等级效标分数的概率神经网络预测方法研究

针对基于统计学的等级效标分数预测存在的问题,提出了运用概率神经网络进行等级效标分数预测的方法。在20种条件下进行了计算机模拟实验,包括测验分数为单变量和多变量,以及各种水平的白噪声干扰条件,结果表明在测验分数为多变量的情况下,或者在有白噪声干扰的条件下,运用概率神经网络方法可以比统计学方法更好地对等级效标分数进行预测。     

Dissimilarity cumulation theory and subjective metrics

We present a new mathematical notion, dissimilarity function, and based on it, a radical extension of Fechnerian Scaling, a theory dealing with the computation of subjective distances from pairwise discrimination probabilities. The new theory is applicable to all possible stimulus spaces subject to the following two assumptions: (A) that discrimination probabilities satisfy the Regular Minimality law and (B) that the canonical psychometric increments of the first and second kind are dissimilarity functions. A dissimilarity function Dab for pairs of stimuli in a canonical representation is defined by the following properties: (1) a≠b?Dab>0; (2) Daa=0; (3) If and , then ; and (4) for any sequence {a_nX_nb_n}_n∈N, where X_n is a chain of stimuli, Da_nX_nb_n→0?Da_nb_n→0. The expression DaXb refers to the dissimilarity value cumulated along successive links of the chain aXb. The subjective (Fechnerian) distance between a and b is defined as the infimum of DaXb+DbYa across all possible chains X and Y inserted between a and b.     

The Equiprobability Bias from a Mathematical and Psychological Perspective

The equiprobability bias (EB) is a tendency to believe that every process in which randomness is involved corresponds to a fair distribution, with equal probabilities for any possible outcome. The EB is known to affect both children and adults, and to increase with probability education. Because it results in probability errors resistant to pedagogical interventions, it has been described as a deep misconception about randomness: the erroneous belief that randomness implies uniformity. In the present paper, we show that the EB is actually not the result of a conceptual error about the definition of randomness. On the contrary, the mathematical theory of randomness does imply uniformity. However, the EB is still a bias, because people tend to assume uniformity even in the case of events that are not random. The pervasiveness of the EB reveals a paradox: The combination of random processes is not necessarily random. The link between the EB and this paradox is discussed, and suggestions are made regarding educational design to overcome difficulties encountered by students as a consequence of the EB.     

What shapes the probability weighting function? Influence of affect,numeric competencies,and information formats

Research suggests that people are less sensitive to variations in probability in affect‐rich compared with affect‐poor risky choices. This effect is modeled by a more curved probability weighting function (PWF). We investigated the role of different numeric competencies and the effectiveness of several intervention strategies to decrease this affect‐laden probability distortion. In two experiments, we manipulated the affect‐richness of a risky prospect. In Experiment 1 (N = 467), we measured numeracy and symbolic‐number mapping (i.e., the ability to accurately map numbers onto their underlying magnitudes). The affect‐based manipulations showed the expected effects only in participants with more accurate symbolic‐number mapping, who also reported more differentiated emotional reactions to the various probabilities and displayed more linear PWFs. Instructions to focus on the probability information decreased probability distortion and revealed differences in the use of probability information on the basis of symbolic‐number mapping ability. In Experiment 2 (N = 417), we manipulated the format in which the probability information was presented: using visual aids versus no visual aids and a positive frame (e.g., one person wins) versus combined frame (e.g., one person wins and 99 persons do not win). The affect‐based manipulations had no effect but both the visual aids and combined frame decreased probability distortion. Whereas affect‐richness manipulations require further research, results suggest that probability weighting is at least partially driven by the inability to translate numerical information into meaningful and well‐calibrated affective intuitions. Visual aids and simple framing manipulations designed to calibrate these intuitions can help decision makers extract the gist and increase sensitivity to probabilities.