Inference for bounded parameters

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive discussion by statisticians. The primary focus however in [1] and the accompanying discussion is on the construction of a confidence interval. We argue that the likelihood function and $p$-value function provide a comprehensive presentation of the information available from the model and the data. This is illustrated for Gaussian and Poisson models with lower bounds for the mean parameter

Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings

We report on thermal noise from the internal friction of dielectric coatings made from alternating layers of Ta2O5 and SiO2 deposited on fused silica substrates. We present calculations of the thermal noise in gravitational wave interferometers due to optical coatings, when the material properties of the coating are different from those of the substrate and the mechanical loss angle in the coating is anisotropic. The loss angle in the coatings for strains parallel to the substrate surface was determined from ringdown experiments. We measured the mechanical quality factor of three fused silica samples with coatings deposited on them. The loss angle of the coating material for strains parallel to the coated surface was found to be (4.2 +- 0.3)*10^(-4) for coatings deposited on commercially polished slides and (1.0 +- 0.3)*10^{-4} for a coating deposited on a superpolished disk. Using these numbers, we estimate the effect of coatings on thermal noise in the initial LIGO and advanced LIGO interferometers. We also find that the corresponding prediction for thermal noise in the 40 m LIGO prototype at Caltech is consistent with the noise data. These results are complemented by results for a different type of coating, presented in a companion paper.Comment: Submitted to LSC (internal) review Sept. 20, 2001. To be submitted to Phys. Lett.

Recent and future trends in synthetic greenhouse gas radiative forcing

Atmospheric measurements show that emissions of hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons are now the primary drivers of the positive growth in synthetic greenhouse gas (SGHG) radiative forcing. We infer recent SGHG emissions and examine the impact of future emissions scenarios, with a particular focus on proposals to reduce HFC use under the Montreal Protocol. If these proposals are implemented, overall SGHG radiative forcing could peak at around 355 mW m[superscript −2] in 2020, before declining by approximately 26% by 2050, despite continued growth of fully fluorinated greenhouse gas emissions. Compared to “no HFC policy” projections, this amounts to a reduction in radiative forcing of between 50 and 240 mW m[superscript −2] by 2050 or a cumulative emissions saving equivalent to 0.5 to 2.8 years of CO2 emissions at current levels. However, more complete reporting of global HFC emissions is required, as less than half of global emissions are currently accounted for.Natural Environment Research Council (Great Britain) (Advanced Research Fellowship NE/I021365/1)United States. National Aeronautics and Space Administration (Upper Atmospheric Research Program Grant NNX11AF17G)United States. National Oceanic and Atmospheric Administratio

An experimental investigation of yarn tension in simulated ring spinning

Yarn tension is a key factor that affects the efficiency of a ring spinning system. In this paper, a specially constructed rig, which can rotate a yarn at a high speed without inserting any real twist into the yarn, was used to simulate a ring spinning process. Yarn tension was measured at the guide-eye during the simulated spinning of different yarns at various balloon heights and with varying yarn length in the balloon. The effect of balloon shape, yarn hairiness and thickness, and yarn rotating speed, on the measured yarn tension, was examined. The results indicate that the collapse of balloon shape from single loop to double loop, or from double loop to triple etc, lead to sudden reduction in yarn tension. Under otherwise identical conditions, a longer length of yarn in the balloon gives a lower yarn tension at the guide-eye. In addition, thicker yarns and/or more hairy yarns generate a higher tension in the yarn, due to the increased air drag acting on the thicker or more hairy yarns

Status of the HIE-ISOLDE project at CERN

The HIE-ISOLDE project represents a major upgrade of the ISOLDE nuclear facility with a mandate to significantly improve the quality and increase the intensity and energy of radioactive nuclear beams produced at CERN. The project will expand the experimental nuclear physics programme at ISOLDE by focusing on an upgrade of the existing Radioactive ion beam EXperiment (REX) linac with a 40 MV superconducting linac comprising thirty-two niobium-on-copper sputter-coated quarter-wave resonators housed in six cryomodules. The new linac will raise the energy of post-accelerated beams from 3 MeV/u to over 10 MeV/u. The upgrade will be staged to first deliver beam energies of 5.5 MeV/u using two high-$\beta$ cryomodules placed downstream of REX, before the energy variable section of the existing linac is replaced with two low-$\beta$ cryomodules and two additional high-$\beta$ cryomodules are installed to attain over 10 MeV/u with full energy variability above 0.45 MeV/u. An overview of the project including a status summary of the different R&D activities and the schedule will outlined.Comment: 7 pages, 12 figures, submitted to the Heavy Ion Accelerator Technology conference (HIAT) 2012, in Chicag

Fractal-like Distributions over the Rational Numbers in High-throughput Biological and Clinical Data

Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are some examples of such technologies. Extracting meaningful information from those technologies requires careful analysis of the large volumes of data they produce. In this note, we present a set of distributions that commonly appear in the analysis of such data. These distributions present some interesting features: they are discontinuous in the rational numbers, but continuous in the irrational numbers, and possess a certain self-similar (fractal-like) structure. The first set of examples which we present here are drawn from a high-throughput sequencing experiment. Here, the self-similar distributions appear as part of the evaluation of the error rate of the sequencing technology and the identification of tumorogenic genomic alterations. The other examples are obtained from risk factor evaluation and analysis of relative disease prevalence and co-mordbidity as these appear in electronic clinical data. The distributions are also relevant to identification of subclonal populations in tumors and the study of the evolution of infectious diseases, and more precisely the study of quasi-species and intrahost diversity of viral populations

Advancing the Sea Ice Hypothesis: Trophic Interactions Among Breeding Pygoscelis Penguins With Divergent Population Trends Throughout the Western Antarctic Peninsula

We evaluated annual and regional variation in the dietary niche of Pygoscelis penguins including the sea ice-obligate Adélie penguin (Pygoscelis adeliae), and sea ice-intolerant chinstrap (Pygoscelis antarcticus) and gentoo (Pygoscelis papua) penguins, three species that nest throughout the western Antarctic Peninsula (AP) to test the sea ice trophic interaction hypothesis, which posits that penguin breeding populations with divergent trends, i.e., declining or increasing, are reliant on differing food webs. Our study relies on values of naturally occurring carbon (13C/12C, δ13C) and nitrogen (15N/14N, δ15N) stable isotopes as integrated proxies of penguin food webs measuredover three years at three different breeding colonies. At Anvers Island in the north, where reductions in sea ice and changes in breeding population trends among sympatric sea ice-obligate (Adélie) and sea ice-intolerant (chinstrap and gentoo) penguins have been most notable, our analyses show that all three species of Pygoscelis penguins became more similar isotopically over the reproductive period

A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

Inferential models: A framework for prior-free posterior probabilistic inference

Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to achieve this goal but, to date, none has given a completely satisfactory picture. This paper presents a new framework for probabilistic inference, based on inferential models (IMs), which not only provides data-dependent probabilistic measures of uncertainty about the unknown parameter, but does so with an automatic long-run frequency calibration property. The key to this new approach is the identification of an unobservable auxiliary variable associated with observable data and unknown parameter, and the prediction of this auxiliary variable with a random set before conditioning on data. Here we present a three-step IM construction, and prove a frequency-calibration property of the IM's belief function under mild conditions. A corresponding optimality theory is developed, which helps to resolve the non-uniqueness issue. Several examples are presented to illustrate this new approach.Comment: 29 pages with 3 figures. Main text is the same as the published version. Appendix B is an addition, not in the published version, that contains some corrections and extensions of two of the main theorem