Asymptotic properties of bivariate k-means clusters

A bounded region in R² with a uniform density function defined over it is partitioned into k sub-regions such that the within cluster sum of squares is minimized. An asymptotic (k+∞) lower bound for the within cluster sum of squares of this optimal k-means partition is obtained. This lower bound is useful in suggesting that the graph-configuration of the optimal k-partition would consist of regular hexagons of equal size when k is large enough. An empirical study illustrating these asymptotic properties of blvariate k-means cluster is also presented.     

Implementation of recursive nonparametric kernel estimation and a monte carlo study on its finite sample properties

The recursive estimator for the conditional mean of a nonparametric regression model with independent observations was thoroughly explored by Ahmad and Lin (1976), and Singh and Ullah (1986). Their studies are mainly concerned with the estimator's asymptotic behaviour. However, they do not include much discussion on the strategy of computing the estimates. In this paper, we provide a convenient implementation of the recursive estimator and examine its finite sample properties through simulation studies. Our study has demonstrated that for relatively short length of recursive updating, the estimates are generally equivalent to their fixed window width counterparts However, we found that substantial recursive updating can seriously lower the estimator's efficiency even though it is a consistent estimator.     

Regression analysis with partially labelled regressors: carbon dating of the Shroud of Turin

The twelve results from the 1988 radio carbon dating of the Shroud of Turin show surprising heterogeneity. We try to explain this lack of homogeneity by regression on spatial coordinates. However, although the locations of the samples sent to the three laboratories involved are known, the locations of the 12 subsamples within these samples are not. We consider all 387,072 plausible spatial allocations and analyse the resulting distributions of statistics. Plots of robust regression residuals from the forward search indicate that some sets of allocations are implausible. We establish the existence of a trend in the results and suggest how better experimental design would have enabled stronger conclusions to have been drawn from this multi-centre experiment.     

The structure and substance of automobile racing, or how hi-tech keeps its greasy side down

Automobile racing is approached as a feature of advanced capitalist society. First, the organized sport of automobile racing is considered in a Levi-Straussian construct, and the myths and structures underlying that sport are examined. A cognitive model is then developed to illustrate further the interaction of the rules or structures that govern this 'game.'
L'auteur aborde le sujet des courses d'automobiles comme étant un attribut des sociétés capitalistes. D'abord, il considère le sport organisé des courses d'automobiles selon 1'approche de Lévi-Strauss, et il examine les mythes et les structures à la base de ce sport. Ensuite, il développe un modèle cognitif, dans la perspective du coureur, pour illustrer davantage l'action réciproque des règies ou des structures qui gouvernent ce 'jeu.'     

Effectiveness of Group Reciprocity Counseling with Married Couples*

This research examined the efficacy of using a reciprocity procedure with married couples in a group format. Seven couples, enrolled in a non-credit extension course, participated in an eight-week workshop. In-workshop and at-home assignments were completed by the participants. Data were collected using daily marital happiness ratings and a pre-workshop inventory. Results were analyzed using t-tests and multiple baseline procedure. Commitment to and optimism about marriage and ratings on 3 of 9 areas of couple interaction significantly increased over the seven-week period. Introduction of specific reciprocity procedures and increased ratings of marital happiness were related in a contingent manner.     

Probabilistic sensitivity analysis of complex models: a Bayesian approach

Summary.  In many areas of science and technology, mathematical models are built to simulate complex real world phenomena. Such models are typically implemented in large computer programs and are also very complex, such that the way that the model responds to changes in its inputs is not transparent. Sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs. This may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application. A broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model's output to variation in its inputs. In practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs, an approach which is known as probabilistic sensitivity analysis. We present a Bayesian framework which unifies the various tools of prob- abilistic sensitivity analysis. The Bayesian approach is computationally highly efficient. It allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard Monte Carlo methods. Furthermore, all measures of interest may be computed from a single set of runs.     

USING REPEATED MEASURES DESIGNS IN PROGRAM EVALUATION OF FAMILY THERAPY*

Data from 14 simulated families were analyzed with both a repeated measures and an ordinary analysis of variance design in order to illustrate the differences between the two approaches. The advantages of repeated measures designs for the analysis of family data in the program evaluation of family therapy are highlighted.