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@@ -6,110 +6,72 @@ Wolfhart Feldmeier - Jena University Hospital - [email protected] | |
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| ## Dates and course organization | ||
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| * Six weeks, two 2-hour lectures plus one 2-hour exercises session per week | ||
| * 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 | ||
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| | Lecture | Date | Weekday | Time | Topic | | ||
| |:---------:|:------------:|:-------:|---------------|:----------------------------------| | ||
| | 1 | Dec 16, 2022 | Fri | 10:15 - 11:45 | Introduction | | ||
| | 2 | Jan 02, 2023 | Mon | 10:15 - 11:45 | Direct Sampling Methods | | ||
| | Ex 1 | Jan 04, 2023 | Wed | 10:15 - 11:45 | Exercises for lectures 1-2 | | ||
| | 3 | Jan 06, 2023 | Fri | 10:15 - 11:45 | Rejection & Importance Sampling | | ||
| | 4 | Jan 09, 2023 | Mon | 10:15 - 11:45 | Markov chains, MCMC | | ||
| | Ex 2 | Jan 11, 2023 | Wed | 10:15 - 11:45 | Exercises for lectures 3-4 | | ||
| | 5 | Jan 13, 2023 | Fri | 10:15 - 11:45 | The Metropolis-Hastings algorithm | | ||
| | 6 | Jan 16, 2023 | Mon | 10:15 - 11:45 | Gibbs sampling | | ||
| | Ex 3 | Jan 18, 2023 | Wed | 10:15 - 11:45 | Exercises for lectures 5-6 | | ||
| | 7 | Jan 20, 2023 | Fri | 10:15 - 11:45 | Hamiltonian Monte Carlo | | ||
| | 8 | Jan 23, 2023 | Mon | 10:15 - 11:45 | Practical aspects of HMC | | ||
| | Ex 4 | Jan 25, 2023 | Wed | 10:15 - 11:45 | Exercises for lectures 7-8 | | ||
| | 9 | Jan 27, 2023 | Fri | 10:15 - 11:45 | Slice sampling | | ||
| | 10 | Jan 30, 2023 | Mon | 10:15 - 11:45 | Practical aspects, Diagnostics | | ||
| | Ex 5 | Feb 01, 2023 | Wed | 10:15 - 11:45 | Exercises for lectures 9-10 | | ||
| | 11 | Feb 03, 2023 | Fri | 10:15 - 11:45 | TBA | | ||
| | 12 | Feb 06, 2023 | Mon | 10:15 - 11:45 | TBA | | ||
| | Ex 6 | Feb 08, 2023 | Wed | 10:15 - 11:45 | Exercises for lectures 11-12 | | ||
| | 13 | Feb 10, 2023 | Fri | 10:15 - 11:45 | TBA | | ||
| | 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 | | ||
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| ## Topics | ||
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| ### Lecture 1: Introduction | ||
| ### Lecture 1: Introduction & Direct Sampling Methods | ||
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| * Motivation | ||
| * Monte Carlo approximation | ||
| * An inefficient way of computing $\pi$ | ||
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| ### Lecture 2: Direct Sampling Methods | ||
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| * Can we beat the curse of dimensionality? | ||
| * Random number generation | ||
| * Direct sampling by variable transformation methods | ||
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| ### Lecture 3: Rejection and Importance Sampling | ||
| ### Lecture 2: Rejection and Importance Sampling | ||
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| * More direct sampling methods | ||
| * Rejection sampling | ||
| * Importance sampling | ||
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| ### Lecture 4: Markov chains | ||
| ### Lecture 3: Markov chains | ||
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| * Markov chains | ||
| * Some mathematical facts about Markov chains | ||
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| ### Lecture 5: The Metropolis-Hastings Algorithm | ||
| ### Lecture 4: The Metropolis-Hastings Algorithm | ||
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| * Fundamental theorem of Markov chains | ||
| * Metropolis-Hastings algorithm | ||
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| ### Lecture 6: Gibbs sampling | ||
| ### Lecture 5: Gibbs sampling | ||
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| * Recap: Metropolis-Hastings algorithm | ||
| * Combining Markov chains | ||
| * Gibbs sampling | ||
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| ### Lecture 6: Hamiltonian Monte Carlo | ||
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| * Auxiliary variable methods | ||
| * Hamiltonian Monte Carlo I | ||
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| ### Lecture 7: Hamiltonian Monte Carlo | ||
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| * Recap: MCMC + Gibbs Sampling | ||
| * More on auxiliary variable methods | ||
| * Hamiltonian Monte Carlo | ||
| * Hamiltonian Monte Carlo II | ||
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| ### Lecture 8: Hamiltonian Monte Carlo, Practical Issues | ||
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| * Hamiltonian Monte Carlo continued | ||
| * Practical Issues (convergence, diagnostic checks) | ||
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| ### Lecture 9: Slice sampling | ||
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| * General slice sampling | ||
| * Neal's bracketing method | ||
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| #### Lecture 10: Practical Aspects of MCMC | ||
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| * Convergence, diagnostic checks | ||
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| ### Lectures 11-13: TBA | ||
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| #### Possible topics | ||
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| * Annealed Importance Sampling | ||
| * Nested Sampling | ||
| * Parallel Tempering / Replica-exchange Monte Carlo | ||
| * Sequential Monte Carlo (SMC) | ||
| * Graphical models | ||
| * Ising model | ||
| * Simulator models | ||
| * Stochastic differential equation & Langevin dynamics | ||
| * Bridge sampling, thermodynamic integration | ||
| * Partition function estimation | ||
| * Intractable models | ||
| * Exchange algorithm | ||
| * Adaptive Monte Carlo methods | ||
| * Wang-Landau | ||
| * Exact sampling: coupling from the past | ||
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| # Literature | ||
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