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

Impact and Cost-Effectiveness of Point-Of-Care CD4 Testing on the HIV Epidemic in South Africa.

Rapid diagnostic tools have been shown to improve linkage of patients to care. In the context of infectious diseases, assessing the impact and cost-effectiveness of such tools at the population level, accounting for both direct and indirect effects, is key to informing adoption of these tools. Point-of-care (POC) CD4 testing has been shown to be highly effective in increasing the proportion of HIV positive patients who initiate ART. We assess the impact and cost-effectiveness of introducing POC CD4 testing at the population level in South Africa in a range of care contexts, using a dynamic compartmental model of HIV transmission, calibrated to the South African HIV epidemic. We performed a meta-analysis to quantify the differences between POC and laboratory CD4 testing on the proportion linking to care following CD4 testing. Cumulative infections averted and incremental cost-effectiveness ratios (ICERs) were estimated over one and three years. We estimated that POC CD4 testing introduced in the current South African care context can prevent 1.7% (95% CI: 0.4% - 4.3%) of new HIV infections over 1 year. In that context, POC CD4 testing was cost-effective 99.8% of the time after 1 year with a median estimated ICER of US$4,468/DALY averted. In healthcare contexts with expanded HIV testing and improved retention in care, POC CD4 testing only became cost-effective after 3 years. The results were similar when, in addition, ART was offered irrespective of CD4 count, and CD4 testing was used for clinical assessment. Our findings suggest that even if ART is expanded to all HIV positive individuals and HIV testing efforts are increased in the near future, POC CD4 testing is a cost-effective tool, even within a short time horizon. Our study also illustrates the importance of evaluating the potential impact of such diagnostic technologies at the population level, so that indirect benefits and costs can be incorporated into estimations of cost-effectiveness

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

The feast of the Encaenia in the fourth century and in the ancient liturgical sources of Jerusalem.

The central concept in this thesis is the Encaenia, particularly the Jerusalem Encaenia of the Martyrium Basilica and the anniversary feast of the same name, but also other, lesser known, inaugurations of churches which occurred in the fourth century. The book commences with a review of the recent scholarship on early Christian buildings, the Holy Land, and the Jerusalem Encaenia feast. Chapter two discusses the appearance of "egkainia" in the Septuagint and early Christian literature before considering the first documented occasion of an encaenia feast, the inauguration of the basilica in Tyre. Chapter three is a detailed study of Constantine's 'New Jerusalem' from the finding of the Cross to the inauguration of the Martyrium basilica in 335. A distinction is drawn between the work of Constantine and the interpretation of Eusebius. The subsequent chapter draws attention to the growth and uniform pattern of imperial involvement in the inauguration of churches under Constantius, paying particular attention to the alleged Encaenia of an Alexandrian basilica by Athanasius without imperial consent. The study of the Jerusalem Encaenia, the anniversary of the Martyrium inauguration, commences in chapter five with an analysis of the feast in the Journal of Egeria and the brief account recorded by Sozomen. Both writers portray the Encaenia as a pilgrim feast. Chapter six examines the liturgical content of the feast reconstructed from the earliest Jerusalem lectionaries and calendar. The theology of the feast is discerned from the biblical texts prescribed for the liturgy. Many of the observations made in previous chapters are drawn together in chapter eight which proposes the Encaenia as a Christian interpretation of the Jewish feast of Tabernacles. The conclusion to the thesis discusses the prominence of the Jerusalem Encaenia in the liturgical calendar, and locates the rite and feast of the Encaenia within the wider context of the dedication of churches in the east and western liturgy. Further avenues of research are outlined regarding the rites and surviving homilies for the dedication of a church