HITS Colloquium Michael Baake – The Markov embedding problem – old and new

by Michael Baake, Fakultät für Mathematik, Universität Bielefeld

Markov matrices are a widely used tool for the empirical description
of real-world data, which are usually sampled in discrete time steps.
Since the underlying processes may (and often do) run in continuous
time, one needs some time interpolation consistency, as the Finnish
statistician Gustav Elfving realised almost a century ago. This led to
the embedding question as an important research problem, where one
needs to know whether a given Markov matrix possesses a real matrix
logarithm that is a Markov generator (or rate matrix).

After initial contributions by David G. Kendall and Sir John F. C.
Kingman in the early 1960s, the embedding problem was finally solved
for three-dimensional matrices by the mid 1990s, after which further
activities faded. This changed again when molecular evolution and
bioinformatics needed the classification in four dimensions, which was
achieved just a few years ago. The field has been active ever since.

Here, we give an introduction to the problem and present some key
results, both old and new. The embedding of Markov matrices is a good
example of a problem that emerged from the applications, but requires
a blend of mathematical tools from different directions, including
probability theory, matrix analysis and abstract algebra.

REGISTRATION:

The talk will be hybrid.

If you would like to participate online, please register in advance here.

After registering, you will receive a confirmation email containing information about joining the meeting.

In case you are not able to attend, you can watch the talk afterwards on the HITS YouTube channel: https://www.youtube.com/user/TheHITSters.