Curriculum

The curriculum consists of three parts:
- i) algorithms for stochastic simulation,
- ii) Markov chain Monte Carlo algorithms,
- iii) expectation-maximization algorithms, bootstrap and classfication methods.
The curriculum is covered in the lectures and the exercises. Part i) and ii) are covered by the following text:
- Stochastic simulation (direct methods and MCMC): D. Gamerman and H.F. Lopes (2006). Markov chain Monte Carlo - Stochastic simulation for Bayesian inference. Chapman and Hall, London.
  - Part i) Section 1: All. IMPORTANT: 1.3.1, 1.3.2, 1.4.1, 1.5.1, 1.5.2.
  - Part i) Section 2: 2.1 - 2.4. IMPORTANT: 2.2.1, 2.3.2, 2.3.3.
  - Part i) Section 3: All (except 3.3 and 3.5.3). IMPORTANT: 3.1, 3.2.1, 3.4, 3.5.1, 3.5.2.
  - Part ii) Section 4: All (most of this material should be known from TMA4265 Stochastic processes). IMPORTANT: 4.4, 4.5, 4.6
  - Part ii) Section 5: 5.1 - 5.4, 5.5 (except 5.5.2, 5.5.3). IMPORTANT: 5.2, 5.3, 5.4.2, 5.4.4.
  - Part ii) Section 6: 6.1 - 6.4. IMPORTANT: 6.2, 6.3.1, 6.3.2, 6.3.3, 6.4
- Part iii) is covered by the following notes:
  - EM algorithm. (Note). IMPORTANT: 8.5.1, 8.5.2 In Hastie et al.
  - Classification and kernels. (Note). IMPORTANT: 4.3 (p 106-112), 6.6.2, 6.8 (p 214-215) in Hastie et al.
  - Bootstrap (Note), IMPORTANT: Chapter 6 (p 45-56) in Efron and Tibshirani.
  - Permutation tests. (Note). IMPORTANT: Chapter 15 (p 202-210) in Efron and Tibshirani.
  - Cross-validation. (Note). IMPORTANT: Chapter 17 (p 237-248) in Efron and Tibshirani.
  - You may also read: An introduction to the bootstrap: B. Efron and R.J. Tibshirani (1993), Chapman and Hall, London.
  - Chapter 4, 5, 6, 15, 17.1-6.
  - You may also read: The elements of statistical learning: T. Hastie, R. Tibshirani and J. Friedman (2009), Springer.
  - Chapter 4.3, 6.6-8, 8.5.1-3.