TMA 4300 Computer Intensive Statistical Methods
Lecture Plan
Note: The slides provided here might change after they have been uploaded for the first time. The slides are used in the lectures and cannot replace READING the literature on the reading list.
Provisional time plan (The corresponding room is given in brackets):
| Week | Monday 08:45 (08:15 for exercises) -10:00 | Thursday 16:15-18:00 | Friday 14:15-15:00 |
|---|---|---|---|
| 2 | 05.01. Lecture (EL4) - Part 1 | 08.01. Lecture (R3) - Part 1 | 09.01. - |
| 3 | 12.01. Lecture (EL4) - Part 1 | 15.01. Lecture (R3) - Part 1 | 16.01. - |
| 4 | 19.01. Lecture (EL4) - Part 1 | 22.01. Lecture (R3) - Part 1 | 23.01. - |
| 5 | 26.01. Exercises (Nullrommet 380A) | 29.01. Exercises (Nullrommet 380A) | 30.01. - |
| 6 | 02.02. Exercises (Nullrommet 380A) | 05.02. Exercises (Nullrommet 380A) | 06.02. - |
| 7 | 09.02. Lecture (EL4) - Part 2 | 12.02. Lecture (R3) - Part 2 | 13.02. Oral presentations (EL4) |
| 8 | 16.02. Lecture (EL4) - Part 2 | 19.02. Lecture (R3) - Part 2 | 20.02. Oral presentations (EL4) |
| 9 | 23.02. Lecture (EL4) - Part 2 | 26.02. Lecture (R3) - Part 2 | 27.02. - |
| 10 | 02.03. Lecture (EL4) - Part 3 | 05.03. Exercises (Nullrommet 380A) | 06.03. - |
| 11 | 09.03. Exercises (Nullrommet 380A) | 12.03. Exercises (Nullrommet 380A) | 13.03. - |
| 12 | 16.03. Exercises (Nullrommet 380A) | 19.03. Lecture (R3) - Part 3 | 20.03. Oral presentations (EL4) |
| 13 | 23.03. Lecture (EL4) - Part 3 | 26.03. Lecture (R3) - Part 3 | 27.03. Oral presentations (EL4) |
| 14 | 30.03. EASTER HOLIDAY | 02.04. EASTER HOLIDAY | 03.04. EASTER HOLIDAY |
| 15 | 06.04. EASTER HOLIDAY | 09.04. Exercises (Nullrommet 380A) | 10.04. - |
| 16 | 13.04. Exercises (Nullrommet 380A) | 16.04. Exercises (Nullrommet 380A) | 17.04. Oral presentations (EL4) |
| 17 | 20.04. cancelled |
Lecture content:
Abbreviations: GH: Book by Givens and Hoeting, GL: Book by Gamerman and Lopes, HTF: Book by Hastie, Tibshirani and Friedman (see here).
| Week | Date | Topics | Slides | Reading |
|---|---|---|---|---|
| 2 | 05.01 | Organizationalt things, Introduction to R and simulations | Slides, Intro to R | GL: 1.1, GH: 1 (repetition) |
| 2 | 08.01 | Review random variables + prob.distributions, sampling from discrete distributions, inversion method, bivariate techniques (Box-Muller), … | Slides | GL: 1.2-1.3.2, GH: 6-6.2.2 |
| 3 | 12.01 | Box-Muller, ratio-of-uniforms | Slides (updated 12.01, 17:00, change on slide 2 (top-right), x_2 to x_1), Simulation Bernoulli and binomial | GL: 1.3.2, 1.3,3, 1.4 (all), GH: 6-6.2.2 |
| 3 | 15.01 | Finish ratio-of-uniforms, methods based on mixtures, rejection sampling | See former slides + Slides, Simulation from a mixture of two normals, Simulation from a mulitivariate normal | GL: 1.3,3, 1.4 (all), 1.5.1, GH: 6.2.3 |
| 4 | 19.01 | Finish rejection sampling, adaptive rejection sampling, Monte Carlo integration, importance sampling | Slides, Demonstration of rejection sampling in R | GL: 1.5 (all), GH: 6.2.3 (all), 6.3.1, 6.4.1 |
| 4 | 22.01 | Intro Bayes | Slides, Demonstration of Monte-Carlo integration/importance sampling in R | GL: 2.1, 2.2, GH: 1.5 |
| 7 | 09.02 | Intro Bayes II | Slides | GL: 2.3 intro, 2.3.1, GH: 1.5 |
| 7 | 12.02 | Review Markov chains, Markov chain Monte Carlo | Slides, Toy example Markov chain with Poisson as limiting distribution, Toy example MCMC with Poisson as target distribution | GL: 4.1-4.6 (repetition MC), 6.1, 6.2, 6.3, GH: 1.7 (repetition MC), 7 intro, 7.1 |
| 8 | 16.02 | Metropolis-Hastings algorithm, Gibbs sampling | Slides, Toy example illustrating random walk proposals, Rao example comparing random walk and independence proposals | GL: 6.4, 5.1, 5.2, GH: 7.2 |
| 8 | 19.02 | Gibbs sampling, full-conditional distributions, convergence diagnostics | Slides, Example of different convergence and mixing checks, R-code to compute the effective sample size (ESS), R-code to implement the univariate and bivariate MCMC updates for the beetle example | GH: 7.2, 7.3 |
| 9 | 23.02 | Finish MCMC, start integrated nested Laplace approximations (INLA) | Conjugate gamma-Poisson hierarchical model + Gaussian approximation, Introduction to INLA | Original INLA paper (only for those interested in having it), R-INLA webpage |
| 9 | 26.02 | INLA basic idea and R-INLA | Slides for R-INLA, Toy example to illustrate INLA call and output processing, Example using INLA for disease mapping | |
| 10 | 02.03 | Classification and cross-validation | Slides, Illustration KNN, Illustration cross-validation | HTF: 4.1, 4.3 (page 106-112), 13.3 (463-468), 7.10 |
| 12 | 19.03 | Classification and bootstrapping | Slides, Illustration bootstrap idea, Illustration of LDA in R The code reproduces figure shown in slides, Section 4 shows the usage of the lda-function in R and the last part how to predict new observations. | GH: 9.1, 9.2 |
| 13 | 23.03 | Bootstrapping | Slides, Illustration of paired bootsrap | GH: 9.2.2, 9.2.3, 9.2.4, 9.3.1, 9.5 (intro), 9.5.1, 9.5.2 (page 304-307 top), 9.8 |
| 13 | 26.03 | Permutation test and EM-algorithm | See slides from 23.03 for permutation test, Slides for EM-algorithm , Illustration how to do first EM-example with modified design matrix, Data for permutation test, Illustration of permutation test | GH: 4 (Intro), 4.1, 4.2 until page 102. |