Mathematical Statistics, University of Gotheburg: MSN040 Stochastic Data Processing and Simulation, 5 credits (Statistisk databehandling, 5 poäng)

Mathematical Statistics, Chalmers University of Technology: TMS150 Stochastic Data Processing and Simulation, 5 credits (Statistisk databehandling, 5 poäng)

The course is given in english with english lecture notes that are distributed freely.

Lectures will be Tuesdays 08.00-10.00 am in Euler and laborations Mondays and Fridays 8.15-12 am in MV:F 25, weeks 36-42, beginning Tuesday 4 September 2007. There is no written exam on the course.

1) There are analytical courses, that teach analytical methods, and numerical courses, that teach numerical methods. But there are very few courses that teach how to move between the analytical and numerical, in a way that is required when solving real world problems: The main goal with the course is to teach this. In particular, this includes active problem solving skills with computer.

2) The course consists of 6 small projects, each of which improves active problem solving skills with computer. At the same time, each project treats an important topic in problem solving with computer. These topics are:

a) Robustness (What happens if there are minor deviations between a real world phenomena and the mathematical model used for the phenomena, as there almost always are? What methods are robust, so that minor such deviations only give minor errors in results?)

b) Decision Theory (What should be optimized, and how should that be done?)

c) Bootstrap and Jackknife (When making deductions about an a priori unknown quantity, from a dataset, the deductions are often valuable only when they come with error estimates. Basically, error estimates require that new datasets are obtained, so that repeated deductions can be made, to show how deduction vary, thereby giving a picture of errors. However, frequently new datasets cannot be obtained, so that classical error estimates are impossible. Bootstrap and Jackknife are resampling schemes, in which new pseudo datasets are obtained by resampling from the original dataset, thus allowing error estimates after all.)

d) Monte-Carlo Simulations to compute Non-Random Quanities (One can often make accurate computations of non-random quantities by the use of randomization. When are random methods better that non-random ones?)

e) Stochastic Processes (The modelling of many real world phenomena involves noise. The noise can represent a real disturbance of a signal, but equally well model that there is a degree of uncertainty in the model, as e.g., when predicting the future. Some basic topics in computational stochastic processes are considered.)

f) Analytical Manipulations with Computer (Mathematical programme packages can often solve analytical problems better and safer than humans.)

3) The course teaches basic programming skills in the following four important programming languages: C/C++, Mathematica, Matlab, R/Splus. Also, the typesetting system LaTeX is a part of this course.

Some things to keep in mind when wrighting reports:

i) Make your figures color independent.

ii) Put the code in an appendix

iii) All sections and subsections shall have a title

iv) Do not have figures that you do not refer to in the text.

v) All figures shall have a caption and it shall be enough to read the caption to understand what is happening in the figure in question.

vi) If you perform statistical tests; give a p-value, do not just say, "Matlab gave a 1 so ..."

Registration for the course can be done at Mathematical Sciences student offices ("expedition") for Chalmers and University of Gotheburg students. Registration can also be done by contacting Erik Brodin and Viktor Olsbo or, possibly, Patrik Albin.

It will not be a problem to be admitted to the course: We do admit all students that want to partcipate in the course.

Viktor Olsbo is responsible for the course, together with Patrik Albin. Welcome to contact Viktor or Patrik for more information.

**Email:**vikol@math.chalmers.se , palbin@math.chalmers.se**Telephone:**Viktor 031/7723544 , Patrik 031/7723512**Fax:**031/7723508**Room:**Viktor 3073, Patrik 3072**Adress:**Matematisk Statistik, CTH & GU, 412 96 Göteborg, Sweden

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