A probabilistic multidimensional scaling with unique axes1

Abstract: A probabilistic multidimensional scaling model is proposed. The model assumes that the coordinates of each stimulus are normally distributed with variance Σ_i = diag(σ²₁, … σ²_Ri). The advantage of this model is that axes are determined uniquely. The distribution of the distance between two stimuli is obtained by polar coordinates transformation. The method of maximum likelihood estimation for means and variances using the EM algorithm is discussed. Further, simulated annealing is suggested as a means of obtaining initial values in order to avoid local maxima. A simulation study shows that the estimates are accurate, and a numerical example concerning the location of Japanese cities shows that natural axes can be obtained without introducing individual parameters.     

Isotonic ordinal probabilistic models (ISOP)

The concept of an ordinal instrumental probabilistic comparison is introduced. It relies on an ordinal scale given a priori and on the concept of stochastic dominance. It is used to define a weakly independently ordered system, or isotonic ordinal probabilistic (ISOP) model, which allows the construction of separate sample-free ordinal scales on a set of subjects and a set of items. The ISOP-model is a common nonparametric theoretical structure for unidimensional models for quantitative, ordinal and dichotomous variables.Fundamental theorems on dichotomous and polytomous weakly independently ordered systems are derived. It is shown that the raw score system has the same formal properties as the latent system, and therefore the latter can be tested at the observed empirical level.I wish to thank 3 reviewers and 2 editors who contributed a lot to the readability and precision of the article.     

Subjects' inferential performance and the interaction of data and hypotheses in probabilistic inference tasks

In a recent paper, Knez (1991) showed an interaction of data and hypotheses in probabilistic inference tasks. The results illustrated two, earlier not obtained, significant main effects on subjects' hypothesis sampling , viz. the effect of different forms of data presentation and subjects' execution of cognitive control over their hypothesis pool throughout the series of trials. The present paper followed up these results in that the subjects' hypothesis testing , in Knez (1991) was subjected to an analysis. Hence, to see if the effects mentioned above significantly influenced the subjects' hypothesis testing, as they did for subjects' hypothesis sampling. The results showed a consistency with Knez (1991), i.e. the results emphasize the interaction of data and hypothesis in probabilistic inference tasks, as well as the subjects' execution of cognitive control over their hypothesis pool concerning both the subjects' hypothesis sampling and testing.     

The Effects of Multiple Presentations on the Ratings and Memorability of Novel Figurative Phrases

How the perceptions of novel figurative phrases change over the course of numerous presentations were addressed in three studies using rating tasks (Studies 1 and 3) and recall tasks (Study 2). The present set of studies replicated much of Schweigert et al.’s (J Psychol Res 32:455–475, 2003) findings of changes in correlations among figurative phrases ratings. The results also suggest that catchiness, frequency heard agreement, and frequency used agreement can be used as predictors of phrase memorability and potential predictors of later idiomaticity.     

Decomposition,Interdependence and Precision in Multiattribute Utility Measurements

Traditionally, parameters of multiattribute utility models, representing a decision maker's preference judgements, are treated deterministically. This may be unrealistic, because assessment of such parameters is potentially fraught with imprecisions and errors. We thus treat such parameters as stochastic and investigate how their associated imprecision/errors are propagated in an additive multiattribute utility function in terms of the aggregate variance. Both a no information and a rank order case regarding the attribute weights are considered, assuming a uniform distribution over the feasible region of attribute weights constrained by the respective information assumption. In general, as the number of attributes increases, the variance of the aggregate utility in both cases decreases and approaches the same limit, which depends only on the variances as well as the correlations among the single-attribute utilities. However, the marginal change in aggregate utility variance decreases rather rapidly and hence decomposition as a variance reduction mechanism is generally useful but becomes relatively ineffective if the number of attributes exceed about 10. Moreover, it was found that utilities which are positively correlated increase the aggregate utility variance, hence every effort should be made to avoid positive correlations between the single-attribute utilities. We also provide guidelines for determining under what condition and to what extent a decision maker should decompose to obtain an aggregate utility variance that is smaller than that of holistic assessments. Extensions of the current model and empirical research to support some of our behavioural assumptions are discussed. © 1997 John Wiley & Sons, Ltd.     

