Computer generation of textures

A method for displaying fixed or time-varying textured patterns under computer control is described. The luminance profiles of these patterns is fixed in one dimension (Y axis), but can be arbitrarily complex in the other dimension (X axis) since they are synthesized by software. An example of the use of the method in texture matching experiments is given.     

Quick approximation of bivariate functions

This paper presents two experiments where participants had to approximate function values at various generalization points of a square, using given function values at a small set of data points. A representative set of standard function approximation models was trained to exactly fit the function values at data points, and models' responses at generalization points were compared to those of humans. Then one defined a large class of possible models (including the best two identified predictors) and the class maximal possible prediction accuracy was evaluated. A new model of quick multivariate function approximation belonging to this class was proposed. Its prediction accuracy was close to the maximum possible, and significantly better than that of all other models tested. The new model also provided a significant account of human response variability. Finally, it was shown that this model is more particularly suitable for problems in which the visual system can perform some specific structuring of the data space. This model is therefore considered as a suitable starting point for further investigations into quick multivariate function approximation, which is to date an inadequately explored question in cognitive psychology.     

Meta-analytic interval estimation for bivariate correlations

The currently available meta-analytic methods for correlations have restrictive assumptions. The fixed-effects methods assume equal population correlations and exhibit poor performance under correlation heterogeneity. The random-effects methods do not assume correlation homogeneity but are based on an equally unrealistic assumption that the selected studies are a random sample from a well-defined superpopulation of study populations. The random-effects methods can accommodate correlation heterogeneity, but these methods do not perform properly in typical applications where the studies are nonrandomly selected. A new fixed-effects meta-analytic confidence interval for bivariate correlations is proposed that is easy to compute and performs well under correlation heterogeneity and nonrandomly selected studies.     

The nontruncated marginal of a truncated bivariate normal distribution

Inference is considered for the marginal distribution ofX, when (X, Y) has a truncated bivariate normal distribution. TheY variable is truncated, but only theX values are observed. The relationship of this distribution to Azzalini's skew-normal distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for largen. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.     

Correlation in a singly truncated bivariate normal distribution

The correlation in a singly truncated binormal distribution is obtained in terms of Mills' ratio using the Mehler identity. A table of the correlation in the underlying distribution as a function of the correlation in the truncated distribution is presented, together with a diagram summarizing this relationship.I wish to express my appreciation to Professor H. O. Lancaster of the Department of Mathematical Statistics, Sydney University, for the suggestion of this problem.     

A note on monotone polygons fitted to bivariate data

The monotone regression function of Kruskal and the rank image function of Guttman and Lingoes were fitted to bivariate normal samples and their statistical properties contrasted.This paper was written while the author was a Visiting Professor in the Department of Psychology, University College, London.     

Humanistic values

International Journal for Philosophy of Religion -     

Recombinant values

An attractive admirer of George Bernard Shaw once wrote to himwith a not-so modest proposal: ``You have the greatest brain in theworld, and I have the most beautiful body; so we ought to producethe most perfect child.'' Shaw replied: ``What if the child inherits mybody and your brains?'' What if, indeed? Shaw's retort is interesting not because it revealsa grasp of elementary genetics, but rather because it suggests his graspof an interesting and important principle of axiology. Since the brainybut ugly Shaw and his beautiful but apparently dim admirer both fallshort of the ideal, she suggests that the best thing would be togenetically recombine his intelligence with her beauty. But what thenwould be the value of another genetic possibility: that of recombininghis ugliness with her stupidity? Underlining the prompted inference is afundamental principle of the theory of value which, perhapssurprisingly, has so far gone largely unnoticed in the ethicalliterature. I will call it the principle of recombinantvalues. It is the purpose of this paper to formulate the principle in a waywhich makes its content obvious and accessible; to motivate theprinciple philosophically; to both disentangle it from, and exhibitits relations to, principles of evaluative reasoning; to show howthis purely qualitative principle meshes with the infamous thesis ofadditivity of value; and finally, to use it to ground a rathersimple but quite general theory of the intrinsic value ofstates.     

Problems with bootstrapping pearson correlations in very small bivariate samples

Efron'sMonte Carlo bootstrap algorithm is shown to cause degeneracies in Pearson'sr for sufficiently small samples. Two ways of preventing this problem when programming the bootstrap ofr are considered.