INTERDISCIPLINARY STOCHASTIC PROCESSES COLLOQUIUM

Thursday Oct. 3rd  380 Soda  3:10-4:00pm

Speaker: Alberto Grunbaum (UC Berkeley, Department of Mathematics)

Title: Nonlinear network tomography

Abstract:
   We consider a multiterminal network whose digraph allows for cycles 
   and is not necessarily planar. Such networks arise as discrete models 
   of "diffuse or optical tomography" but may be of interest beyond their
   place of origin. We formulate the inverse problem of recovering the
   one-step transition probability matrix for the underlying Markov chain
   from boundary measurements of the distribution of "time of flight". In 
   certain situations we obtain a complete description of the (nonlinear)
   set of unrecoverable unknowns as well as explicit formulas for the 
   remaining ones in terms of data and these free parameters. We concentrate
   on "explicit formulas" and do not consider the important issue of 
   building good estimators that has been considered in similar (but linear) 
   problems starting with Y. Vardi and later workers such as Bin Yu.