Stability and coherence of health experts' upper and lower subjective probabilities about dose-response functions

As part of a method for assessing health risks associated with primary National Ambient Air Quality Standards. T. B. Feagans and W. F. Biller (Research Triangle Park, North Carolina. EPA Office of Air Quality Planning and Standards, May 1981) developed a technique for encoding experts' subjective probabilities regarding dose--response functions. The encoding technique is based on B. O. Koopman's (Bulletin of the American Mathematical Society, 1940, 46, 763-764; Annals of Mathematics, 1940, 41, 269-292) probability theory, which does not require probabilities to be sharp, but rather allows lower and upper probabilities to be associated with an event. Uncertainty about a dose--response function can be expressed either in terms of the response rate expected at a given concentration or, conversely, in terms of the concentration expected to support a given response rate. Feagans and Biller (1981, cited above) derive the relation between the two conditional probabilities, which is easily extended to upper and lower conditional probabilities. These relations were treated as coherence requirements in an experiment utilizing four ozone and four lead experts as subjects, each providing judgments on two separate occasions. Four subjects strongly satisfied the coherence requirements in both conditions. and three more did no in the second session only. The eighth subject also improved in Session 2. Encoded probabilities were highly correlated between the two sessions, but changed from the first to the second in a manner that improved coherence and reflected greater attention to certain parameters of the dose--response function.     

A computer program to generate and measure random forms

A computer program is described that generates random form stimuli by a method parallel to that described by Attneave & Arnoult (1956) for construction forms with both angles and arcs in their perimeters. The program also performs a physical analysis of the forms by computing the values of a large number of physical variables describing each form. Already existing forms also may be analyzed by the program. Thus, it has the capability to perform physical analyses of approximations to natural forms.     

On the relations between random walk models for two-choice response times

We state a condition on the moment-generating functions of the random walk model derived by Link and Heath (1975), which is necessary and sufficient to yield the sequential probability ratio test of Wald (1947) and the reaction-time model proposed by Stone (1960). A restricted form of this condition can also be obtained by imposing the types of symmetries on the moment-generating functions considered by Link and Health (1975) and Thomas (1975). The various conditions are contrasted and their implications for empirical investigation are discussed.     

The proactive brain: using analogies and associations to generate predictions

Rather than passively 'waiting' to be activated by sensations, it is proposed that the human brain is continuously busy generating predictions that approximate the relevant future. Building on previous work, this proposal posits that rudimentary information is extracted rapidly from the input to derive analogies linking that input with representations in memory. The linked stored representations then activate the associations that are relevant in the specific context, which provides focused predictions. These predictions facilitate perception and cognition by pre-sensitizing relevant representations. Predictions regarding complex information, such as those required in social interactions, integrate multiple analogies. This cognitive neuroscience framework can help explain a variety of phenomena, ranging from recognition to first impressions, and from the brain's 'default mode' to a host of mental disorders.     

Coordination of the upper and lower extremities

Simultaneous walking and hand clapping were utilized to examine the patterns of coordination between upper and lower limbs. Eighteen normal adult subjects were filmed at high speed under instructions to: (a) walk and clap at a self-determined “preferred” speed, (b) walk as fast as possible while clapping at the preferred speed, (c) walk at the preferred speed while clapping as fast as possible and (d) walk and clap as fast as possible. Temporal data and individual patterns of phase relations were analyzed. Results indicated a disruption of the preferred clap cycle when combine with fast walking. The degree of disruption was a function of the individual coordinative pattern at the preferred rate. It is concluded that: (a) the temporal patterning of the clap cycle can be dictated by the step cycle, (b) heel strike is the point about which the clap cycle is modulated, and (c) subjects can select from various modes of phase linkage.     

The upper and lower twenty-seven per cent rule

A simplified re-derivation of the formula underlying the rule is presented, followed by a derivation of the comparable rule for the unitrectangular distribution, which turns out to be a 33-per cent rule. Critical comments are offered concerning two assumptions: normality of the score distribution and equality of mean standard errors of measurement in the high and low groups.     

