, L.: Experimentell och industriell statistik, Lund 2000. (KFS). Matematisk statistik för kemitekniker: Övningsuppgifter med lösningar, VT2001, Lund 2001 (KFS). Datorlaborationer, projekthandledning, formelsamling, etc.

Teaching language: Swedish

Course-description: Basic knowledge of probability and statistics. Data analysis. Point and interval estimation. Test of hypothesis. Experimental design. Regression and variance analysis. Applications: Data analysis. Measurement errors and propagation. Comparisons between expectations and variances, quality control, optimization of design parameters, response surface methodology. Special attention to applications in chemical engineering.

MASB03: Mathematical statistics, 9 ECTS CREDITS

Period: Autumn term, halftime 2nd half

Pre-requisites: At least 12 ECTS credits i mathematics.

Literature: Blom, G., Enger, J., Englund, G. Grandell, J. och Holst, L.: Sannolikhetslära och statistikteori med tillämpningar. Studentlitteratur, Lund 2004

Teaching language: Swedish

Course-description:

MASB11: Biostatistics, basic course, 7.5 ECTS CREDITS

Period: Spring term,

Pre-requisites:

Literature: Olsson Ulf, Englund Jan-Eric och Engstrand Ulla: Biometri - Grundläggande biologisk statistik, Studentlitteratur 2005, ISBN:9789144045778

Teaching language: Swedish

Course-description:

MASC01: Probability theory, 7.5 ECTS CREDITS

Period: Spring term, halftime 1st half

Pre-requisites: 45 ECTS credits in mathematics and a basic course in mathematical statistics.

Literature: A. Gut, An Intermediate Course in Probability Theory, Springer 1995.

Teaching language: Swedish

Course-description: Basic probability theory, random variables in one and several dimensions, multivariate Gaussian distribution, convergence of random variables and distributions, conditional distributions. Moment generating functions and characteristic functions.

MASC02: Inference theory, 7.5 ECTS CREDITS

Period: Spring term, halftime 2nd half

Pre-requisites: 45 ECTS credits in mathematics and a basic course in mathematical statistics.

Literature: E.L. Lehman, G. Casella, Theory of Point Estimation, Springer 1998. E.L. Lehman, J.P. Romano, Testing Statistical Hypothesis, Springer 2005.

Teaching language: English at request

Course-description: Factorization Theorem, exponential families, Rao-Blackwell's theorem, ancillary estimators, Cramér Rao's inequality, Neyman-Pearson's Lemma, permuation tests, interrelations between hypothesis testing and confidence intervals, asymptotic methods, maximum likelihood estimators, standard errors, marginal, conditional and penalized likelihood, likelihood ratio, Wald scores method, Baysian inference, sequential tests, inference for finite populations

MASC03: Markov processes, 6 ECTS CREDITS

Period: Spring term, halftime 2nd half

Pre-requisites: 45 ECTS credits in mathematics and a basic course in mathematical statistics

Literature: Rydén, T. & Lindgren, G.: Markovprocesser, Lund 2002.

Teaching language: Swedish

Course-description: Markov chains Markov processes. Classification of states and Markov chains. Stationary distributions and asymptotic distributions. Asorbing states and time to absorption. Intensities, the Poisson process and spatial Poisson processes, Hidden Markov models

MASC04: Stationary stochastic processes, 7.5 ECTS CREDITS

Period: Autumn term, halttime 1st half

Pre-requisites: A basic course in mathematical statistics and knowledge in complex and linear analysis.

Literature: Lindgren, G & Rootzén, H: Compendium in Stationary Stochastic Processes. Lund 2009.

Teaching language: English

Course-description: Models for stochastic dependence. Concepts of description of stationary stochastic processes in the time domain: expectation, covariance, and cross-covariance functions. Concepts of description of stationary stochastic processes in the frequency domain: effect spectrum, cross spectrum. Special processes: Gaussian process, Wiener process, white noise, Gaussian fields in time and space. Stochastic processes in linear filters: relationships between in- and out-signals, auto regression and moving average (AR, MA, ARMA), derivation and integration of stochastic processes. The basics in statistical signal processing: estimation of expectations, covariance function, and spectrum. Application of linear filters: frequency analysis and optimal filters.

MASC05: Design of Experiments, 7.5 ECTS CREDITS

Period: Spring term, halftime 2nd half

Pre-requisites: 45 ECTS credits in mathematics and a basic course in mathematical statistics

Literature: Montgomery D C: Design and Analysis of Experiments. Wiley, New York, 5th ed, 2000.

Teaching language: English at request

Course-description: The course gives theory and methodology of how to model, design and evaluate experiments. Important concepts are: Simple comparative experiments. Analysis of variance; transformations, model validation and residual analysis. Factorial design with fixed, random and mixed effects. Additivity and interaction. Complete and incomplete designs. Randomized block designs. Latin squares and confounding. Regression analysis and analysis of covariance. Response surface methodology. Off-line quality control and Taguchi methods.

