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

Habitat Use by Greater Snow Geese During the Brood-Rearing Period

Observations of habitat use by the Greater Snow Goose (Anser caerulescens atlanticus) were conducted at Jungersen Bay, northern Baffin Island, from 27 July-17 August 1981. Density of geese using the study area was estimated at 425 birds/sq km. The average of 2.8 young per family did not change during our study. Non-breeding geese were first observed in flight on 1 August and were seen regularly until 13 August. Three types of habitat used by geese during the brood-rearing period were distinguished: tidal marshes dominated by Carex subspathacea and Puccinellia phryganodes; wet moss-covered meadows with up to 5 cm of standing water, dominated by Carex stans, Dupontia fisheri, Calamagrostis neglecta, and Arctagrostis latifolia; and, around ponds, bands of vegetation 1-2 m wide dominated by Carex stans. The three most important species of monocots grazed by geese were Puccinellia phryganodes, Carex subspathacea, and C. stans. It is unlikely that habitat and food resources are limiting factors for Greater Snow Geese in the High Arctic during the brood-rearing period. We suggest that potential breeding areas for this species be identified and given special protection.Key words: Greater Snow Goose (Anser caerulescens atlanticus), habitat use, brood, Baffin Island, grazing, monocots, wet meadowsMots clés: Grande Oie Blanche (Anser caerulescens atlanticus), utilisation de l'habitat, élevage des jeunes, Terre de Baffin, alimentation, monocotylédones, zones humide

Historique de la psychiatrie de secteur québécoise

Pionnier de la première politique de santé mentale au Québec, demeurée non officielle, l'auteur en trace les suites depuis son adoption en 1962.Pioneer of the first mental health policy in Québec which remained unofficial, the author retraces what followed since its adoption in 1962