Threshold Knot Selection for Large-Scale Spatial Models With Applications to the Deepwater Horizon 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 a priori, 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. Our proposed algorithm, Threshold Knot Selection (TKS), estimates knot locations by identifying clusters of large residuals and placing a knot in the centroid of those clusters. We conduct a simulation study showing TKS in relation to several comparable methods of estimating knot locations. Our case study utilizes data of particulate matter concentrations collected during the course of the response and clean-up effort from the 2010 Deepwater Horizon oil spill in the Gulf of Mexico.

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® HeritageTM System. The same general trend was observed for each caliber of firearm where the equivalence percentage increased from 10 to 30 cartridge cases. Overall, 15 cartridge cases are sufficient for above an 80% probability of representing the full match distribution for an unknown firearm. To approach full equivalence, 25 cartridge cases are enough because 30 cartridge cases were not found to be significantly higher in equivalence percentage for any caliber of firearm tested.

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. In recent years there is considerable, and growing, interest in developing methods for situations in which the estimated variance matrix is nearly singular. However, there is no corresponding methodology for addressing one-sided, i.e., constrained or ordered alternatives. In this paper we develop a unified framework for analyzing such problems. Our approach may be viewed as the trimming or winsorizing of the eigenvalues of the corresponding variance matrix. The proposed methodology is applicable to a wide range of scientific problems and to a variety of statistical models in which inequality constraints arise. We illustrate the methodology using data from a gene expression microarray experiment obtained from the NIEHS' Fibroid Growth Study.

Determining the number of test fires needed to represent the variability present within 9mm Luger firearms.

Many studies have been performed in recent years in the field of firearm examination with the goal of providing an objective method for comparisons of fired cartridge cases. No published research to support the number of test fires needed to represent the variability present within the impressions left on a cartridge case could be found. When a suspect firearm is submitted to a firearm examiner, typically two to four test fires are performed. The recovered cartridge cases are compared to each other to determine which characteristics from the firearm are reproducing, and then compared to any cartridge cases collected at a crime scene. The aim of this research was to determine the number of test fires examiners should perform when a suspect firearm is submitted to the lab to balance cartridge case acquisition time with performance accuracy. Each firearm in the IBIS® database at West Virginia University® is represented by approximately 100 fired cartridge case entries. Random samples of cartridge cases were taken separately from the breech face match score and firing pin match score lists. This subset was compared to the total match distribution of the firearm using a hybrid equivalence test to determine if the subset of similarity scores were statistically equivalent to the larger distribution of scores. For the sampled distribution to remain above 80% equivalent to the match distribution, a minimum of 15 cartridge cases should be used to model the match distribution, based on IBIS® scores. Thirty cartridge cases is a conservative estimate, allowing one to determine that the location and dispersion of the match and sampling distributions are equivalent with nearly 100% probability.

CLME: An R Package for Linear Mixed Effects Models under Inequality Constraints.

In many applications researchers are typically interested in testing for inequality constraints in the context of linear fixed effects and mixed effects models. Although there exists a large body of literature for performing statistical inference under inequality constraints, user friendly statistical software for implementing such methods is lacking, especially in the context of linear fixed and mixed effects models. In this article we introduce CLME, a package in the R language that can be used for testing a broad collection of inequality constraints. It uses residual bootstrap based methodology which is reasonably robust to non-normality as well as heteroscedasticity. The package is illustrated using two data sets. The package also contains a graphical interface built using the shiny package.