This dissertation investigates the strengths and weaknesses of the current methods of residual analysis for spatial point process models. The primary focus is on the manner in which the space should be partitioned to form residuals. It proposes a new method whereby the differences between the modeled conditional intensity and the observed number of points are assessed over the Voronoi cells generated by the observations. The resulting residuals are substantially less skewed and can be used to construct diagnostic methods of greater statistical power than residuals based on a regular rectangular grid. These advantages are particularly evident for point processes with conditional intensities close to zero, such as those in seismology. Performance is compared using simulated data and applied to models for Southern California earthquakes.

Nolan and Temple Lang argue that “the ability to express statistical computations is an es- sential skill.” A key related capacity is the ability to conduct and present data analysis in a way that another person can understand and replicate. The copy-and-paste workflow that is an artifact of antiquated user-interface design makes reproducibility of statistical analysis more difficult, especially as data become increasingly complex and statistical methods become increasingly sophisticated. R Markdown is a new technology that makes creating fully-reproducible statistical analysis simple and painless. It provides a solution suitable not only for cutting edge research, but also for use in an introductory statistics course. We present experiential and statistical evidence that R Markdown can be used effectively in introductory statistics courses, and discuss its role in the rapidly-changing world of statistical computation.