Theses/Dissertations - Statistical Sciences
Permanent URI for this collectionhttps://hdl.handle.net/2104/4798
Browse
Browsing Theses/Dissertations - Statistical Sciences by Author "Bratcher, Thomas L."
Now showing 1 - 2 of 2
- Results Per Page
- Sort Options
Item Conjugate hierarchical models for spatial data: an application on an optimal selection procedure.(2006-07-24T15:25:43Z) McBride, John Jacob.; Bratcher, Thomas L.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.The theory of generalized linear models provides a unifying class of statistical distributions that can be used to model both discrete and continuous events. In this dissertation we present a new conjugate hierarchical Bayesian generalized linear model that can be used to model counts of occurrences in the presence of spatial correlation. We assume that the counts are taken from geographic regions or areal units (zip codes, counties, etc.) and that the conditional distributions of these counts for each area are distributed as Poisson having unknown rates or relative risks. We incorporate the spatial association of the counts through a neighborhood structure which is based on the arrangement of the areal units. Having defined the neighborhood structure we then model this spatial association with a conditionally autoregressive (CAR) model as developed by Besag (1974). Once the spatial model has been created we adapt a subset selection procedure created by Bratcher and Bhalla (1974) to select the areal unit(s) having the highest relative risks.Item Spatial Poisson regression : Bayesian approach correcting for measurement error with applications.(2010-10-08T16:13:31Z) Atkinson, William H., 1980-; Bratcher, Thomas L.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Under and over reporting is a common problem in social science research, adverse events associated with drug use, and many other areas of research. Furthermore, overdispersion is another common problem that plagues count data. McBride (2006) proposed a Bayesian Poisson regression model which accounts for overdispersion in count data. We extend this model by adding parameters to accommodate the problems associated with under and over reporting in the count data. We then study the model's coverage, power, accuracy of point estimates, and credible set widths through simulation using a spatial lattice grid. We find that our proposed model produces reliable point estimates and reasonable credible set widths, coverage, and power. We also provide two examples of the models use: disease mapping of habitat burglary from the city of Waco Texas and an analysis of sports data similar to that of Albert's (1992) analysis of homerun data. Research questions of interest are answered using the subset selection procedure proposed by Bratcher and Bhalla (1974), used by Hamilton, Bratcher, and Stamey (2008) and Stamey, Bratcher, and Young (2007), to demonstrate the ease of use for combining the our model developed here and the subset selection procedure itself, as was also done in McBride (2006).