Model Diagnostics in the presence of measurement error

The problem of using information available from one variable X to make inferenceabout another Y is classical in many physical and social sciences. In statistics this isoften done via regression analysis where mean response is used to model the data. Onestipulates the model Y = µ(X) +ɛ. Here µ(X) is the mean response at the predictor variable value X = x, and ɛ = Y - µ(X) is the error. In classical regression analysis, both (X; Y ) are observable and one then proceeds to make inference about the mean response function µ(X). In practice there are numerous examples where X is not available, but a variable Z is observed which provides an estimate of X. As an example, consider the herbicidestudy of Rudemo, et al. [3] in which a nominal measured amount Z of herbicide was applied to a plant but the actual amount absorbed by the plant X is unobservable. As another example, from Wang [5], an epidemiologist studies the severity of a lung disease, Y , among the residents in a city in relation to the amount of certain air pollutants. The amount of the air pollutants Z can be measured at certain observation stations in the city, but the actual exposure of the residents to the pollutants, X, is unobservable and may vary randomly from the Z-values. In both cases X = Z+error: This is the so called Berkson measurement error model.In more classical measurement error model one observes an unbiased estimator W of X and stipulates the relation W = X + error: An example of this model occurs when assessing effect of nutrition X on a disease. Measuring nutrition intake precisely within 24 hours is almost impossible. There are many similar examples in agricultural or medical studies, see e.g., Carroll, Ruppert and Stefanski [1] and Fuller [2], , among others. In this talk we shall address the question of fitting a parametric model to the re-gression function µ(X) in the Berkson measurement error model: Y = µ(X) + ɛ; X = Z + η; where η and ɛ are random errors with E(ɛ) = 0, X and η are d-dimensional, and Z is the observable d-dimensional r.v.

Decreased GyBAA Receptor Function in the Brain Stem during Pancreatic Regeneration in Rats

Gamma amino outyric acid is a major inhibitory neurotrarsr titter in the central nervous system. In the preset study sv, Have investigate(' the alteration of GABA receptor, In t he hrain stem of rats during pancreatic regeneration. Three groups of rats were used for the study: sham operated, 72 It and 7 days partially pancreatectonnsea. GABA was (juan- (ified by [H]GABA receptor iispiacement method. GABA receptor kin: 10, pat at i et•ers were studied by using the binding of F'.](iAhA as ligand to the Triton X-100 treated me,i1,;-:mes a1,J displacement with unlabelled GABA. GhRA,v receptor activity was studied by using the [` -1 h3cuculline and displacement with unlabellecV euculline. ;.\13A content significantly decreased (1' < (1.(101 ) it, 0-e brain stern during the regeneration of pancreas. 'I hl, high affinity (IAI3A receptor binding sho?:ed it sigii'f cant decrease in 131„.,\ (P < 11.01) and K,I 1).05) n 72 h and 7 days after partial pancreatee 'timv. ";:flhicuculline hin(Iing showed it signih eat, 'le ( r(, :,e in /Jn1,s and K,I (P < 0.001) in 72 h pa^.rcreaw,, mised rats when compared with sham wt--tt' as P,n and K,I reversed to near sham after 7 da,s of pancreatectomv. The results sugge,) that GAB A throur,r; ('GABA receptors in brain Atcem has a regulatory uie during active regeneration of pancreas which will have inunense clinical significance in the treatment of cliahetcs.

On the remoteness function in median graphs

A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x 2 V.G/ the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary median graphs with respect to their isometric embeddings in hypercubes. In particular, a relation between the vertices in a median graph G whose remoteness function is maximum (antimedian set of G) with the antimedian set of the host hypercube is found. While for odd profiles the antimedian set is an independent set that lies in the strict boundary of a median graph, there exist median graphs in which special even profiles yield a constant remoteness function. We characterize such median graphs in two ways: as the graphs whose periphery transversal number is 2, and as the graphs with the geodetic number equal to 2. Finally, we present an algorithm that, given a graph G on n vertices and m edges, decides in O.mlog n/ time whether G is a median graph with geodetic number 2

The median function on graphs with bounded profiles

The median of a profile = (u1, . . . , uk ) of vertices of a graph G is the set of vertices x that minimize the sum of distances from x to the vertices of . It is shown that for profiles with diameter the median set can be computed within an isometric subgraph of G that contains a vertex x of and the r -ball around x, where r > 2 − 1 − 2 /| |. The median index of a graph and r -joins of graphs are introduced and it is shown that r -joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles.