# Untitled

**Source**: https://teaching.scss.tcd.ie/wp-json/wp/v2/module/3827
**Parent**: https://teaching.scss.tcd.ie/module/stu34503-stochastic-models-in-space-and-time-1/

{"id":3827,"date":"2022-03-09T12:54:52","date\_gmt":"2022-03-09T11:54:52","guid":{"rendered":"https:\/\/teaching.scss.tcd.ie\/?post\_type=module&p=3827"},"modified":"2026-03-11T16:27:55","modified\_gmt":"2026-03-11T16:27:55","slug":"stu34503-stochastic-models-in-space-and-time-1","status":"publish","type":"module","link":"https:\/\/teaching.scss.tcd.ie\/module\/stu34503-stochastic-models-in-space-and-time-1\/","title":{"rendered":"STU34503 – Stochastic Models in Space and Time I"},"content":{"rendered":"\n

**Not offered in 2023\/24<\/strong><\/p>\n\n\n\n

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| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| **Module Code<\/strong><\/td> STU34503<\/td><\/tr>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Module Name<\/strong> <\/td> Stochastic Models in Space and Time I<\/td><\/tr>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **ECTS Weighting [**[1]<\/strong><\/a><\/strong><\/td> 5 ECTS<\/td><\/tr>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Semester Taught<\/strong><\/td> Semester 1<\/td><\/tr>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Module Coordinator\/s  <\/strong><\/td> Jason Wyse<\/td><\/tr>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Academic Year<\/strong><\/td> 2026\/2027<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nModule Learning Outcomes <\/h2>\n\n\n\n On successful completion of this module, students will be able to: <\/p>\n\n\n\n  \n1. Discuss and model real world phenomena using stochastic models <\/li>\n<\/ol>\n\n\n\n    \n1. Define and apply the Markov property <\/li>\n<\/ol>\n\n\n\n       \n1. Describe and derive long run properties of Markov chains  <\/li>\n<\/ol>\n\n\n\n          \n1. Describe and derive examples of Markov processes and apply to examples from biology, business and finance <\/li>\n<\/ol>\n\n\n\nModule Content<\/h2>\n\n\n\n Specific topics addressed in this module include: <\/p>\n\n\n\n             \n- Examples of Stochastic processes <\/li>\n\n\n\n- The Markov property and Markov chains <\/li>\n\n\n\n- Classification of states of Markov chains <\/li>\n\n\n\n- Convergence of a Markov chain to a stationary distribution <\/li>\n\n\n\n- Markov processes and the matrix exponential <\/li>\n\n\n\n- Poisson processes and their properties <\/li>\n\n\n\n- Brownian motion and geometric Brownian motion <\/li>\n<\/ul>\n\n\n\n This module gives students exposure to statistical models for applications where a random phenomenon evolves according to a time (or other) ordering. We will encounter Markov models motivated and used in biology, physics and finance and discuss the historical and fundamental significance of these probabilistic constructions. Concepts and ideas will be demonstrated through simulation and model fitting using the statistical computing language R. Code libraries tailored to the module are provided to accompany lecture material. <\/p>\n\n\n\nTeaching and Learning Methods <\/h2>\n\n\n\n Lectures including code demonstrations and tutorials. <\/p>\n\n\n\nAssessment Details <\/h2>\n\n\n\n 2 hour real-time examination and homework assignments.<\/p>\n\n\n\n                            |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |                           | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |                           | **Assessment Component<\/strong><\/td> **Brief Description<\/strong> <\/td> **Learning Outcomes Addressed<\/strong><\/td> **% of Total<\/strong><\/td> **Week Set<\/strong><\/td> **Week Due<\/strong><\/td><\/tr>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Examination<\/td> 2 hour written examination<\/td> LO1, LO2, LO3, LO4 <\/td> 90%<\/td> N\/A<\/td> N\/A<\/td><\/tr>|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Assignments<\/td> Four assignments throughout semester <\/td> LO1, LO2, LO3, LO4 <\/td> 10%<\/td> 2,4,7,9<\/td> 3,5,8,10<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nReassessment Details<\/h2>\n\n\n\n Written examination (2 hours, 100%) <\/p>\n\n\n\nContact Hours and Indicative Student Workload<\/h2>\n\n\n\n  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Contact Hours (scheduled hours per student over full module), broken down by<\/strong>: <\/td> **33 hours<\/strong><\/td><\/tr>|  |  |  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Lecture<\/td> 29 hours<\/td><\/tr>|  |  |  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Tutorial or seminar<\/td> 4 hours<\/td><\/tr>|  |  |  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | --- | --- | | **Independent Study (outside scheduled contact hours), broken down by:<\/strong><\/td> **82 hours<\/strong><\/td><\/tr>|  |  |  |  |  |  | | --- | --- | --- | --- | --- | --- | | Preparation for classes and review of material (including preparation for examination, if applicable)<\/td> 42 hours<\/td><\/tr>|  |  |  |  | | --- | --- | --- | --- | | Completion of assessments (including examination, if applicable)<\/td> 40 hours<\/td><\/tr>|  |  | | --- | --- | | **Total Hours<\/strong><\/td> **115 hours<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nRecommended Reading List<\/h2>\n\n\n\n Two comprehensive texts which are good companions for this module are: <\/p>\n\n\n\n \u201cMarkov Chains (Cambridge Series in Statistical and Probabilistic Mathematics)\u201d by J.R. Norris <\/p>\n\n\n\n \u201cPattern Recognition and Machine Learning\u201d by Christopher M. Bishop, published by Springer <\/p>\n\n\n\n Neither of these texts are compulsory. Notes provided in class should be sufficient for self-study. <\/p>\n\n\n\nModule Pre-requisites <\/h2>\n\n\n\n **Prerequisite modules<\/strong><\/p>\n\n\n\n **Mathematics students:<\/strong> STU23501<\/p>\n\n\n\n **MSISS students: <\/strong>STU11002, STU22004<\/p>\n\n\n\n <\/p>\n\n\n\nModule Co-requisites <\/h2>\n\n\n\n N\/A<\/p>\n\n\n\nModule Website<\/h2>\n\n\n\n [Blackboard <\/a><\/p>\n","protected":false},"excerpt":{"rendered":" (Semester 1, 5 ECTS)<\/p>\n","protected":false},"author":63,"menu\_order":0,"template":"","meta":[],"module\_category":[],"class\_list":["post-3827","module","type-module","status-publish","hentry"],"\_links":{"self":[{"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/module\/3827","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/module"}],"about":[{"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/types\/module"}],"author":[{"embeddable":true,"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/users\/63"}],"wp:attachment":[{"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/media?parent=3827"}],"wp:term":[{"taxonomy":"module\_category","embeddable":true,"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/module\_category?post=3827"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](https://teaching.scss.tcd.ie/wp-json/wp/v2/module/\"https:\/\/tcd.blackboard.com\/webapps\/login\/\")******** |** | | | | |** |** | | | | |** |** | | | | | | | | | | | | |** |** |** |** |** |** | |** | |** | |** | |**](https://teaching.scss.tcd.ie/wp-json/wp/v2/module/\"#_ftn1\")** | |** | |** |**