NMAA13024U Conditioning and Markov Properties (Beting)

Volume 2013/2014
Education
Master Programme in Statistics
Master Programme in Mathematics-Economics
Content
  • Markov kernels and conditional distributions: Properties, integration, uniqueness, disintegration
  • The relation between conditional expectations and conditional distributions
  • Existence of conditional distributions
  • Conditional independence: For events, sigma algebras, and random variables
  • General definition of Markov chains
  • Time homogeneity, strong Makrov property, and ergodicity of Markov chains in discrete time with a general state space
  • Bayesian networks
Learning Outcome
Knowledge:

Basic knowledge of the topics covered by the course: Conditional distributions, conditional independence, definition, stationarity, strong Markov property, and ergodicity of Markov chains in discrete time on general state spaces, Bayesian networks.

Skill:

  • Use concepts such as Markov kernels and conditional distributions.
  • Compute conditional expectations using conditional distributions.
  • Describe and compute the distribution of a Markov chain on a general state space.
  • Use the strong Markov property in concrete examples.
  • Establish time homogeneity, stationarity, and ergodicity of Markov chains in concrete cases.
  • 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 to the construction of Markov chains.
  • Discuss the drift criterion with a view to establish asymptotic stability and ergodicity.
  • Discuss the relation between Markov chains and Bayesian networks.
Advanced probability theory 2(VidSand2) or equivalent
5 hours of lectures and 4 hours of exercises per week.
  • 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.