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

An evolutionarily stable joining policy for group foragers

For foragers that exploit patchily distributed resources that are challenging to locate, detecting discoveries made by others with a view to joining them and sharing the patch may often be an attractive tactic, and such behavior has been observed across many taxa. If, as will commonly be true, the time taken to join another individual on a patch increases with the distance to that patch, then we would expect foragers to be selective in accepting joining opportunities: preferentially joining nearby discoveries. If competition occurs on patches, then the profitability of joining (and of not joining) will be influenced by the strategies adopted by others. Here we present a series of models designed to illuminate the evolutionarily stable joining strategy. We confirm rigorously the previous suggestion that there should be a critical joining distance, with all joining opportunities within that distance being accepted and all others being declined. Further, we predict that this distance should be unaffected by the total availability of food in the environment, but should increase with decreasing density of other foragers, increasing speed of movement towards joining opportunities, increased difficulty in finding undiscovered food patches, and decreasing speed with which discovered patches can be harvested. We are further able to make predictions as to how fully discovered patches should be exploited before being abandoned as unprofitable, with discovered patches being more heavily exploited when patches are hard to find: patches can be searched for remaining food more quickly, forager density is low, and foragers are relatively slow in traveling to discovered patches

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

Effect of Preventive Home Visits by a Nurse on the Outcomes of Frail Elderly People in the Community: a randomized controlled trial

Background: Timely recognition and prevention of health problems among elderly people have been shown to improve their health. In this randomized controlled trial the authors examined the impact of preventive home visits by a nurse compared with usual care on the outcomes of frail elderly people living in the community. Methods: A screening questionnaire identified eligible participants (those aged 70 years or more at risk of sudden deterioration in health). Those randomly assigned to the visiting nurse group were assessed and followed up in their homes for 14 months. The primary outcome measure was the combined rate of deaths and admissions to an institution, and the secondary outcome measure the rate of health services utilization, during the 14 months; these rates were determined through a medical chart audit by a research nurse who was blind to group allocation. Results: The questionnaire was mailed to 415 elderly people, of whom 369 (88.9%) responded. Of these, 198 (53.7%) were eligible, and 142 consented to participate and were randomly assigned to either the visiting nurse group (73) or the usual care group (69). The combined rate of deaths and admissions to an institution was 10.0% in the visiting nurse group and 5.8% in the usual care group (p = 0.52). The rate of health services utilization did not differ significantly between the 2 groups. Influenza and pneumonia vaccination rates were significantly higher in the visiting nurse group (90.1% and 81.9%) than in the usual care group (53.0% and 0%) (p \u3c 0.001). Interpretation: The trial failed to show any effect of a visiting nurse other than vastly improved vaccination coverage

Screening Seniors for Risk of Functional Decline: Results of a Survey in Family Practice

To measure functional status, determine risk of functional decline and assess consistency between responses and standardized instruments. Design: A mailed survey which measured functional impairment, recent hospitalization and bereavement. A positive response on at least one of these factors indicated that the individual was “at risk” for functional decline. A random sample (n=73) of “at risk” subjects (specifically, family practice patients aged 70 and older) were assessed by a nurse. Results: The response rate was 89% (369/415), 59% of seniors were female and the mean age was 77.1 (SD=5.5) years. Self-reported risk, based on activities of daily living (ADLs), was associated with impairment in at least one basic ADL (p\u3c0.0005) using a standardized instrument. The positive predictive value of the survey for ADL impairment was 65%. Conclusion: Response to a mailed survey was high and self-reported ADL risks were consistent with findings from standardized assessment tools

Carrier dynamics in ion-implanted GaAs studied by simulation and observation of terahertz emission

We have studied terahertz (THz) emission from arsenic-ion implanted GaAs both experimentally and using a three-dimensional carrier dynamics simulation. A uniform density of vacancies was formed over the optical absorption depth of bulk GaAs samples by performing multi-energy implantations of arsenic ions (1 and 2.4MeV) and subsequent thermal annealing. In a series of THz emission experiments the frequency of peak THz power was found to increase significantly from 1.4 to 2.2THz when the ion implantation dose was increased from 10^13 to 10^16 cm-3. We used a semi-classical Monte-Carlo simulation of ultra-fast carrier dynamics to reproduce and explain these results. The effect of the ion-induced damage was included in the simulation by considering carrier scattering at neutral and charged impurities, as well as carrier trapping at defect sites. Higher vacancy concentrations and shorter carrier trapping times both contributed to shorter simulated THz pulses, the latter being more important over experimentally realistic parameter ranges.Comment: 6 pages, 7 figure

The quick and the dead: Finding the surviving binary companions of Galactic supernovae with Gaia

We use Gaia Data Release 2 to search for possible surviving binary companions to three of the best studied historical Milky Way core-collapse supernovae. Consistent with previous work, we find there to be no plausible binary companion to either the Crab or Cas A supernovae. For the first time, we present a systematic search for a former companion to the Vela supernova, and rule out essentially any surviving luminous ($>L_\odot$) companion. Based on parallax and proper motion, we identify a faint source (Star A; Gaia Source ID 5521955992667891584) which is kinematically consistent with being a former binary companion to the Vela SN progenitor. However, the inferred absolute magnitude of this source is extremely faint, raising the possibility that it may in fact be a background interloper. In addition, we derive a new distance ($3.37^{+4.04}_{-0.97}$ kpc) to the Crab SN based on the Gaia parallax measurements, which is significantly further than the 2 kpc distance typically adopted. Finally, we demonstrate that Gaia can be used to measure the secular decline in the luminosity of the Crab pulsar, and provide a new test of pulsar models.Comment: Revised version submitted to ApJ after referee repor

MobGeoSen: facilitating personal geosensor data collection and visualization using mobile phones

Mobile sensing and mapping applications are becoming more prevalent because sensing hardware is becoming more portable and more affordable. However, most of the hardware uses small numbers of fixed sensors that report and share multiple sets of environmental data which raises privacy concerns. Instead, these systems can be decentralized and managed by individuals in their public and private spaces. This paper describes a robust system called MobGeoSens which enables individuals to monitor their local environment (e.g. pollution and temperature) and their private spaces (e.g. activities and health) by using mobile phones in their day to day life