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

The Company You Keep: Qualitative Uncertainty in Providing Club Goods

Clubs are typically experience goods. Potential members cannot ascertain precisely beforehand their quality (dependent endogenously on the club's facility investment and number of users, itself dependent on its pricing policy). Members with unsatisfactory initial experiences discontinue visits. We show that a monopoly profit maximiser never offers a free trial period for such goods but, for a quality function homogeneous of any feasible degree, a welfare maximiser always does. When the quality function is homogeneous of degree zero, the monopolist provides a socially excessive level of quality to repeat buyers. In other possible regimes, the monopolist permits too little club usage.Clubs, qualitative uncertainty, monopoly, welfarist

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

Mass segregation trends in SDSS galaxy groups

It has been shown that galaxy properties depend strongly on their host environment. In order to understand the relevant physical processes driving galaxy evolution it is important to study the observed properties of galaxies in different environments. Mass segregation in bound galaxy structures is an important indicator of evolutionary history and dynamical friction timescales. Using group catalogues derived from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) we investigate mass segregation trends in galaxy groups at low redshift. We investigate average galaxy stellar mass as a function of group-centric radius and find evidence for weak mass segregation in SDSS groups. The magnitude of the mass segregation depends on both galaxy stellar mass limits and group halo mass. We show that the inclusion of low mass galaxies tends to strengthen mass segregation trends, and that the strength of mass segregation tends to decrease with increasing group halo mass. We find the same trends if we use the fraction of massive galaxies as a function of group-centric radius as an alternative probe of mass segregation. The magnitude of mass segregation that we measure, particularly in high-mass haloes, indicates that dynamical friction is not acting efficiently.Comment: 6 pages, 2 figures, accepted for publication in MNRAS Letter

The Effect of Straw on the Behaviour of Sows in Tether Stalls

The behaviour of sows in tether stalls with and without straw was studied in two experiments. Sows lay down more when 1 kg of straw was provided daily, especially when it was chopped and mixed wet with the food (dietary effect). Sows without straw performed a variety of stereotyped oral and other activities which were greatly reduced by the provision of loose straw that could be chewed and manipulated throughout the day (recreational effect). Sows were frequently seen standing or sitting motionless with the head drooping, probably in a state of drowsiness. This behaviour was virtually eliminated by full straw bedding (bedding effect). Certain \u27comfort movements\u27, bar-biting at feeding time, and biting the neighbouring sows, were not influenced by straw. It is concluded that the dietary, recreational and bedding aspects of straw are all significant, but influence different aspects of the animals\u27 behaviour. The significance of bar-biting and other activities is discussed

Assessing Animal Welfare at the Farm and Group Level: The Interplay of Science and Values

In the social debate about animal welfare we can identify three different views about how animals should be raised and how their welfare should be judged: (1) the view that animals should be raised under conditions that promote good biological functioning in the sense of health, growth and reproduction, (2) the view that animals should be raised in ways that minimise suffering and promote contentment, and (3) the view that animals should be allowed to lead relatively natural lives. When attempting to assess animal welfare, different scientists select different criteria, reflecting one or more of these value-dependent views. Even when ostensibly covering all three views, scientists may differ in what they treat as inherently important versus only instrumentally important, and their selection of variables may be further influenced by a desire to use measures that are scientifically respected and can be scored objectively. Value assumptions may also enter animal welfare assessment at the farm and group level (1) when empirical data provide insufficient guidance on important issues, (2) when we need to weigh conflicting interests of different animals, and (3) when we need to weigh conflicting evidence from different variables. Although value assumptions cannot be eliminated from animal welfare assessment, they can be made more explicit as the first step in creating animal welfare assessment tools. Different value assumptions could lead to different welfare assessment tools, each claiming validity within a given set of assumptions

Mammals, Birds, and Butterflies at Sodium Sources in Northern Ontario Forests

Wildlife seen at natural sodium-rich springs and at roadside pools contaminated by highway de-icing salt in northern Ontario included two species of wild ungulates, one species of rodent, three species of birds, and two species of butterflies. The three birds were finches of the sub-family Carduelinae, noted for feeding almost exclusively on plant material. The mammalian species were also herbivorous. Apart from Porcupines (Erethizon dorsaturn), small mammals were rarely seen at the saltwater locations, perhaps because of their apparent preference to ingest salt in solid form rather than in water