Second order ancillary: A differential view from continuity

Second order approximate ancillaries have evolved as the primary ingredient for recent likelihood development in statistical inference. This uses quantile functions rather than the equivalent distribution functions, and the intrinsic ancillary contour is given explicitly as the plug-in estimate of the vector quantile function. The derivation uses a Taylor expansion of the full quantile function, and the linear term gives a tangent to the observed ancillary contour. For the scalar parameter case, there is a vector field that integrates to give the ancillary contours, but for the vector case, there are multiple vector fields and the Frobenius conditions for mutual consistency may not hold. We demonstrate, however, that the conditions hold in a restricted way and that this verifies the second order ancillary contours in moderate deviations. The methodology can generate an appropriate exact ancillary when such exists or an approximate ancillary for the numerical or Monte Carlo calculation of $p$-values and confidence quantiles. Examples are given, including nonlinear regression and several enigmatic examples from the literature.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ248 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Vehicle Steering control: A model of learning

A hierarchy of strategies were postulated to describe the process of learning steering control. Vehicle motion and steering control data were recorded for twelve novices who drove an instrumented car twice a week during and after a driver training course. Car-driver describing functions were calculated, the probable control structure determined, and the driver-alone transfer function modelled. The data suggested that the largest changes in steering control with learning were in the way the driver used the lateral position cue

Higher Accuracy for Bayesian and Frequentist Inference: Large Sample Theory for Small Sample Likelihood

Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual evaluation of such $p$-values is by simulations, and such simulations do verify that the global distribution of the $p$-values is uniform(0, 1), to high accuracy in repeated sampling. The derivation of the $p$-values, however, asserts a stronger statement, that they have a uniform(0, 1) distribution conditionally, given identified precision information provided by the data. We take a simple regression example that involves exact precision information and use large sample techniques to extract highly accurate information as to the statistical position of the data point with respect to the parameter: specifically, we examine various $p$-values and Bayesian posterior survivor $s$-values for validity. With observed data we numerically evaluate the various $p$-values and $s$-values, and we also record the related general formulas. We then assess the numerical values for accuracy using Markov chain Monte Carlo (McMC) methods. We also propose some third-order likelihood-based procedures for obtaining means and variances of Bayesian posterior distributions, again followed by McMC assessment. Finally we propose some adaptive McMC methods to improve the simulation acceptance rates. All these methods are based on asymptotic analysis that derives from the effect of additional data. And the methods use simple calculations based on familiar maximizing values and related informations. The example illustrates the general formulas and the ease of calculations, while the McMC assessments demonstrate the numerical validity of the $p$-values as percentage position of a data point. The example, however, is very simple and transparent, and thus gives little indication that in a wide generality of models the formulas do accurately separate information for almost any parameter of interest, and then do give accurate $p$-value determinations from that information. As illustration an enigmatic problem in the literature is discussed and simulations are recorded; various examples in the literature are cited.Comment: Published in at http://dx.doi.org/10.1214/07-STS240 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Beam Dynamics Studies for the HIE-ISOLDE Linac at CERN

The upgrade of the normal conducting (NC) Radioactive Ion Beam EXperiment (REX)-ISOLDE heavy ion accelerator at CERN, under the High Intensity and Energy (HIE)-ISOLDE framework, proposes the use of superconducting (SC) quarter-wave resonators (QWRs) to increase the energy capability of the facility from 3 MeV/u to beyond 10 MeV/u. A beam dynamics study of a lattice design comprising SC QWRs and SC solenoids has confirmed the design's ability to accelerate ions, with a mass-to-charge ratio in the range 2.5 < A/q < 4.5, to the target energy with a minimal emittance increase. We report on the development of this study to include the implementation of realistic fields within the QWRs and solenoids. A preliminary error study is presented in order to constrain tolerances on the manufacturing and alignment of the linac.Comment: 3 pages, 8 figures, 1 table, submitted to the Particle Accelerator Conference (PAC) 2009 in Vancouver. Page formatting changed to US letter siz

