German Molina, M.J. Bayarri and James Berger
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.
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