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Telephone: +45 39 56 41 71 Skype: peterharremoes Private
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ResearchMy research is centred
around information theory. Information theory was
developed to optimize communication between humans but
the relevant concepts have much wider applications. A
main goal of my research is to tie information theory
closer together with probability theory, statistics, and
physics. List
of Publications Bayesian networks I have worked on the relation between Bayesian
networks and irreversibility, and my ultimate goal is to
build a bridge between these ideas and information
theory. For a longer period I have been working on the
idea of using lattice theory to describe Bayesian
networks. This approach will also lead to new
non-Shannon inequalities. I have some unpublished
results on this already. Convergence theorems in probabilityThe second law of thermodynamics states that the
entropy of a closed system increases to its maximum.
Most of the major convergence theorems in probability
theory can be stated in a similar fasion or related
fasion. These information theoretic convergence theorems
are typically stronger that what one finds int he
traditional literature in that they give convergence in
information rather than convergence in total variation.
I have published results on central limit theorem, law
of large numbers, law of small numbers, law of thin
numbers, martingale and reversed martingale convergence,
Markov chains and ergodicity. some result on law of
iterated logarithms are still to be published. InequalitiesConvergence is controled by inequalities and
information theoretic problems often boil down to
inequalities. I have in particular worked on the use of
topology, new plotting techniques and interval
arithmetics. StatisticsThe link between information theory and statistics has
been known for a long time, but the research area is
still very active and new results are found all the
time. One idea is to use ideas from information theory
to analyse problems of traditional statistical
inference. The asymptotic efficiency of various test
statistics can be analyzed and the main result is that
the likelihood ratio statistic (based on information
divergence/KL-divergence) is more Bahadur efficient than
other statistics. At the moment I am working on
extimates of the tail probabiblities of likelihood ratio
statistic. Game theoryThe theory of combinatorial games like board games and
the theory of social games with Nash-equilibria are
normally considered as separate theories. Nevertheless
the two theories can be combined by considering social
games where the payoff function has combinatorial games
as values rather than money. Quantum theoryThe statistical aspects of quantum theory are quite
challanging. One way of viewing this field is that it is
a theory dominated by symmetries. Actually a lot of the
results that are normally formulated in the framwork of
Hilbert spaces can be formulated as results on spaces
with certain symmetries. |
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