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.     

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.     

Differentiation of press durations with upper and lower limits on reinforced values

Rats received food following lever-press durations between t and t+t′ sec where t was 2, 4, or 8 sec and t′ was 0.25t, 0.50t, or 1.00t sec. Modal press durations were greater than t but less than t+t′ in all cases. Distributions of press durations were lower and broader for larger values of t. Lower t′/t ratios produced lower median press durations and relatively narrower press-duration distributions. Median press duration was a power function of t within a t′/t ratio condition, corresponding to previous results for latency, interresponse time, and response durations.     

Tooley on causation and probabilities

In this paper, I argue that there is an inconsistency between two presentist doctrines: that of ontological symmetry and asymmetry of fixity. The former refers to the presentist belief that the past and future are equally unreal. The latter refers to the A-Theoretic intuition that the past is closed or actual, and the future is open or potential. My position in this paper is that the presentist is unable to account for the temporal asymmetry that is so fundamentally a part of her theory. In Section I, I briefly outline a recent defence of presentism due to Craig, and argue that a flaw in this defence highlights the tension between the presentist's doctrines of ontological symmetry and asymmetry of fixity. In Section II, I undertake an investigation, on the presentist's behalf, in order to determine whether she is capable of reconciling these two doctrines. In the course of the investigation, I consider different asymmetries, other than that of ontology, which might be said fundamentally to constitute temporal asymmetry, and the asymmetry of fixity in particular. In Section III, I also consider whether the presentist is able to avail herself of some of the standard B-Theoretic accounts of the asymmetry of fixity, and argue that she cannot. Finally, I conclude that temporal asymmetry cannot be accounted for (or explained) other than through the postulation of an ontological asymmetry.     

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.     

Note on guessing probabilities

A hypothesis of stationary response probabilities (SRP), or that subjects equate the unconditional probability of each response to its frequency of occurrence in the task, is shown to be equivalent to the proposal of Atkinson et al. (1965) that guessing may occur only among unlearned responses. This hypothesis is contrasted with the usual assumption of stationary guessing probabilities (SGP). It is shown that assuming SGP when SRP is true results in a biased estimate of learning which first increases and then decreases with the actual degree of learning, and is a decreasing function of list length. This can lead to improper inferences, including erroneous rejection of an all-or-none model and spurious evidence of increasing difficulty in long lists.     

Averaged occipital responses to stimulation of sites in the upper and lower halves of the retina

Averaged responses of the occipital lobes to flashes imposed along the midline of the upper part of the retina are larger and of shorter latency than responses to flashes imposed on the lower retina. Since reaction times also are shorter when the upper retina is stimulated, this study provides further evidence for the generalization that reaction time varies inversely with amplitude and directly with latency of the evoked response.     

Perception of words and non-words in the upper and lower visual fields

The findings of previous investigations into word perception in the upper and the lower visual field (VF) are variable and may have incurred non-perceptual biases caused by the asymmetric distribution of information within a word, an advantage for saccadic eye-movements to targets in the upper VF and the possibility that stimuli were not projected to the correct retinal locations. The present study used the Reicher-Wheeler task and an eye-tracker to show that, using stringent methodology, a right over left VF advantage is observed for word recognition, but that no differences were found between the upper and the lower VF for either word or non-word recognition. The results are discussed in terms of the neuroanatomy and perceptual abilities of the upper and the lower VF and implications for other studies of letter-string perception in the upper and the lower VF are presented.     

How to use probabilities in reasoning

Conclusions Probabilities are important in belief updating, but probabilistic reasoning does not subsume everything else (as the Bayesian would have it). On the contrary, Bayesian reasoning presupposes knowledge that cannot itself be obtained by Bayesian reasoning, making generic Bayesianism an incoherent theory of belief updating. Instead, it is indefinite probabilities that are of principal importance in belief updating. Knowledge of such indefinite probabilities is obtained by some form of statistical induction, and inferences to non-probabilistic conclusions are carried out in accordance with the statistical syllogism. Such inferences have been the focus of much attention in the nonmonotonic reasoning literature, but the logical complexity of such inference has not been adequately appreciated.     

Conditions under which thurstone case III representations for binary choice probabilities are also Fechnerian

By a Thurstone Case III representation for binary symmetric choice probabilities P_x,y we mean that there exist functions F, μ, σ > 0 such that $\text{P}{}_{\mathrm{x,y}}\text{= F[}\text{(μ(x) ? μ(y))}\text{(σ}{}^2\text{(x) + σ}{}^2\text{(y))}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{]}$. We show that the constraint σ = constant, or μ = ασ + β, α ≠ 0, is both necessary and sufficient for a Thurstone Case III representation to be Fechnerian, i.e., to be reexpressable as as P_x,y = G(u(x) ? u(y)) for some suitably chosen functions G, u.     

Effects of background color on detecting spot stimuli in the upper and lower visual fields

Participants were required to detect spot stimuli briefly presented to the upper, central, or lower visual fields. The stimuli were presented either on a green or a red background. Results showed that reaction time (RT) was shorter for the lower visual field (LVF) compared to the upper visual field (UVF). Furthermore, this LVF advantage was significantly reduced in the red background condition compared to the green one. A red light is known to suppress activity of the magno-dominated stream. Therefore, the LVF advantage in RT can be explained as resulting from the biased representation of the magno-dominated stream in the LVF.     

Time but not force is transferred between ipsilateral upper and lower limbs

The authors compared the force and time endpoint accuracy of goal-directed ipsilateral upper and lower limb isometric contractions and determined the components of motor performance that can be transferred from 1 limb to the other after practice. Ten young adults (27.4 +/- 4.4 years) performed 100 trials that involved their matching peak force to a force-time target with ankle dorsiflexor and elbow flexor muscles. The peak force error and variability was greater for ankle dorsiflexor contractions than for elbow flexor contractions, whereas the timing error and variability did not significantly vary with limb. There was transfer of timing, but not force, of motor output between upper and lower limbs. The timing error of the elbow flexor contractions decreased by 23% when those contractions were preceded by ankle dorsiflexor contractions, and the timing error of the ankle dorsiflexors decreased by 24% when those contractions were preceded by elbow flexor contractions. These finding therefore suggest that timing of an aiming isometric contraction may be organized at a common part of the brain for the upper and lower limbs.     

A note on combining probabilities

The weakness in the usual application of the Fisher method of combining probabilities is pointed out and a supplementary method is suggested.