A Picture Can Be Worth a Thousand Formulae - An Adventure in Model Fitting

We often teach in data analysis courses that one should look at the data before beginning any serious modeling endeavor. Indeed, visualization and modeling should go hand in hand. Each can inform the other and each process is enriched by the use of the other. Judicious use of graphics can save the practitioner from trying to fit overly-complicated models, while at the same time opening a window on interpretation. The power of simple plots as a tool for learning about moderately complex data structures is demonstrated via example.</p

Assessing the Effect of Individual Data Points on Inference from Empirical Likelihood

An oft-cited advantage of empirical likelihood is that the confidence intervals that are produced by this non-parametric technique are not necessarily symmetric. Rather, they reflect the nature of the underlying data and hence give a more representative way of reaching inferences about the functional of interest. However, this advantage can easily become a disadvantage if the resultant intervals are unduly influenced by some of the data points. In this paper, we consider the effect of extreme points, not necessarily outliers, on the profile empirical likelihood ratio and on empirical likelihood confidence intervals. In addition to suggesting diagnostics for detecting important observations, we examine the use of bootstrap and of jackknife influence functions to assess the extremity of suspect points.</p

The ASA's Statement on <i>p</i>-Values: Context, Process, and Purpose

The ASA's Statement on <i>p</i>-Values: Context, Process, and Purpos

Using Classical and Resampling Methods for Face Recognition based on Quantified Asymmetry Measures

Face recognition has important applications in psychology and biometric-based authentication, which increases the need for developing automatic face identification systems. Psychologists have long been studying the link between symmetry and attractiveness of the human face, but based on qualitative human judgment alone. The use of objective facial asymmetry information in automatic face recognition tasks is relatively new. The current paper presents a statistical analysis of the role of facial asymmetry measures in face recognition, under expression variation. We first describe a baseline classification method and show that the results are comparable with those based on certain popular (non-asymmetry based) classes of features used in computer vision. We find that facial asymmetry further improves upon the classification performance of these popular features by providing complementary information. Next, we consider two resampling methods to improve upon the baseline method used in previous work, and present a detailed comparison study. We demonstrate that resampling methods succeed in obtaining near perfect classification results on a database of 55 individuals, a statistically significant improvement over the baseline method. Results regarding the role of asymmetry of different parts of the face in distinguishing between individuals, expressions and between males and females are also reported as additional aspects of the study.</p

Thresholding of Statistical Maps in Functional Neuroimaging Using the False Discovery Rate

Thresholding of Statistical Maps in Functional Neuroimaging Using the False Discovery Rate

Persistence Terrace for Topological Inference of Point Cloud Data

<p>Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing function to convert the point cloud into a manifold and then apply persistent homology to a Morse filtration. A significant challenge is that this smoothing process involves the choice of a parameter and persistent homology is highly sensitive to that choice; moreover, important scale information is lost. We propose a novel topological summary plot, called a persistence terrace, that incorporates a wide range of smoothing parameters and is robust, multi-scale, and parameter-free. This plot allows one to isolate distinct topological signals that may have merged for any fixed value of the smoothing parameter, and it also allows one to infer the size and point density of the topological features. We illustrate our method in some simple settings where noise is a serious issue for existing frameworks and then we apply it to a real dataset by counting muscle fibers in a cross-sectional image. Supplementary material for this article is available online.</p

Corbelled Domes in Two and Three Dimensions: The Treasury of Atreus

Before the development of the true dome, many ancient cultures used the technique of corbelling to roof spaces. Recently, a series of related statistical models have been proposed in the literature for explaining how corbelled domes might have been constructed. The most sophisticated of these models is based on a piecewise linear structure, with an unknown number of changepoints, to guide the building process. This model is analyzed by the reversible jump Markov Chain Monte Carlo (MCMC) technique. All models considered to date have been two-dimensional, that is, they have taken a single cross section through the dome; even when more extensive data, in the form of measurements on multiple slices through the dome, have been available, these have been averaged together for the purposes of analysis. In this paper, we extend the two-dimensional analysis to a three-dimensional analysis, that takes full advantage of the data collected by the archaeologists and of the rotational symmetries inherent in the structure. We also explore ways of graphically presenting the results from a complex, reversible jump MCMC implementation, in order to check convergence, good mixing, and appropriate exploration of the (high dimensional and varying dimension) parameter space. The model and the graphical techniques are demonstrated on the Treasury of Atreus in Mycenae, Greece, one of the finest extant examples of the corbelling method.</p

Semantic-based Biomedical Image Indexing and Retrieval

This paper summarizes our work and our understanding on volumetric pathological neuroimage retrieval under the framework of classification-driven feature selection. The main effort concerns off-line image feature space reduction for improved image indexing feature discriminating power as well as reduced computational cost during on-line pathological neuroimage retrieval.</p