NMAA13024U Conditioning and Markov Properties (Beting)

Volume 2015/2016
Education

MSc Programme in Statistics
 

Content
  • Markov kernels and conditional distributions: Properties, integration, uniqueness, disintegration
  • The relation between conditional expectations and conditional distributions
  • Existence of conditional distributions
  • Conditional distributions given a transformation; sufficiency
  • Conditional independence: For events, sigma algebras, and random variables
  • Conditional independence models and graphs
  • Markov properties on undirected graphs
  • Bayesian networks
  • Alternative graphical Markov properties
Learning Outcome

Knowledge:

Basic knowledge of the topics covered by the course: Conditional distributions, conditional independence,  Bayesian networks, and other Markov structures.

Skill:

  • Use concepts such as Markov kernels and conditional distributions.
  • Compute conditional expectations using conditional distributions.
  • Describe and compute the distribution of a system of random variables given a transformation
  • Discuss and understand general properties of conditional independence
  • Discuss and understand specific examples of graphical Markov models
  • Discuss and understand Bayesian networks in concrete examples.
  •  

Competence:

  • Discuss the relation between conditional expectations and conditional distributions.
  • Understand the concept of conditional independence and relate it distributions relevant to statistical arguments
  • Discuss the relation between Markov chains, Bayesian networks, and other Markov structures

Lecture notes and selected parts of suitable monographs

Advanced probability theory 2(VidSand2) or equivalent
5 hours of lectures and 4 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Exam
  • 24
  • Lectures
  • 35
  • Preparation
  • 119
  • Theory exercises
  • 28
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written assignment, 24 hours
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Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.