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

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

Rejoinder to "Is Bayes Posterior just Quick and Dirty Confidence?"

Rejoinder to "Is Bayes Posterior just Quick and Dirty Confidence?" by D. A. S. Fraser [arXiv:1112.5582]Comment: Published in at http://dx.doi.org/10.1214/11-STS352REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rating Harms to Wildlife: A Survey Showing Convergence between Conservation and Animal Welfare Views

Human activities may cause conservation concerns when animal populations or ecosystems are harmed and animal welfare concerns when individuals are harmed. In general, people are concerned with one or the other, as the concepts may be regarded as separate or even at odds. An online purposive survey of 339 British Columbians explored differences between groups that varied by gender, residency, wildlife engagement level and value orientation (conservation-oriented or animal welfare-oriented), to see how they rated the level of harm to wildlife caused by different human activities. Women, urban residents, those with low wildlife engagement, and welfare-orientated participants generally scored activities as more harmful than their counterparts, but all groups were very similar in their rankings. Activities that destroy or alter habitat (urban development, pollution, resource development and agriculture) were rated consistently as most harmful by all groups, including the most conservation-oriented and the most welfare-oriented. Where such a high level of agreement exists, wildlife managers should be able to design management actions that will address both conservation and animal welfare concerns. However, the higher level of concern expressed by female, low engagement and welfare-oriented participants for activities that involve direct killing indicates a need for wildlife managers to consult beyond traditional stakeholders

Rating Harms to Wildlife: A Survey Showing Convergence between Conservation and Animal Welfare Views

Human activities may cause conservation concerns when animal populations or ecosystems are harmed and animal welfare concerns when individuals are harmed. In general, people are concerned with one or the other, as the concepts may be regarded as separate or even at odds. An online purposive survey of 339 British Columbians explored differences between groups that varied by gender, residency, wildlife engagement level and value orientation (conservation-oriented or animal welfare-oriented), to see how they rated the level of harm to wildlife caused by different human activities. Women, urban residents, those with low wildlife engagement, and welfare-orientated participants generally scored activities as more harmful than their counterparts, but all groups were very similar in their rankings. Activities that destroy or alter habitat (urban development, pollution, resource development and agriculture) were rated consistently as most harmful by all groups, including the most conservation-oriented and the most welfare-oriented. Where such a high level of agreement exists, wildlife managers should be able to design management actions that will address both conservation and animal welfare concerns. However, the higher level of concern expressed by female, low engagement and welfare-oriented participants for activities that involve direct killing indicates a need for wildlife managers to consult beyond traditional stakeholders

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

An Attempt to Estimate Teat Quality of Sows by Hand Milking During Farrowing

For 21 sows, teats were hand milked individually in a standard way during farrowing in an attempt to produce an index of teat quality. The piglets\u27 teat selection and 14-day weights were then compared with the hand milking results. Of within-litter variation in 14-day weight, 38.67% was explained by 1-day weight, and only 4.6% extra variation by the index derived from hand milking. Use of the index gave no improvement over previous models involving 1-day weight and teat number (anterior to posterior). Hand milking showed a pronounced decline in colostrum yield from the most anterior teat pair (46.8 g) to the most posterior (13.7 g); this may help to explain the piglets\u27 strong tendency to select anterior positions. Piglets of high, medium and low 1-day weight differed significantly in liveweight gain, but not in their selection of anterior or posterior teats