Lecturer
Dr. Tim Brereton

Teaching assistant
Lisa Handl

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Time and Place

Lecture
Wednesday, 10 am - noon (220, Helmholtzstr. 18)
Friday, 10 am - noon (220, Helmholtzstr. 18)

Excercise session
Thursday, noon - 2 pm (220, Helmholtzstr. 18)

We agreed to start at 12:30 for being able to have lunch before. There might be exceptions around public holidays (check the news section).

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Type

4 hours lecture and 2 hours excercise

Credit points: 9

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Prerequisites

Basic knowledge of probability calculus and statistics as taught, for example, in "Elementare Wahrscheinlichkeitsrechnung und Statistik". In particular, the course Methods of Monte Carlo Simulation is not required.

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Intended Audience

Bachelor students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"; Master students in "Finance"

Students from other fields (in particular Physics, Computer Science or Chemistry) are welcome as well; the respective examination board (Prüfungsausschuss) decides on the possible recognition of examinations.

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Contents

This course is not a sequel to Methods of Monte Carlo Simulation , but rather a complimentary course. As such, MMCS1 is not a required prerequisite.

In this course, we focus on simulating probabilistic objects, including many important stochastic processes and structures. No prior knowledge of the probabilistic objects we study will be assumed. They will be introduced and some key properties will be examined. We also cover some basic results for measuring the accuracy of Monte Carlo estimates.

We will begin by considering random walks on graphs. We will then cover some basic theory about Markov chains that allows us to develop a number of simulation techniques. We will use these techniques to explore some spatial objects. We will look at some bounds on errors of various Monte Carlo estimators and also investigate some methods to improve efficiency when estimating various quantities related to stochastic processes and spatial objects. A number of real-world examples will be considered, mainly from physics and finance.

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Requirements and Exam

In order to participate in the final exam, it is necessary to earn 50% of the points on all theory and 50% of the points on all programming exercises. Students who want to do so are kindly asked to register for the 'Vorleistung' in the LSF-'Hochschulportal'.

Time and place

First exam:

Friday, July 31
from 10 am to noon in H14

Second exam:

Thursday, October 8
from 10 am to noon in room 1.20 (Helmholtzstr. 18)

The second exams are corrected!

You can find the number of points you obtained in the SLC in the section "Prüfungsleistung". The associated marks are indicated in the following table (it is the same for both exams):

MarkPoints

1,0	44 - 50
1,3	42 - 43,5
1,7	40 - 41,5
2,0	37,5 - 39,5
2,3	35,5 - 37
2,7	33,5 - 35
3,0	31,5 - 33
3,3	29 - 31
3,7	27 - 28,5
4,0	25 - 26,5
5,0	0 - 24,5

The post-exam review will take place on Thursday and Friday, August 6+7 from 2 to 3 pm (each day) in Dr. Brereton's office (room 1.43 in Helmholtzstr. 18).

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Problem Sheets

In order to receive points for your problem sheets, a registration at SLC is required.

Problem Sheet 01     Matlab Solution 01

Problem Sheet 02     Matlab Solution 02

Problem Sheet 03     Matlab Solution 03

Problem Sheet 04     Matlab Solution 04

Problem Sheet 05     Matlab Solution 05

Problem Sheet 06     Matlab Solution 06    Files: hiking.txt

Problem Sheet 07     Matlab Solution 07

Problem Sheet 08     Matlab Solution 08

Problem Sheet 09     Matlab Solution 09

Problem Sheet 10     Matlab Solution 10

Problem Sheet 11     Matlab Solution 11

Programming exercises have to be solved in Matlab. Student licenses can be bought for 20 € at O26/5101, or you can use it for free on many computers on campus, see this page for more information.

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Lecture Notes

Lecture notes will be provided in this section, roughly one week after the corresponding lectures.

Lecture notes

Swendsen-Wang code

SW

state_i

state_j

ij_state

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Literature

Asmussen, S. and P. Glynn. Stochastic Simulation. Springer, 2007.

Brémaud, P. Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, 1999.

Dubhashi, D. P. and A. Panconesi. Concentration of Measure for the Analysis of Randomized Algorithms. Cambridge University Press, 2009.

Glasserman, P. Monte Carlo Methods in Financial Engineering. Springer, 2004.

Graham, C. and D. Talay. Stochastic Simulation and Monte Carlo Methods: Mathematical Foundations of Stochastic Simulation. Springer, 2013.

Kroese, D. P., T. Taimre and Z. Botev. Handbook of Monte Carlo Methods. Wiley, 2011.

Levin, D. A., Y. Peres and E. L. Wilmer. Markov Chains and Mixing Times. American Mathematical Society, 2009.

Møller, J. and Waagepetersen, R. P. Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, 2003.

Ross, S. M. Simulation, Fifth Edition. Academic Press, 2012.

Winkler, G. Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction. Springer, 2003.