Abstract by Madeline Morris
Mixture Model Approximation for Point Pattern Data
The main goal of this research project is to use a mixture model to model point pattern data (data collected on event locations). Using data from car crashes along I-15 in Utah, we develop a fully conjugate model to accurately capture where and with what frequency crashes occur using Poisson process methodology. The key aspect to this model, is that the height of the curve of the density of the accidents can be approximated using a Log-Normal distribution. Thus, the effect coefficients for how frequently crashes occur in a given location can be approximated from a Normal distribution. Due to the approximations, this method can calculate results very quickly and is computationally efficient. Additionally, the results seem to match non-approximated methods, such as Metropolis Hastings to calculate the beta coefficients. The next step in our research is to expand this model to accommodate two-dimensional data, such as the spread of disease in a population.