NMAA13024U Conditioning and Markov Properties (Beting)

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.