GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
MONTE CARLO SIMULATION/6321303
Course Title: MONTE CARLO SIMULATION
Credits 3 ECTS 7.5
Semester 1 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Prof.Dr.Mustafa Y. Ata
 -- WEB SITE(S) OF LECTURER(S)
  http://websitem.gazi.edu.tr/site/myata; http://istatistikseliletisim.net
 -- EMAIL(S) OF LECTURER(S)
  myata@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
• Knowledge of a collection of simulation methods including Markov chain Monte Carlo (MCMC); understanding of Monte Carlo procedures, their advantages
• Ability to develop and implement (in BUGS) an MCMC algorithm for a given probability distribution.
• Ability to implement an MCMC algorithm in a programming language such as FORTRAN or C for a well-defined problem in a scientific application.
• Ability to use Monte Carlo methods for scientific applications.
• Ability to evaluate a stochastic simulation algorithm with respect to both its efficiency and the validity of the inference results produced by it.
 -- MODE OF DELIVERY
   The mode of delivery of this course is Face to face
 -- PREREQUISITES AND CO-REQUISITES
  • A good working knowledge of a scientific programming language. • A basic background in Probability and Statistics. • A basic knowledge of the statistical programming language R.
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  5331301 Simulation Techniques.
 --COURSE CONTENT
1. Week  Introduction: Virtual and actual world.
2. Week  Scientific Modelling: Systems, random variables as inputs and outputs of a system, parameters vs statistics.
3. Week  Monte Carlo Estimation: Direct estimation of parameters via the Law of Large Numbers.
4. Week  General Methods of Generating Virtual Observations: Inverse transformation technique, acceptance-rejection technique.
5. Week  Generating Pseudo Random Numbers
6. Week  Random Sampling from Some Special Probability Distributions
7. Week  Midterm Exam.
8. Week  Some Efficiency Methods in Designing Virtual Experiments: Antithetic variables, control variates, conditioning, importance sampling.
9. Week  Fundamentals of Bayesian Inference: Bayesian vs frequentist approach in statistical inference, prior and posterior distributions.
10. Week  Fundamentals of Markov Chain Theory: Convergence of Markov chains, detailed balance, limit theorems, ergodic Markov processes.
11. Week  Random Sampling from Any Multidimensional Distribution: Metropolis-Hastings algorithm and Gibbs sampler.
12. Week  Sequential Monte Carlo Methods: Sequential importance sampling, sequential imputation, the bootstrap techniques.
13. Week  Implementational issues: Burn In, Convergence diagnostics, Monte Carlo error.
14. Week  More Advanced Algorithms: Auxiliary variable methods, simulated and parallel tempering, simulated annealing; reversible jump MCMC, EM algorithm
15. Week  Applications of Monte Carlo.
16. Week  Final Exam.
 -- RECOMMENDED OR REQUIRED READING
  • W.R. Gilks, S.,Richardson, and D.J. Spiegelhalter (eds.) Markov chain Monte Carlo in practice, London : Chapman & Hall, 1996 • Christian P. Robert and George Casella Introducing Monte Carlo Methods with R, New York: Springer, 2010. • Sheldon M. Ross, Simulation, 5th ed., San Diego, CA:Academic Press, 2013.
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
  -
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
20
 Assignment
8
10
 Exercises
0
0
 Projects
1
10
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
40
 Contribution of Final Examination to Overall Grade  
60
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
14
3
42
 Practising Hours of Course Per Week
0
0
0
 Reading
14
4
56
 Searching in Internet and Library
14
1
14
 Designing and Applying Materials
8
3
24
 Preparing Reports
8
3
24
 Preparing Presentation
2
3
6
 Presentation
2
1
2
 Mid-Term and Studying for Mid-Term
1
10
10
 Final and Studying for Final
1
10
10
 Other
0
 TOTAL WORKLOAD: 
188
 TOTAL WORKLOAD / 25: 
7.52
 ECTS: 
7.5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1X
2X
3X
4X
5X
6X
7X
8X
9X
10X