#### Statistical Inverse Analysis for a Network Microsimulator

German Molina, M.J. Bayarri and James Berger

CORSIM is a large microsimulator for vehicular traffic, and is
being studied with respect to its ability to successfully model
and predict behavior of traffic in a 36 block section of Chicago.
Inputs to the simulator include information about street
configuration, driver behavior, traffic light timing, turning
probabilities at each corner and distributions of traffic ingress
into the system.
Data is available concerning the turning proportions in the actual
neighborhood, as well as counts as to vehicular input into the
system and internal system counts, during a day in May, 2000. Some
of the data is accurate (video recordings), but some is quite
inaccurate (observer counts of vehicles). Previous utilization of
the full data set was to `tune' the parameters of CORSIM -- in an
ad hoc fashion -- until CORSIM output was reasonably close to the
actual data. This common approach, of simply tuning a complex
computer model to real data, can result in poor parameter choices
and will completely ignore the often considerable uncertainty
remaining in the parameters.

To overcome these problems, we adopt a Bayesian approach, together
with a measurement error model for the inaccurate data, to derive
the posterior distribution of turning probabilities and of the
parameters of the CORSIM input distribution. This posterior
distribution can then be used to initialize runs of CORSIM,
yielding outputs that reflect that actual uncertainty in the
analysis.

Computation must be via Markov Chain Monte Carlo methodology, but
this is not feasible because of the expense in running CORSIM.
Hence we develop a fast approximation to CORSIM that can be used
directly to carry out the MCMC analysis. The resulting MCMC has
some novel features that should be useful in dealing with general
discrete network structures.

Postscript File (1.5 MB)