**Here you will find current information for the autumn semester 2002.
This information in entirely in English, as we expect that
several exchange students will take the course.**

The teacher in MH:362D will be Mats Pihlsgård, and this class will be held in Swedish. The teacher in MH:331 will be Tobias Rydén, and this class will be bilingual, that is, held in English/Swedish.

Discrete Markov chains and Markov processes. Classification of states and chains/processes. Stationary distributions and convergence. Absorbing states and absorption times. Simulation and inference. The Poisson processes on the real line and more general spaces. Markov random fields: introduction, Gibbs fields, simulation, some inference. Hidden Markov models: definition, inference, the EM algorithm. Various applications.

Tu 29/10 | Introduction, stochastic processes. Discrete Markov chains: definition, transition probabilities (Ch 1, 2.1-2.2). Discrete Markov processes: definition, transition intensities, waiting times, embedded Markov chain (Ch 4.1, parts of 4.2). Lack of memory of the exponential distribution (Ch 3.1). |

Th 31/10 | Modelling with Markov chains and processes (Ch 4.1). The Chapman-Kolmogorov equations (Ch 3.3, 4.2). |

Tu 5/11 | Absolute probabilities (Ch 2.2, 4.2). Stationarity, classification of states and chains (Ch 2.3, 2.4). |

Th 7/11 | Stationarity, classification of states and chains for Markov processes (Ch 4.3, 4.4). Birth-and-death processes (Ch 4.6 4.7). |

Tu 12/11 | Absorbing states and absorption times (Ch 2.5, 4.5). |

Th 14/11 | Inference, simulation (Ch 2.7, 2.8, 4.9, 4.10). |

Tu 19/11 | The Poisson process: characterisations, the Poisson limit (law of small numbers), recurrence times, conditional distributions (Ch 3.2-3.3). |

Th 21/11 | Non-homogeneous Poisson processes, operations on Poisson processes, spatial and general Poisson processes, inference (Ch 3.4-3.8). |

Tu 26/11 | Markov random fields: definition, examples, local specification, Gibbs distributions (lecture notes here: PostScript or pdf format). |

Th 28/11 | Markov random fields: Markov chain Monte Carlo simulation, pseudo-likelihood (lecture notes as above). |

Tu 3/12 |
Hidden Markov models: definition, examples. Filtering and
smoothing, the forward-backward algorithm.
Gibbs distributions (lecture notes here:
PostScript or
pdf format).
These notes have now been updated. Pages 11-13
differ from the previous version. |

Th 5/12 | Hidden Markov models: parameter estimation and the EM algorithm (lecture notes as above). |

Tu 10/12 |
Seminar on perfect simulation of Markov random fields
and (hopefully!) an application of Markov chain
modelling to analysis of DNA.
This is not part of the course curriculum. |

Th 12/12 |
No class. |

The exercises themselves can be downloaded here in PostScript or pdf format, and answers and hints can be downloaded here in PostScript or pdf format.

Week 1: | 101, 102, 104, 105, 201, 203. |

Week 2: | 301, 302, 403, 404, 405, 409, 412. |

Week 3: | 501, 502, 503, 601, 602. |

Week 4: | 701, 704, 706, 707, 708, 709, 714. |

Week 5: | 801, 802, 803. |

Week 6: | 901, 902. |

Week 7: | Course overview, opportunity to ask questions, solution of old exam problems, ... |

**OBS! Övningen fredagen den 6:e december 10-12 i MH:362D
är inställd pga sjukdom!**

Matlab files needed: knapp.m, monopgata.m, pestimering.m, seep.m, eigv.m, move.m, simulering.m, field.m, monop.m, pchk.m, psimulering.m.

The second lab will be given during study week 6 (2-6 December). There are three time slots scheduled for the lab (Monday afternoon, Tuesday night, Thursday morning), and you choose one of them by signing up at the lists that are posted on the department's billboard in the lobby in the math buildning (course code FMS180). Instructions for the second lab are available here in PostScript or pdf format.

Matlab files needed: coal.dat, porand.m, riodej.mat, icm.m.

Students taking MAS204 must also do an oral examination (

At the exam you may use the table of formulas (see above), a table of formulas from the basic course in mathematical statistics, and a pocket calculator without pre-stored information (such as formulas, programs,...).

Tobias Rydén Last modified: Mon Oct 20 13:16:39 MEST 2003