Response to the Letter to the Editor

This paper has attracted interest around the world from the media (both TV and newspapers). In addition, we have received letters, emails and telephone calls. One of our favorites was a voicemail message asking us to return a call to Australia at which point we would learn who really killed JFK. We welcome the opportunity to respond to the letter to the editor from Mr. Fiorentino. Mr. Fiorentino claims that our ``statement relating to the likelihood of a second assassin based on the premise of three or more separate bullets is demonstrably false.'' In response we would like to simply quote from page 327 of Gerald Posner's book Case Closed, one of the most well known works supporting the single assassin theory: ``If Connally was hit by another bullet, it had to be fired from a second shooter, since the Warren Commission's own reconstructions showed that Oswald could not have operated the bolt and refired in 1.4 seconds.'' Mr. Fiorentino also claims that the ``second fatal flaw is the use of a rather uncomplicated formula based on Bayes Theorem.'' Let $E$ denote the evidence and $T$ denote the theory that there were just two bullets (and hence a single shooter). We used Bayes Theorem to hypothetically calculate $P(T|E)$ from $P(E|T)$ and the prior probability $P(T)$. In order to make $P(T|E)$ ten times more likely than $P(\bar{T}|E)$, the ratio of the prior probabilities [i.e., $P(T) / P(\bar{T})$] would have to be greater than 15. Thus, we again conclude that this casts serious doubt on Dr. Guinn's conclusion that the evidence supported just two bullets. Sadly, this is far from the first time that probability has been misunderstood and/or misapplied in a case of public interest. A notable British example is the Clark case. See Nobles and Schiff (2005) for details. Finally, we welcome and, in fact, encourage members of the scientific community to provide alternative analyses of the data.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS154 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Morphological Classification of Galaxies by Shapelet Decomposition in the Sloan Digital Sky Survey II: Multiwavelength Classification

We describe the application of the `shapelet' linear decomposition of galaxy images to multi-wavelength morphological classification using the $u,g,r,i,$ and $z$-band images of 1519 galaxies from the Sloan Digital Sky Survey. We utilize elliptical shapelets to remove to first-order the effect of inclination on morphology. After decomposing the galaxies we perform a principal component analysis on the shapelet coefficients to reduce the dimensionality of the spectral morphological parameter space. We give a description of each of the first ten principal component's contribution to a galaxy's spectral morphology. We find that galaxies of different broad Hubble type separate cleanly in the principal component space. We apply a mixture of Gaussians model to the 2-dimensional space spanned by the first two principal components and use the results as a basis for classification. Using the mixture model, we separate galaxies into three classes and give a description of each class's physical and morphological properties. We find that the two dominant mixture model classes correspond to early and late type galaxies, respectively. The third class has, on average, a blue, extended core surrounded by a faint red halo, and typically exhibits some asymmetry. We compare our method to a simple cut on $u-r$ color and find the shapelet method to be superior in separating galaxies. Furthermore, we find evidence that the $u-r=2.22$ decision boundary may not be optimal for separation between early and late type galaxies, and suggest that the optimal cut may be $u-r \sim 2.4$.Comment: 42 pages, 18 figs, revised version in press at AJ. Some modification to the technique, more discussion, addition/deletion/modification of several figures, color figures have been added. A high resolution version may be obtained at http://bllac.as.arizona.edu/~bkelly/shapelets/shapelets_ugriz.ps.g

A kernel extension to handle missing data

An extension for univariate kernels that deals with missing values is proposed. These extended kernels are shown to be valid Mercer kernels and can adapt to many types of variables, such as categorical or continuous. The proposed kernels are tested against standard RBF kernels in a variety of benchmark problems showing different amounts of missing values and variable types. Our experimental results are very satisfactory, because they usually yield slight to much better improvements over those achieved with standard methods.Postprint (author’s final draft

A 2dF spectroscopic study of globular clusters in NGC 5128: Probing the formation history of the nearest giant Elliptical

We have performed a spectroscopic study of globular clusters (GCs) in the giant elliptical NGC 5128 using the 2dF facility at the Anglo-Australian telescope. We obtained integrated optical spectra for a total of 254 GCs, 79 of which are newly confirmed on the basis of their radial velocities and spectra. In addition, we obtained an integrated spectrum of the galaxy starlight along the southern major axis. We derive an empirical metallicity distribution function (MDF) for 207 GCs (~14 of the estimated total GC system) based upon Milky Way GCs. This MDF is multimodal at high statistical significance with peaks at [Z/H]~-1.3 and -0.5. A comparison between the GC MDF and that of the stellar halo at 20 kpc (~4 Reff) reveals close coincidence at the metal-rich ends of the distributions. However, an inner 8 kpc stellar MDF shows a clear excess of metal-rich stars when compared to the GCs. We compare a higher S/N subsample (147 GCs) with two stellar population models which include non-solar abundance ratio corrections. The vast majority of our sample (~90%) appears old, with ages similar to the Milky Way GC system. There is evidence for a population of intermediate-age (~4-8 Gy) GCs (<15% of the sample) which are on average more metal-rich than the old GCs. We also identify at least one younger cluster (~1-2 Gy) in the central regions of the galaxy. Our observations are consistent with a picture where NGC 5128 has undergone at least two mergers and/or interactions involving star formation and limited GC formation since z=1, however the effect of non-canonical hot stellar populations on the integrated spectra of GCs remains an outstanding uncertainty in our GC age estimates.Comment: 17 figures, some long table