The Mass, Orbit, and Tidal Evolution of the Quaoar-Weywot System

Here we present new adaptive optics observations of the Quaoar-Weywot system. With these new observations we determine an improved system orbit. Due to a 0.39 day alias that exists in available observations, four possible orbital solutions are available with periods of $\sim11.6$, $\sim12.0$, $\sim12.4$, and $\sim12.8$ days. From the possible orbital solutions, system masses of $1.3-1.5\pm0.1\times10^{21}$ kg are found. These observations provide an updated density for Quaoar of 2.7-5.0{g cm^{-3}}. In all cases, Weywot's orbit is eccentric, with possible values $\sim0.13-0.16$. We present a reanalysis of the tidal orbital evolution of the Quoaor-Weywot system. We have found that Weywot has probably evolved to a state of synchronous rotation, and have likely preserved their initial inclinations over the age of the Solar system. We find that for plausible values of the effective tidal dissipation factor tides produce a very slow evolution of Weywot's eccentricity and semi-major axis. Accordingly, it appears that Weywot's eccentricity likely did not tidally evolve to its current value from an initially circular orbit. Rather, it seems that some other mechanism has raised its eccentricity post-formation, or Weywot formed with a non-negligible eccentricity.Comment: Accepted to Icarus, Nov. 8 201

Modulation of individual components of gastric motor response to duodenal glucose

AIM: To evaluate individual components of the antro-pyloro-duodenal (APD) motor response to graded small intestinal glucose infusions in healthy humans. METHODS: APD manometry was performed in 15 healthy subjects (12 male; 40 ± 5 years, body mass index 26.5 ± 1.6 kg/m2) during four 20-min intraduodenal infusions of glucose at 0, 0.5, 1.0 and 1.5 kcal/min, in a randomised double-blinded fashion. Glucose solutions were infused at a rate of 1 mL/min and separated by 40-min “wash-out” period. Data are mean ± SE. Inferential analyses are repeated measure analysis of variance with Bonferroni post-hoc testing. RESULTS: At 0 kcal/min frequency of pressure waves were: antrum (7.5 ± 1.8 waves/20 min) and isolated pyloric pressure waves (IPPWs) (8.0 ± 2.3 waves/20 min) with pyloric tone (0.0 ± 0.9 mmHg). Intraduodenal glucose infusion acutely increased IPPW frequency (P < 0.001) and pyloric tone (P = 0.015), and decreased antral wave frequency (P = 0.007) in a dose-dependent fashion. A threshold for stimulation was observed at 1.0 kcal/min for pyloric phasic pressure waves (P = 0.002) and 1.5 kcal/min for pyloric tone and antral contractility. CONCLUSION: There is hierarchy for the activation of gastrointestinal motor responses to duodenal glucose infusion. An increase in IPPWs is the first response observed.Adam M Deane, Laura K Besanko, Carly M Burgstad, Marianne J Chapman, Michael Horowitz, Robert JL Frase

Potential solar axion signatures in X-ray observations with the XMM-Newton observatory

The soft X-ray flux produced by solar axions in the Earth's magnetic field is evaluated in the context of ESA's XMM-Newton observatory. Recent calculations of the scattering of axion-conversion X-rays suggest that the sunward magnetosphere could be an observable source of 0.2-10 keV photons. For XMM-Newton, any conversion X-ray intensity will be seasonally modulated by virtue of the changing visibility of the sunward magnetic field region. A simple model of the geomagnetic field is combined with the ephemeris of XMM-Newton to predict the seasonal variation of the conversion X-ray intensity. This model is compared with stacked XMM-Newton blank sky datasets from which point sources have been systematically removed. Remarkably, a seasonally varying X-ray background signal is observed. The EPIC count rates are in the ratio of their X-ray grasps, indicating a non-instrumental, external photon origin, with significances of 11(pn), 4(MOS1) and 5(MOS2) sigma. After examining the constituent observations spatially, temporally and in terms of the cosmic X-ray background, we conclude that this variable signal is consistent with the conversion of solar axions in the Earth's magnetic field. The spectrum is consistent with a solar axion spectrum dominated by bremsstrahlung- and Compton-like processes, i.e. axion-electron coupling dominates over axion-photon coupling and the peak of the axion spectrum is below 1 keV. A value of 2.2e-22 /GeV is derived for the product of the axion-photon and axion-electron coupling constants, for an axion mass in the micro-eV range. Comparisons with limits derived from white dwarf cooling may not be applicable, as these refer to axions in the 0.01 eV range. Preliminary results are given of a search for axion-conversion X-ray lines, in particular the predicted features due to silicon, sulphur and iron in the solar core, and the 14.4 keV transition line from 57Fe.Comment: Accepted for publication in MNRAS. 67 pages total, including 39 figures, 6 table