The course may be cancelled if less than 16 students register.

Advanced courses

BINP12: Biostatistics, 7.5 ECTS CREDITS

Period: Spring term,

Pre-requisites: Requirements for access to the course are: qualifications for the master programme in Bioinformatics or knowledge corresponding to 120 ECTS credits on the basic level in Biomedicine or Molecular biology, including 15 ECTS credits in Cell biology, or corresponding knowledge. Previous knowledge corresponding to BINP11 Sequence analysis is recommended.

Literature: Douglas G. Altman: Practical Statistics for Medical Research; Chapman & Hall, 1991. ISBN: 0-412-27630-5

Teaching language: English

Course-description: Basic probability theory, stochastic variables and distributions, Normal distribution, Binomial distribution, descriptive statistics, point estimates, interval estimates, the Maximum-likelihood method, the Least Squares method, and linear regression, t-test, χ2-test, and Wilcoxon test.

MASM11: Monte Carlo methods for stochastic inference, 7.5 ECTS CREDITS

Period: Autumn term, halttime 1st half

Pre-requisites: MASC03 and MASC04 or equivalent. English language proficiency demonstrated in one of the following ways: Previously completed University degree taught in English, IELTS score (Academic) of 6.0 or more (with none of the sections scoring less than 5.0), TOEFL score of 550 or more (computer based test 213, internet based 79), Cambridge/Oxford - Advanced or Proficiency level, O level/GCSE, or having received a passing grade in English course B (Swedish secondary school).

Literature: Computer Intensive Methods, Lund 2004

Teaching language: English at request

Course-description: Simulation based methods of statistical analysis. Markov chain methods for complex problems, e.g. Gibbs sampling and the Metropolis-Hastings algorithm. Bayesian modelling and inference. The re-sampling principle, both non-parametric and parametric. The Jack-knife method of variance estimation. Methods for constructing confidence intervals using re-sampling. Re-sampling in regression. Permutations test as an alternative to both asymptotic parametric tests and to full re-sampling. Examples of mor complicated situations. Effective numerical calculations in re-sampling. The EM-algorithm for estimation in partially observed models.

MASM12: Non-linear Time Series Analysis, 7.5 ECTS CREDITS

Period: Autumn term, quartertime whole term

Pre-requisites: Stationary stochastic processes, times series analysis.

Literature: Henrik Madsen and Jan Holst: Lecture Notes in Non-linear and Non-stationary Time Series Analysis, IMM, DTU, 2001.

Teaching language: English at request

Course-description: The graduate course in Advanced Time Series Analysis has its target audience amongst students with technical or natural science background and with adequate basic knowledge in mathematical statistics. The primary goal to give a thorough knowledge on modeling dynamic systems. A special attention is paid to non-linear and non-stationary systems, and the use of stochastic differential equations for modeling physical systems.

The course is given in cooperation with DTU (Danish technical university, Lyngby)

MASM13: Statistical image analysis, 7.5 ECTS CREDITS

Period: Autumn term, halftime 2nd half

Pre-requisites: One of the courses Markov processes (FMS180/MAS204), Stationary Stochastic Processes (FMS045/MAS210), Image analysis (FMA170) or equivalent.

Literature: Lindgren F: Image modelling and estimation -- A statistical approach, Lund 2002.

Teaching language: English at request

Course-description: The course deals with Bayesian methods for modelling, classification and reconstruction. Markov random fields. Gibbs distributions, deformable templates such as snakes and ballons. Correlation structures, multivariate techniques, discriminant analysis. Simualtion methods (MCMC). Three levels of image analysis: high level classification of objects, general shape reconstruction, and pixel analysis such as noise reduction and segmentation through pixel classification.

MASM14: The Mathematical Basis for Probability Theory, 7.5 ECTS CREDITS

Period: Autumn term, halftime 2nd half

Pre-requisites: 45 ECTS credits in mathematics. Knowledge of probability theory at the level of MASC01 is desirable.

Literature: Shiryaev, A. N.: Probability, Springer 1996.

Teaching language: English at request

Course-description: The course extends and deepens basic knowledge in Probability Theory. Central topics are existence and uniqueness of measures defined on sigma fields, integration theory, Radon-Nikodyn derivatives and conditional expectation, weak convergence of probability measures on metric spaces.

MASM15: Statistical Modelling of Extreme Values, 7.5 ECTS CREDITS

Period: Autumn term, halftime 2nd half

Pre-requisites: A basic course in mathematical statistics.

Literature: Coles, S.: An Introduction to Statistical Modelling of Extreme Values. Springer-Verlag, London, 2001. Föreläsningsanteckningar och artiklar.

