Threshold Knot Selection for Large-Scale Spatial Models With Applications to the Disaster.

Large spatial datasets are typically modeled through a small set of knot locations; often these locations are specified by the investigator by arbitrary criteria. Existing methods of estimating the locations of knots assume their number is known , or are otherwise computationally intensive. We develop a computationally efficient method of estimating both the location and number of knots for spatial mixed effects models.

Determining the number of test fires needed to represent the variability present within firearms of various calibers.

The Association of Firearm and Toolmark Examiners recommends a minimum of two test fires be performed when an unknown firearm is submitted to a laboratory prior to doing a comparison with a cartridge case collected from a crime scene. Limited research has been performed to determine how many test fires are necessary to be representative of the match distribution of a firearm. Various makes and models of firearms comprising five calibers were tested using a hybrid equivalence test to determine how many cartridge cases were required to represent the match distribution of an unknown firearm based on both breech face and firing pin correlation scores from an IBIS Heritage System.

Past and future drought in Mongolia.

The severity of recent droughts in semiarid regions is increasingly attributed to anthropogenic climate change, but it is unclear whether these moisture anomalies exceed those of the past and how past variability compares to future projections. On the Mongolian Plateau, a recent decade-long drought that exceeded the variability in the instrumental record was associated with economic, social, and environmental change. We evaluate this drought using an annual reconstruction of the Palmer Drought Severity Index (PDSI) spanning the last 2060 years in concert with simulations of past and future drought through the year 2100 CE.

Testing for inequality constraints in singular models by trimming or winsorizing the variance matrix.

There are many applications in which a statistic follows, at least asymptotically, a normal distribution with a singular or nearly singular variance matrix. A classic example occurs in linear regression models under multicollinearity but there are many more such examples. There is well-developed theory for testing linear equality constraints when the alternative is two-sided and the variance matrix is either singular or non-singular.