KDENS: Stata module for univariate kernel density estimation

kdens produces univariate kernel density estimates and graphs the result. kdens supplements official Stata's kdensity. Important additions are: adaptive (i.e. variable bandwidth) kernel density estimation, several automatic bandwidth selectors including the Sheather-Jones plug-in estimator, pointwise variability bands and confidence intervals, boundary correction for variables with bounded domain, fast binned approximation estimation. Note that the moremata package, also available from SSC, is required.

Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Sexual dimorphism dominates divergent host plant use in stick insect trophic morphology

Background: Clear examples of ecological speciation exist, often involving divergence in trophic morphology. However, substantial variation also exists in how far the ecological speciation process proceeds, potentially linked to the number of ecological axes, traits, or genes subject to divergent selection. In addition, recent studies highlight how differentiation might occur between the sexes, rather than between populations. We examine variation in trophic morphology in two host-plant ecotypes of walking-stick insects (Timema cristinae), known to have diverged in morphological traits related to crypsis and predator avoidance, and to have reached an intermediate point in the ecological speciation process. Here we test how host plant use, sex, and rearing environment affect variation in trophic morphology in this species using traditional multivariate, novel kernel density based and Bayesian morphometric analyses. Results: Contrary to expectations, we find limited host-associated divergence in mandible shape. Instead, the main predictor of shape variation is sex, with secondary roles of population of origin and rearing environment. Conclusion: Our results show that trophic morphology does not strongly contribute to host-adapted ecotype divergence in T. cristinae and that traits can respond to complex selection regimes by diverging along different intraspecific lines, thereby impeding progress toward speciation.

Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).