Teaching language: English at request

Course-description: Extreme value theory concerns mathematical modelling of extreme events. Recent developments have introduced very flexible and theoretically well-motivated semi-parametric models for extreme values which are now at the stage where they can be used to address important technological problems on handling risks in areas such as large insurance claims or large fluctuations in financial data (volatility), climatic changes, wind engineering, hydrology, flood monitoring and prediction and structural reliability. In many applications of extreme value theory, predictive inference for unobserved events in the main interest. One wishes to make inference about events over a time period much longer than for which data is available. Statistical modelling of extreme events has been the subject of much practical and theoretical work in the last few years. The course will give an overview of a number of different topics in modern extreme value theory including the following: (i) statistical methods for extreme event, (ii) some examples of applications of the theory in large insurance claims due to wind storms, flood monitoring and pit corrosion, (ii) exercises on detailed step-by-step use of extreme value modelling, and (iv) discussion of some open problems in the field.

MASM17: Time series analysis, 7.5 ECTS CREDITS

Period: Spring term, halftime 2nd half

Pre-requisites: A course in stationary stochastic processes.

Literature: Henrik Madsen, Time Series Analysis, Chapman & Hall, 2007

Teaching language: English at request

Course-description: Stationary and nonstationary processes, ARIMA processes, seasonal variation, prediction, filtering and reconstruction in transfer function models and state space models, parameter and structure estimation by least squares, maximum likelihood and predictive error methods, spectral analysis, recursive estimation, adaptive techniques, robustness and outlier detection, multivariate time series, spectral density estimation

MASM19: Valuation of Derivative Assets, 9 ECTS CREDITS

Period: Spring term, quartertime whole term

Pre-requisites: A course in stochastic processes

Literature: Björk, T: Arbitrage Theory in Continuous Time. Oxford University Press, Oxford.

Teaching language: English at request

Course-description: The course consists of three related parts. In the first part we will look at option theory in discrete time. The purpose is to quickly introduce fundamental concepts of financial markets such as free of arbitrage and completeness as well as martingales and martingale measures. We will use tree structures to model time dynamics of stock prices and information flows. In the second part we will study alternative models formulated in continuous time. The models we focus on are formulated as stochastic differential equations (SDE:s). Most of the second part is devoted to the probability theory required to understand the SDE models. This include e.g. Brownian motion, stochastic integrals and Ito's formula. Finally in the third part we study various applications of the theory from part two. Here we come back to option theory and derive e.g. the Black-Scholes formula. After that we will study the bond market and interest rate derivatives.

MASM21: Survival analysis, 7.5 ECTS CREDITS

Period: Autumn term, halftime 2nd half

Pre-requisites: MASA01 Mathematical statistics, 15 ECTS and MASC02 Inference theory, 7,5 ECTS or equivalent and 60 ECTS mathematics.

Literature: Aalen, O.O., Borgan, Ø. and Gjessing, H.K. Survival and Event History Analysis: A Process Point of View. Springer-Verlag, 2008. Klein and Moechberger (2003), "Survival Analysis-Techniques for Censored and Truncated Data", Springer Verlag.(Complementary reading) Both books available electronically: http://elin.lub.lu.se.ludwig.lub.lu.se/elin?func=goToEbook&ebookId=95721 http://elin.lub.lu.se.ludwig.lub.lu.se/elin?func=goToEbook&ebookId=85673

Teaching language: English at request

Course-description: Survival data; censured and truncated data. Covariates. Distributions and models for survival data. Counting processes and martingale theory. Estimation of survival function and cumulative hazard function (Kaplan-Meier and Nelson- Aalen estimators). Non-parametric one- and multi-sample test. Kernel estimation of hazard function. Semi parametric regression models for data with covariates. Cox model. Aalens model. Likelihood theory for estimation in the Cox model. Projection methods in counting processes for estimation in the Aalens model. Competing risk methods for analysis of several different final states. Bootstrap methods for survival data. Statistic functionals for limiting distributions in survival analysis.

Master's and Bachelor's thesis

MASK01: Degree Project for a Bachelor of Science in Mathematical Statistics, 15 HP

Pre-requisites: At least 60 credits i mathematics consisting of the courses MATA11 Matematik 1 alfa, 15 hp, MATA12 Matematik 1 beta, 15 hp, MATB15 Flervariabelanalys, 15 hp, MATB11 Linjär algebra, 7,5 hp, as well as at least one of the courses MATB12 Fourieranalys, 7,5 hp, MATB13 Diskret matematik, 7,5 hp, MATB14 Vektoranalys, 7,5

Course-description:

MASM01: Degree Project for Master of Science in Mathematical Statistics, 30 HP

Pre-requisites: At least 45 credits on advanced level in Mathematical Statistics. Among these credits at least three of the courses of the four courses MASM11 Monte Carlo methods for stochastic inference, MASM14 The Mathematical Basis for Probability Theory, MASM15 Statistical Modelling of Extreme Values, MASM17 Time-series-analysis should be included.

MASX01: Degree Project for a Bachelor of Science in Mathematical Statistics, 15 HP

Pre-requisites: At least 45 credits in Mathematical Statistics

Course-description:

MASY01: Master's degree project, 30 HP

Pre-requisites: At least 60 credits in Mathematical Statistics