Optimum stratification with two variates

For the 2×2 rectilinear stratification of a bivariate normal distribution with proportional and optimum allocation the dependence of the objective function z(x₁;y₁) on the coefficient of correlation ρ and the sampling fraction q=n/N is investigated. With proportional allocation for great values of ρ (but already for q=0) a so-called ρ-effect arises, which results in a saddle-point of z as “optimum” stratification point in the center of gravity of the distribution and two additional minima. With optimum allocation first for smaller values of q also the ρ-effect arises; for grater values of q a so-called q-effect is superposed, which results in a multitude of minima, saddle-points and maxima of z. All these points satisfy the generalized conditions of Dalenius, but for practical use only the global minimum is of interest.     

Non-parametric estimation of population size from capture–recapture data when the capture probability depends on a covariate

Summary.  In capture–recapture experiments the capture probabilities may depend on individual covariates such as an individual's weight or age. Typically this dependence is modelled through simple parametric functions of the covariates. Here we first demonstrate that misspecification of the model can produce biased estimates and subsequently develop a non-parametric procedure to estimate the functional relationship between the probability of capture and a single covariate. This estimator is then incorporated in a Horvitz–Thompson estimator to estimate the size of the population. The resulting estimators are evaluated in a simulation study and applied to a data set on captures of the Mountain Pygmy Possum.     

CURRICULUM CHANGES TO MEET CHALLENGES: PREPARING MFT STUDENTS FOR MANAGED CARE SETTINGS

Fledgling therapists who graduate from family therapy traning programs will have to navigate the world of managed care. In this article, faculty of University of San Diego share changes in its accredited training program that prepare students for practice in an increasingly multidisciplinary world where health maintenence organizations and other versions of managed care predominate. The paper touches on contextual issues, provides a detailed outline of coursework presenting basic knowledge and skills involved in clinical pracice in a managed care environment, and comments on clinical placements and the challenge of helping the next generation of clinicans "fit" into the future of health care delivery while maintaining their unique identity as family therapists.     

Methodological Approaches to Assessing Risk Perceptions Associated with Food-Related Hazards

The psychometric approach developed by Slovic and his co-workers has been effectively used to assess risk perceptions associated with different food-related hazards. However, further examination (using questionnaire data and partial correlation techniques) has indicated that technological hazards are highly differentiated from lifestyle hazards, in terms of both hazard control and knowledge about the hazard. Optimistic bias was also seen to vary between hazards. Further research has focused on a particular hazard, genetic engineering. Risk perceptions associated with genetic engineering are underpinned by ethical concern and questions relating to perceived need for the technology, as well as perceptions of risk or harm. However, increasing the specificity of hazard stimuli was found to alter the factor structure of underlying risk perceptions. The utility of preference mapping procedures in determining individual differences in trust in risk regulators is also discussed.     

Statistical methodology for assessing homology of intronic regions of genes

We consider the problem of statistically evaluating the similarity of DNA intronic regions of genes. Present algorithms are based on matching a sequence of interest with known DNA sequences in a gene bank and are designed primarily to assess homology among exonic regions of genes. Most research focuses on exonic regions because they have a clear biological significance, coding for proteins, and therefore tend to be more conserved in evolution than intronic regions. To investigate whether the intronic features of genes whose expression is highly sensitive to environmental perturbations differ from genes that have a more constant expression, a collection of oncogenes, tumor suppressor genes, and nonregulatory genes involved in energy metabolism are compared. An analysis of the features of these genes' intronic regions result in clustering by regulatory group. In addition, Billingsley's test for Markov structure (1961) suggests that 67% of the intronic regions in this collection of genes show evidence of nonrandom structure, indicating the possibility of a biological function for these regions. The result of Billingsley's test for homology is used as input to a clustering algorithm. The biological significance of this methodology lies in the identification of groups based on the intronic regions from genes of unknown function. With the advent of rapid sequencing techniques, there is a great need for statistical techniques to help identify the purpose of poorly understood portions of genes. These methods can be utilized to assess the functional group to which such a gene might possibly belong.     

Statistical mechanical analysis of the dynamics of learning in perceptrons

We describe the application of tools from statistical mechanics to analyse the dynamics of various classes of supervised learning rules in perceptrons. The character of this paper is mostly that of a cross between a biased non-encyclopaedic review and lecture notes: we try to present a coherent and self-contained picture of the basics of this field, to explain the ideas and tricks, to show how the predictions of the theory compare with (simulation) experiments, and to bring together scattered results. Technical details are given explicitly in an appendix. In order to avoid distraction we concentrate the references in a final section. In addition this paper contains some new results: (i) explicit solutions of the macroscopic equations that describe the error evolution for on-line and batch learning rules; (ii) an analysis of the dynamics of arbitrary macroscopic observables (for complete and incomplete training sets), leading to a general Fokker–Planck equation; and (iii) the macroscopic laws describing batch learning with complete training sets. We close the paper with a preliminary expose´ of ongoing research on the dynamics of learning for the case where the training set is incomplete (i.e. where the number of examples scales linearly with the network size).     

Some useful Wishart expectations based on the multivariatet-model

In this note we derive some useful expectations of some functions of the Wishart matrix based on the multivariatet-model. The results are generalizations of similar expectations of the usual Wishart matrix. Some applications are outlined.