Sampling Plans for Control-Inspection Schemes Under Independent and Dependent Sampling Designs With Applications to Photovoltaics

The evaluation of produced items at the time of delivery is, in practice, usually amended by at least one inspection at later time points. We extend the methodology of acceptance sampling for variables for arbitrary unknown distributions when additional sampling infor- mation is available to such settings. Based on appropriate approximations of the operating characteristic, we derive new acceptance sampling plans that control the overall operating characteristic. The results cover the case of independent sampling as well as the case of dependent sampling. In particular, we study a modified panel sampling design and the case of spatial batch sampling. The latter is advisable in photovoltaic field monitoring studies, since it allows to detect and analyze local clusters of degraded or damaged modules. Some finite sample properties are examined by a simulation study, focusing on the accuracy of estimation

Devolution dynamics of Spanish local government

Over the last few years, ther has been a devolutionary tendency in many developed and developing countries. In this article we propose a methodology to decompose whether the benefits in terms of effciency derived from transfers of powers from higher to municipal levels of government "the "economic dividend" of devolution) might increase over time. This methodology is based on linear programming approaches for effciency measurement. We provide anapplication to Spanish municipalities, which have had to adapt to both the European Stability and Growth Pact as well as to domestic regulation seeking local governments balanced budget. Results indicate that efficiency gains from enhaced decentralization have increased over time. However, the way through which these gains accrue differs across municipalities -in some cases technical change is the main component, whereas in others catching up dominates

Contingent Kernel Density Estimation

Kernel density estimation is a widely used method for estimating a distribution based on a sample of points drawn from that distribution. Generally, in practice some form of error contaminates the sample of observed points. Such error can be the result of imprecise measurements or observation bias. Often this error is negligible and may be disregarded in analysis. In cases where the error is non-negligible, estimation methods should be adjusted to reduce resulting bias. Several modifications of kernel density estimation have been developed to address specific forms of errors. One form of error that has not yet been addressed is the case where observations are nominally placed at the centers of areas from which the points are assumed to have been drawn, where these areas are of varying sizes. In this scenario, the bias arises because the size of the error can vary among points and some subset of points can be known to have smaller error than another subset or the form of the error may change among points. This paper proposes a “contingent kernel density estimation” technique to address this form of error. This new technique adjusts the standard kernel on a point-by-point basis in an adaptive response to changing structure and magnitude of error. In this paper, equations for our contingent kernel technique are derived, the technique is validated using numerical simulations, and an example using the geographic locations of social networking users is worked to demonstrate the utility of the method

Markov models for ocular fixation locations in the presence and absence of colour

In response to the 2015 Royal Statistical Society's statistical analytics challenge, we propose to model the fixation locations of the human eye when observing a still image by a Markov point process in R$_{2}$. Our approach is data driven using $\textit{k}$-means clustering of the fixation locations to identify distinct salient regions of the image, which in turn correspond to the states of our Markov chain. Bayes factors are computed as the model selection criterion to determine the number of clusters. Furthermore, we demonstrate that the behaviour of the human eye differs from this model when colour information is removed from the given image.This work was supported by UK Engineering and Physical Sciences Research Council grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, Cambridge Centre for Analysis

Brood parasitism, provisioning rates and breeding phenology of male and female magpie hosts

Parental care is a costly behaviour that raises the prospects of offspring survival. In species with biparental care these costs are shared by both parents, although there may be a conflict regarding the relative investment of each sex. Avian brood parasites leave all the costs of rearing offspring to their hosts. The magnitude of these costs and their consequences on the relative role of both sexes in parental care and future reproduction remain mostly unknown. Here, we investigate whether provisioning rate of nestlings by magpie hosts Pica pica differs between broods parasitized by the great spotted cuckoo Clamator glandarius and non-parasitized broods, and whether the relative contribution of each sex to provisioning is affected by parasitism. Furthermore, we explore the effect of parasitism on magpie’s future reproduction. We found that provisioning rate was similar in parasitized and non-parasitized broods, and that the relative contribution of males and females was also similar, irrespectively of the parasitism status. However, rearing parasitic offspring seems to have a negative long-term effect on magpie’s breeding phenology in the following breeding season. Our results suggest that, although brood parasitism by great spotted cuckoos does not seem to influence the relative contribution of both sexes to parental care, it may entail long-term extra costs in terms of breeding delay for magpies.Junta de Andalucía (Proyecto P06-RNM-01862)Ministerio de Ciencia (proyecto CGL2014-55362-P)Programa Juan de la Cierva –Incorporación (IJC2018-036411-I)German Research Foundation (SFB TRR 212 (NC3) – Projectos n. 316099922 y 396782608