RESUMEN
The analysis of traffic accident data is crucial to address numerous concerns, such as understanding contributing factors in an accident's chain-of-events, identifying hotspots, and informing policy decisions about road safety management. The majority of statistical models employed for analyzing traffic accident data are logically count regression models (commonly Poisson regression) since a count - like the number of accidents - is used as the response. However, features of the observed data frequently do not make the Poisson distribution a tenable assumption. For example, observed data rarely demonstrate an equal mean and variance and often times possess excess zeros. Sometimes, data may have heterogeneous structure consisting of a mixture of populations, rather than a single population. In such data analyses, mixtures-of-Poisson-regression models can be used. In this study, the number of injuries resulting from casualties of traffic accidents registered by the General Directorate of Security (Turkey, 2005-2014) are modeled using a novel mixture distribution with two components: a Poisson and zero-truncated-Poisson distribution. Such a model differs from existing mixture models in literature where the components are either all Poisson distributions or all zero-truncated Poisson distributions. The proposed model is compared with the Poisson regression model via simulation and in the analysis of the traffic data.
RESUMEN
To study chromosomal aberrations that may lead to cancer formation or genetic diseases, the array-based Comparative Genomic Hybridization (aCGH) technique is often used for detecting DNA copy number variants (CNVs). Various methods have been developed for gaining CNVs information based on aCGH data. However, most of these methods make use of the log-intensity ratios in aCGH data without taking advantage of other information such as the DNA probe (e.g., biomarker) positions/distances contained in the data. Motivated by the specific features of aCGH data, we developed a novel method that takes into account the estimation of a change point or locus of the CNV in aCGH data with its associated biomarker position on the chromosome using a compound Poisson process. We used a Bayesian approach to derive the posterior probability for the estimation of the CNV locus. To detect loci of multiple CNVs in the data, a sliding window process combined with our derived Bayesian posterior probability was proposed. To evaluate the performance of the method in the estimation of the CNV locus, we first performed simulation studies. Finally, we applied our approach to real data from aCGH experiments, demonstrating its applicability.
