MML mixture models of heterogeneous Poisson processes with uniform outliers for bridge deterioration

Effectiveness of maintenance programs of existing concrete bridges is highly dependent on the accuracy of the deterioration parameters utilised in the asset management models of the bridge assets. In this paper, bridge deterioration is modelled using non-homogenous Poisson processes, since deterioration of reinforced concrete bridges involves multiple processes. Minimum Message Length (MML) is used to infer the parameters for the model. MML is a statistically invariant Bayesian point estimation technique that is statistically consistent and efficient. In this paper, a method is demonstrated estimate the decay-rates in non-homogeneous Poisson processes using MML inference. The application of methodology is illustrated using bridge inspection data from road authorities. Bridge inspection data are well known for their high level of scatter. An effective and rational MML-based methodology to weed out the outliers is presented as part of the inference.