An Approximate Bayesian Approach to Modeling Crash Data via a Poisson Markov Random Field

• Activity Number: 263
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ignacio Alvarez* and Kristian Schmidt and Alicia Carriquiry and Jarad Niemi and Michael Pawlovich
• Companies: Iowa State University and Iowa State University and Iowa State University and Iowa State University and Iowa Department of Transportation
• Keywords: Markov field ; abc ; Crash frequency data

Abstract

Crash frequencies are often modeled using hierarchical Poisson models where the Poisson mean is allowed to depend on covariates. There are different ways to introduce spatial depen- dence into crash frequency models. Many authors propose the use of (latent) spatial random effects that permit introducing spatial correlation at the level of the Poisson mean. We adopt a different approach and use a Poisson Markov random field (PMRF) approach to introduce spatial dependence. While this allows for directly modeling dependence on the data level, it introduces computational challenges, for estimating model parameters within the Bayesian framework. This is due to the presence of potentially intractable normalizing constants in the joint posterior distribution. We use approximate Bayesian computation (ABC) and develop algorithms to perform parameter estimation via ABC in a PMRF model. The neighborhood structure in our approach is anisotropic to allow for the spatial dependence parameters to differ in different directions.