Resource-origins of Nonmonotonicity

Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles. Edited by Hannes Leitgeb     

Delusion‐proneness or miscomprehension? A re‐examination of the jumping‐to‐conclusions bias

Previous research has consistently shown that individuals with delusions typically exhibit a jumping‐to‐conclusions (JTC) bias when administrated the probabilistic reasoning ‘beads task’ (i.e., decisions made on limited evidence and/or decisions over‐adjusted in light of disconfirming evidence). However, recent work in this area has indicated that a lack of comprehension of the task may be confounding this finding. The purpose of the present study was to evaluate the influence of task administration, delusion‐proneness, and miscomprehension on the elucidation of the JTC bias. A total of 92 undergraduate university students were divided into one of two task conditions (i.e., non‐computerised and computerised) and were further identified as either delusion‐prone or non‐delusion‐prone and as comprehending or non‐comprehending the task. Overall, 25% of the sample demonstrated a JTC bias, and just over half made illogical responses consistent with a failure to comprehend the task. Qualitative evidence of comprehension revealed that these ‘illogical responses’ were being driven by a misunderstanding of task instructions. The way the task was administrated and levels of delusion‐proneness did not significantly influence JTC. However, miscomprehending participants were significantly more likely to exhibit the bias than those who did comprehend. These results suggest that miscomprehension rather than delusion‐proneness may be driving the JTC bias, and that future research should include measures of miscomprehension.     

Conditionals Right and Left: Probabilities for the Whole Family

The fact that the standard probabilistic calculus does not define probabilities for sentences with embedded conditionals is a fundamental problem for the probabilistic theory of conditionals. Several authors have explored ways to assign probabilities to such sentences, but those proposals have come under criticism for making counterintuitive predictions. This paper examines the source of the problematic predictions and proposes an amendment which corrects them in a principled way. The account brings intuitions about counterfactual conditionals to bear on the interpretation of indicatives and relies on the notion of causal (in)dependence.     

Building phrases in language production: An MEG study of simple composition

Although research on language production has developed detailed maps of the brain basis of single word production in both time and space, little is known about the spatiotemporal dynamics of the processes that combine individual words into larger representations during production. Studying composition in production is challenging due to difficulties both in controlling produced utterances and in measuring the associated brain responses. Here, we circumvent both problems using a minimal composition paradigm combined with the high temporal resolution of magnetoencephalography (MEG). With MEG, we measured the planning stages of simple adjective–noun phrases (‘red tree’), matched list controls (‘red, blue’), and individual nouns (‘tree’) and adjectives (‘red’), with results indicating combinatorial processing in the ventro-medial prefrontal cortex (vmPFC) and left anterior temporal lobe (LATL), two regions previously implicated for the comprehension of similar phrases. These effects began relatively quickly (∼180 ms) after the presentation of a production prompt, suggesting that combination commences with initial lexical access. Further, while in comprehension, vmPFC effects have followed LATL effects, in this production paradigm vmPFC effects occurred mostly in parallel with LATL effects, suggesting that a late process in comprehension is an early process in production. Thus, our results provide a novel neural bridge between psycholinguistic models of comprehension and production that posit functionally similar combinatorial mechanisms operating in reversed order.     

Imminent Danger? Probabilistic Classification Learning of Threat-Related Information in Obsessive-Compulsive Disorder

A tendency to overestimate threat has been shown in individuals with OCD. We tested the hypothesis that this bias in judgment is related to difficulties in learning probabilistic associations between events. Thirty participants with OCD and 30 matched healthy controls completed a learning experiment involving 2 variants of a probabilistic classification learning task. In the neutral weather-prediction task, rainy and sunny weather had to be predicted. In the emotional task danger of an epidemic from virus infection had to be predicted (epidemic-prediction task). Participants with OCD were as able as controls to improve their prediction of neutral events across learning trials but scored significantly below healthy controls on the epidemic-prediction task. Lower performance on the emotional task variant was significantly related to a heightened tendency to overestimate threat. Biased information processing in OCD might thus hamper corrective experiences regarding the probability of threatening events.