Michael Habeck - Jena University Hospital - michael.habeck@uni-jena.de
Wolfhart Feldmeier - Jena University Hospital - wolfhart.feldmeier@uni-jena.de
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Four weeks, two 2-hour lectures plus one 2-hour exercise session per week
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Lectures on Monday and Friday, exercises on Wednesday
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Timetable
| Lecture | Date | Weekday | Time | Topic |
|---|---|---|---|---|
| 1 | Jan 15, 2024 | Mon | 10:15 - 11:45 | Introduction / Direct Sampling Methods |
| Ex 1 | Jan 17, 2024 | Wed | 10:15 - 11:45 | Exercises for lecture 1 |
| 2 | Jan 19, 2024 | Fri | 10:15 - 11:45 | Rejection & Importance Sampling |
| 3 | Jan 22, 2024 | Mon | 10:15 - 11:45 | Markov chains, MCMC |
| Ex 2 | Jan 24, 2024 | Wed | 10:15 - 11:45 | Exercises for lectures 2-3 |
| 4 | Jan 26, 2024 | Fri | 10:15 - 11:45 | The Metropolis-Hastings algorithm |
| 5 | Jan 19, 2024 | Mon | 10:15 - 11:45 | Gibbs sampling |
| Ex 3 | Jan 31, 2024 | Wed | 10:15 - 11:45 | Exercises for lectures 4-5 |
| 6 | Feb 02, 2024 | Fri | 10:15 - 11:45 | Hamiltonian Monte Carlo |
| 7 | Feb 05, 2024 | Mon | 10:15 - 11:45 | Hamiltonian Monte Calro II |
| Ex 4 | Feb 07, 2024 | Wed | 10:15 - 11:45 | Exercises for lectures 6-7 |
| 8 | Feb 09, 2024 | Fri | 10:15 - 11:45 | Practical aspects of HMC |
- Motivation
- Monte Carlo approximation
- An inefficient way of computing
$\pi$ - Can we beat the curse of dimensionality?
- Random number generation
- Direct sampling by variable transformation methods
- More direct sampling methods
- Rejection sampling
- Importance sampling
- Markov chains
- Some mathematical facts about Markov chains
- Fundamental theorem of Markov chains
- Metropolis-Hastings algorithm
- Combining Markov chains
- Gibbs sampling
- Auxiliary variable methods
- Hamiltonian Monte Carlo I
- Hamiltonian Monte Carlo II
- Practical Issues (convergence, diagnostic checks)
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Matti Vihola: Lectures on Stochastic Simulation
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Radford Neal: Probabilistic Inference Using Markov Chain Monte Carlo Methods
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Chris Bishop: Pattern Recognition and Machine Learning, Chap. 11
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David MacKay: Information Theory, Inference, and Learning Algorithms, Chap. 29 + 30
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Iain Murray: Advances in Markov chain Monte Carlo methods
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Andrieu, de Freitas, Doucet, Jordan: An Introduction to MCMC for Machine Learning
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Charles Geyer: Introduction to Markov Chain Monte Carlo
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Jun S. Liu: Monte Carlo Strategies in Scientific Computing
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David A Levin, Yuval Peres: Markov chains and mixing times