The instructor will be Abel Rodriguez .
Classes will be held at Humanities & Social Sciences 250 on Tuesday and Thursday between 2:00 and 3:45 pm.
Office hours will be held at Jack Baskin Engineering Building, Office 147 on Tuesday and Thursday 3:50-4:50 pm (right after class).
The course introduces the fundamental concepts of probability theory associated with Markov chains (both in discrete and continuous time) and Poisson processes. Some limited inference for these processes is also discussed. The course requires good working knowledge of calculus-based probability theory (at the level of AMS-131) and some knowledge of statistical inference (at the level of AMS-132). Although no background in measure theory is required per-se, maturity handling mathematical proofs is required.
04/01 - Review of basic probability.
04/03 - Review of basic probability and introduction to stochastic processes.
04/08 - Introduction to Markov chains.
04/10 - Limit theorems. HW1 due. Problems, Chapter 1.
04/15 - More on limit theorems.
04/17 - Inference in discrete-time Markov chains. Semi-markov processes.
04/22 - Branching process.
04/24 - Introduction to Hidden Markov Chains. HW2 due. A new york times article to train your chain.
04/29 - Inference on Hidden Markov Chains. CG islands: An example of inference in HMM. Slides on Forward-Backward algorithm Example of Forward-Backward code
05/01 - Introduction to continuous-time Markov Chains.
05/06 - Birth and death processes.
05/08 - Kolmogorov diferential equations. HW3 due. DNA sequence for problem 4..
05/13 - Limiting distributions.
05/15 - Examples and inference.
05/20 - Introduction to Poisson Processes.
05/22 - More on homogenous Poisson Processes. HW4 due. Problems, Chapter 5.
05/27 - Non-homogenous poisson process.
05/29 - Inference in Poisson processes.
06/03 - Compound and conditional Poisson processes.
06/05 - No class. HW5 due. Problems, Chapter 2.
06/16 - Final exam due, noon.
Between 4 and 5 homeworks, to be posted in this webpage and worth 50% of the grade, plus a final (take-home) exam worth 50% of the grade. All evaluations should be completed out individually; the UCSC code of conduct will be enforced, and violators will receive no credit for joint work.
The textbook for the course will be Ross, Sheldon, M. Stochastic Processes, second edition. Wiley. Other recommended readings include Guttorp, P. Stochastic Modelling of Scientific Data, Chapman & Hall/CRC and Grimmett, G. and Stirzaker, D. Probability and Random Processes, Third Edition, Oxford University Press.