Mathematical Model of Person Judgment, Part 1 - Manuscript

We present the first part of a fully parametrized mathematical model of person judgment, in an attempt to streamline and better organize theory in this research area. The model integrates several key concepts from Kenny’s (1994) Weighted Average Model and Brunswik’s (1956) lens model with one another. It incorporates time as a continuous variable and also accounts for target-effects, situation-effects, target by situation interaction-effects, randomness overall and between-target differences in randomness. All of these can influence the average level of a substance variable that may be observed by perceivers („cues“) and thus inform their judgments of targets. We discuss the model’s implications with regard to reliability, inter-rater agreement, and predictive validity. We also explain how the model connects to – and sometimes helps specify – several important concepts from the person judgment literature.

Mathematical Model of Person Judgment: Part 1 (Cue Emergence)

We present the first part of a fully parametrized mathematical model of person judgment, in an attempt to streamline and better organize theory in this research area. The model integrates several key concepts from Kenny’s (1994) Weighted Average Model and Brunswik’s (1956) lens model with one another. It incorporates time as a continuous variable and also accounts for target-effects, situation-effects, target by situation interaction-effects, randomness overall and between-target differences in randomness. All of these can influence the average level of a substance variable that may be observed by perceivers („cues“) and thus inform their judgments of targets. We discuss the model’s implications with regard to reliability, inter-rater agreement, and predictive validity. We also explain how the model connects to – and sometimes helps specify – several important concepts from the person judgment literature.

The anisotropic field of ensemble coding

Human observers can accurately estimate statistical summaries from an ensemble of multiple stimuli, including the average size, hue, and direction of motion. The efficiency and speed with which statistical summaries are extracted suggest an automatic mechanism of ensemble coding that operates beyond the capacity limits of attention and memory. However, the extent to which ensemble coding reflects a truly parallel and holistic mode of processing or a non-uniform and biased integration of multiple items is still under debate. In the present work, we used a technique, based on a Spatial Weighted Average Model (SWM), to recover the spatial profile of weights with which individual stimuli contribute to the estimated average during mean size adjustment tasks. In a series of experiments, we derived two-dimensional SWM maps for ensembles presented at different retinal locations, with different degrees of dispersion and under different attentional demands. Our findings revealed strong spatial anisotropies and leftward biases in ensemble coding that were organized in retinotopic reference frames and persisted under attentional manipulations. These results demonstrate an anisotropic spatial contribution to ensemble coding that could be mediated by the differential activation of the two hemispheres during spatial processing and scene encoding.

Consistency of Pairwise Comparisons and Its Role in Optimal Detection of Customers’ Preferences

<p><strong>Purpose:</strong> This paper analyses a problem that originates in the weighted-average model, a mathematical construct introduced by the theory of multicriteria decision-making that can be used to detect what product a customer desires. The problem occurs because the model needs to know the weight the customer assigns to each product feature, aside from the levels of all the product characteristics, in order to calculate the overall value of the product. And since by one approach the weights can be estimated by optimization, the question arises which optimization criterion to select for the procedure, as different criteria will lead to different weights and thus to different product evaluations. The paper analyses the problem in connection with the so-called consistency of pairwise comparisons, which are utilized in the optimization and describe how much the customer prefers one product feature to another. The analysis shows that the problem of which criterion to use to calculate the weights can be eliminated if the pairwise comparisons are consistent. The analysis is performed within pre-defined criteria and is supplemented with case studies supporting the findings.</p><p><strong>Methodology/Approach:</strong> Linear algebra, optimization techniques, case studies.</p><p><strong>Findings:</strong> The results represent a prescription customers can use if they want to avoid the pitfalls of selecting a specific optimization criterion when informing the product maker about what they want based on the weighted-average model.</p><p><strong>Research Limitation/Implication:</strong> The results are related to a specific decision-making model, although that model is still very general and natural.</p><strong>Originality/Value of paper:</strong> The problem of selecting an optimization criterion to determine decision weights is not discussed in the theory.

New Strategy for Improving the Accuracy of Aircraft Positioning Based on GPS SPP Solution

The paper describes and presents a new calculation strategy for the determination of the aircraft’s resultant position using the GPS (Global Positioning System) SPP (Single Point Positioning) code method. The paper developed a concept of using the weighted average model with the use of measuring weights to improve the quality of determination of the coordinates and accuracy of GPS SPP positioning. In this research, measurement weights were used as a function of the number of GPS satellites being tracked, and geometric PDOP (Position Dilution of Precision) coefficient. The calculations were made using navigation data recorded by two independent GPS receivers: Thales Mobile Mapper and Topcon HiPerPro. On the basis of the obtained results, it was found that the RMS (Root Mean Square) accuracy of positioning for XYZ geocentric coordinates was better than 1.2% to 33.7% for the weighted average method compared to a single GPS SPP solution. The proposed approach is therefore of practical application in air navigation to improve the quality of aircraft positioning.

Velocity structure and the role of fluids in the West Bohemia Seismic Zone

In this study, we apply the double-difference tomography to investigate the detailed 3-D structure within and around the Nový Kostel Seismic Zone, an area in the Czech Republic known for frequent occurrences of earthquake swarms. We use data from the 2008 swarm since it has already been analysed in terms of earthquake focal mechanisms, principal faults, tectonic stress and foci migration. We selected about 500 microearthquakes recorded at 22 local seismic stations of the West Bohemia seismic monitoring network (WEBNET). Applying double-difference tomography, combined with weighted average model (WAM) post-processing to correct for parameter dependence effects, we produce and interpret 3-D models of the Vp-to-Vs ratio (Vp/Vs) in and around the focal zone. The modelled Vp/Vs ratio shows several distinct structures, namely an area of high Vp/Vs ratio correlating with the foci of the microearthquakes, and a layer of low values directly above it. These structures may reflect changes in lithology and/or fluid concentration. The overlaying low Vp/Vs ratio layer coincides with the base of the Fichtelgebirge (Smrčiny) granitic intrusion. It is possible that the base of the layer acts as a fluid trap and an upper limit to the seismicity, resulting in observed periodic swarms.