We present a new family of graphical models that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them can be seen as the result of marginalizing out some nodes in an AMP chain graph. However, MAMP chain graphs do not only subsume AMP chain graphs but also regression chain graphs. We describe global and local Markov pr...

Ion channels are protein molecules that are intimately involved in the transmission of information through the nervous system. Their behaviour is modelled as a Markov chain, but one which cannot be observed directly. The deeciencies of the observation process make the study of ion channel data diicult. Several methods have been proposed for making inference about the parameters of the underlyin...

Hierarchical models are one of the central tools of Bayesian analysis. They offer many advantages, including the ability to borrow strength to estimate individual parameters and the ability to specify complex models that reflect engineering and physical realities. Markov chain Monte Carlo is a set of algorithms that allow Bayesian inference in a variety of models. We illustrate hierarchical mod...

The objective of this tutorial is to introduce basic concepts of a Hidden Markov Model (HMM) as a fusion of more simple models such as a Markov chain and a Gaussian mixture model. The tutorial is intended for the practicing engineer, biologist, linguist or programmer who would like to learn more about the above mentioned fascinating mathematical models and include them into one’s repertoire. Th...

Hierarchical Markovian models are a useful paradigm for the speciication and quantitative analysis of models arising from complex systems. Although techniques for a very eecient analysis of large scale hierarchical Markovian models have been developed recently, the size of the Markov chain underlying a complex hierarchical model often prohibits an analysis on contemporary computer equipment. Ho...