Sequential Bahadur Efficiency

The notion of Bahadur efficiency for test statistics is extended to the sequential case and illustrated in the specific context of testing one-sided hypotheses about a normal mean. An analog of Bahadur\u27s theorem on the asymptotic optimality of the likelihood ratio statistic is seen to hold in the normal case. Some possible definitions of attained level for a sequential experiment are considered

Statistical Inference After Model Selection

Conventional statistical inference requires that a model of how the data were generated be known before the data are analyzed. Yet in criminology, and in the social sciences more broadly, a variety of model selection procedures are routinely undertaken followed by statistical tests and confidence intervals computed for a “final” model. In this paper, we examine such practices and show how they are typically misguided. The parameters being estimated are no longer well defined, and post-model-selection sampling distributions are mixtures with properties that are very different from what is conventionally assumed. Confidence intervals and statistical tests do not perform as they should. We examine in some detail the specific mechanisms responsible. We also offer some suggestions for better practice and show though a criminal justice example using real data how proper statistical inference in principle may be obtained

Properties of Bayes Sequential Tests

Consider the problem of sequentially testing composite, contiguous hypotheses where the risk function is a linear combination of the probability of error in the terminal decision and the expected sample size. Assume that the common boundary of the closures of the null and the alternative hypothesis is compact. Observations are independent and identically distributed. We study properties of Bayes tests. One property is the exponential boundedness of the stopping time. Another property is continuity of the risk functions. The continuity property is used to establish complete class theorems as opposed to the essentially complete class theorems in Brown, Cohen and Strawderman

Bounded Stopping Times for a Class of Sequential Bayes Tests

Consider the problem of sequentially testing a null hypothesis vs an alternative hypothesis when the risk function is a linear combination of probability of error in the terminal decision and expected sample size (i.e., constant cost per observation.) Assume that the parameter space is the union of null and alternative, the parameter space is convex, the intersection of null and alternative is empty, and the common boundary of the closures of null and alternative is nonempty and compact. Assume further that observations are drawn from a p-dimensional exponential family with an open p-dimensional parameter space. Sufficient conditions for Bayes tests to have bounded stopping times are given

Hot Dust Clouds with Pure Graphite Composition around Type-I Active Galactic Nuclei

We fitted the optical to mid-infrared (MIR) spectral energy distributions (SEDs) of ~15000 type-I, 0.75<z<2, active galactic nuclei (AGNs) in an attempt to constrain the properties of the physical component responsible for the rest-frame near-infrared (NIR) emission. We combine optical spectra from the Sloan Digital Sky Survey (SDSS) and MIR photometry from the preliminary data release of the Wide Infrared Survey Explorer (WISE). The sample spans a large range of AGN properties: luminosity, black hole mass, and accretion rate. Our model has two components: a UV-optical continuum source and very hot, pure-graphite dust clouds. We present the luminosity of the hot-dust component and its covering factor, for all sources, and compare it with the intrinsic AGN properties. We find that the hot-dust component is essential to explain the (rest) NIR emission in almost all AGNs in our sample, and that it is consistent with clouds containing pure-graphite grains and located between the dust-free broad line region (BLR) and the "standard" torus. The covering factor of this component has a relatively narrow distribution around a peak value of ~0.13, and it correlates with the AGN bolometric luminosity. We suggest that there is no significant correlation with either black hole mass or normalized accretion rate. The fraction of hot-dust-poor AGNs in our sample is ~15-20%, consistent with previous studies. We do not find a dependence of this fraction on redshift or source luminosity.Comment: Accepted for publication in ApJ

Simulation of Hyperspectral Images

A software package generates simulated hyperspectral imagery for use in validating algorithms that generate estimates of Earth-surface spectral reflectance from hyperspectral images acquired by airborne and spaceborne instruments. This software is based on a direct simulation Monte Carlo approach for modeling three-dimensional atmospheric radiative transport, as well as reflections from surfaces characterized by spatially inhomogeneous bidirectional reflectance distribution functions. In this approach, "ground truth" is accurately known through input specification of surface and atmospheric properties, and it is practical to consider wide variations of these properties. The software can treat both land and ocean surfaces, as well as the effects of finite clouds with surface shadowing. The spectral/spatial data cubes computed by use of this software can serve both as a substitute for, and a supplement to, field validation data

The Role of Relapse Prevention and Goal Setting in Training Transfer Enhancement

This article reviews the effect of two post-training transfer interventions (relapse prevention [RP] and goal setting [GS]) on trainees’ ability to apply skills gained in a training context to the workplace. Through a review of post-training transfer interventions literature, the article identifies a number of key issues that remain unresolved or underexplored, for example, the inconsistent results on the impact of RP on transfer of training, the lack of agreement on which GS types are more efficient to improve transfer performance, the lack of clarity about the distinction between RP and GS, and the underlying process through which these two post-training transfer interventions influence transfer of training. We offer some recommendations to overcome these problems and also provide guidance for future research on transfer of training

Detection of Gaseous Plumes using Basis Vectors

Detecting and identifying weak gaseous plumes using thermal imaging data is complicated by many factors. There are several methods currently being used to detect plumes. They can be grouped into two categories: those that use a chemical spectral library and those that don't. The approaches that use chemical libraries include physics-based least squares methods (matched filter). They are “optimal” only if the plume chemical is actually in the search library but risk missing chemicals not in the library. The methods that don't use a chemical spectral library are based on a statistical or data analytical transformation applied to the data. These include principle components, independent components, entropy, Fourier transform, and others. These methods do not explicitly take advantage of the physics of the signal formulation process and therefore don't exploit all available information in the data. This paper describes generalized least squares detection using gas spectra, presents a new detection method using basis vectors, and compares detection images resulting from applying both methods to synthetic hyperspectral data