Response preparation and stimulus-response congruence to fractionating reaction time of upper and lower limbs

We measured the fractionating reaction time for upper and lower limbs of 18 young men, using an electromyogram to clarify the interaction of response preparation and stimulus-response congruence on premotor and motor time. The reaction time was divided into two periods with respect to the onset of the electromyogram, premotor and motor components. Manipulating the probability of the Go versus NoGo signals varied three different amounts of response preparation. Prior to the imperative stimulus, precue information about the position of a stimulus was presented. In the stimulus-response congruent task, subjects were required to release a key on the same side of the body using either an upper or lower limb in response to an imperative Go stimulus. In the stimulus-response incongruent task, subjects were required to act in a reverse manner. Subjects were not supposed to respond to the NoGo stimulus. The premotor time of the upper and lower limb responses was affected by the respective effects of response preparation and stimulus-response congruence. The motor time of the upper and lower limb responses increased as the probability of the Go signal decreased but not in relation to stimulus-response congruence. These results suggest that response preparation affects not only information processing time but also peripheral motor activity due to motor programming, and that the stimulus-response congruence effect on motor time disappears when information about the position of the imperative stimulus is precued.     

A comparison of upper vs. lower and right vs. left visual fields using lexical decision

A series of experiments using the lexical decision task was conducted in order to investigate the functional differences between the upper and lower visual fields (UVF, LoVF) in word recognition. Word-nonword discrimination was swifter and more accurate for word stimuli presented in the UVF. Changing the eccentricity did not affect the UVF advantage over the LoVF. UVF superiority over LoVF was found to be equivalent for both right and left visual hemifield (RVF, LVF). In general, presenting related word primes enhanced all visual field differences in a similar manner (UVF over LoVF and RVF over LVF). However, primes consisting of semantically constraining sentences enhanced the RVF advantage over the LVF, but did not affect the UVF and LoVF differentially. The argument is made that UVF superiority cannot be due to perceptual or attentional differences alone, but must also reflect top-down information flow.     

On the logic of nonmonotonic conditionals and conditional probabilities

I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, , in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, CB holds just in case P[B|C]r. Thus, each conditional in a given family behaves like conditional probability above some specific support level.Chris Swoyer provided very helpful comments on drafts of this paper.     

On the greatest lower bound to reliability

Certain ambiguities in a recent paper on the computation and statistics of the greatest lower bound are clarified.     

New lower and upper bounds for communality in factor analysis

We derive several relationships between communalities and the eigenvalues for ap ×p correlation matrix under the usual factor analysis model. For suitable choices ofj, _j (), where _j () is thej-th largest eigenvalue of , provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - _p () improves on the use of squared mulitiple correlation coefficient as a lower bound.This research was done while the second author was at Tokyo Institute of Technology.     

On the a priori and a posteriori assessment of probabilities

We argue that in spite of their apparent dissimilarity, the methodologies employed in the a priori and a posteriori assessment of probabilities can both be justified by appeal to a single principle of inductive reasoning, viz., the principle of symmetry. The difference between these two methodologies consists in the way in which information about the single-trial probabilities in a repeatable chance process is extracted from the constraints imposed by this principle. In the case of a posteriori reasoning, these constraints inform the analysis by fixing an a posteriori determinant of the probabilities, whereas, in the case of a priori reasoning, they imply certain claims which then serve as the basis for subsequent probabilistic deductions. In a given context of inquiry, the particular form which a priori or a posteriori reason may take depends, in large part, on the strength of the underlying symmetry assumed: the stronger the symmetry, the more information can be acquired a priori and the less information about the long-run behavior of the process is needed for an a posteriori assessment of the probabilities. In the context of this framework, frequency-based reasoning emerges as a limiting case of a posteriori reasoning, and reasoning about simple games of chance, as a limiting case of a priori reasoning. Between these two extremes, both a priori and a posteriori reasoning can take a variety of intermediate forms.