[Nets-seminars] Seminar today (Friday 15th) 4pm GS/302

[Richard G. Clegg]

  Title: Design of Experiments for Markov Chains, or how often should we
open the box?

Ben Parker, Joint work with Steven Gilmour and John Schormans

Suppose we have a system that we can measure a fixed number of times,
but at any chosen interval. Motivated by an example of probing data
networks, we model this as a black box system: we can either chose to
open the box or not at any time period, our aim to find out how the
system evolves over time.

We use the statistical principles of design of experiments to model
numerical experiments that can be designed optimally. We demonstrate how
to analyse the evolution of a system as a Markov Chain, and deduce its
likelihood function, and hence the Fisher information matrix. From this,
numerical results provide a guide to the best design for the experiment
for different values of input parameters. We further develop our ideas
to show what happens when we take into account the effect of the
observations interfering with the experiment, as would always be the
case with active probing. We present examples, and demonstrate how this
could be useful to many fields, with particular reference to experiments
on packet networks.

We present a general result for showing how to optimally measure any
system that evolves according to the Markov principle.

-- 
Richard G. Clegg,
Dept of Elec. Eng.,
University College London
http://www.richardclegg.org/