Stochastic independence,causal independence,and shieldability

The aim of the paper is to explicate the concept of causal independence between sets of factors and Reichenbach's screening-off-relation in probabilistic terms along the lines of Suppes' probabilistic theory of causality (1970). The probabilistic concept central to this task is that of conditional stochastic independence. The adequacy of the explication is supported by proving some theorems about the explicata which correspond to our intuitions about the explicanda.I am indebted to the referee for his most valuable report and to the editor for taking more trouble than usual, I fear.     

非参数认知诊断方法下诊断结果的概率化表征

非参数认知诊断分类方法非常适合课堂评估,其诊断结果采用0-1形式而缺乏概率化表征,不能精细地区分被试属性掌握程度的差异或变化,还缺乏可用于评价真实测验分类结果的信度和效度指标。要刻画被试属性掌握程度的差异,首要的问题是要为非参数认知诊断方法提供一种可以量化属性掌握概率的方法。针对此问题,基于二项分布和玻尔兹曼分布提出非参数认知诊断方法下诊断结果的概率化表征方法,并用于构建分类准确性和分类一致性指标。模拟研究与实测数据分析结果显示：概率化表征方法与非参数认知诊断方法的分类结果高度一致;概率化表征方法与认知诊断模型所得的属性掌握概率十分接近;概率化表征方法所得的属性（模式）掌握概率可用于计算属性（模式）分类准确性和分类一致性指标,在实际测验情景下可作为信度和效度指标,评价诊断结果的重测一致率和判准率。     

Towards classifying propositional probabilistic logics

This paper examines two aspects of propositional probabilistic logics: the nesting of probabilistic operators, and the expressivity of probabilistic assessments. We show that nesting can be eliminated when the semantics is based on a single probability measure over valuations; we then introduce a classification for probabilistic assessments, and present novel results on their expressivity. Logics in the literature are categorized using our results on nesting and on probabilistic expressivity.     

The exchangeable multinomial model as an approach to testing deterministic axioms of choice and measurement

The multinomial (Dirichlet) model, derived from de Finetti's concept of exchangeability, is proposed as a general Bayesian framework to test axioms on data, in particular, deterministic axioms characterizing theories of choice or measurement. For testing, the proposed framework does not require a deterministic axiom to be cast in a probabilistic form (e.g., casting deterministic transitivity as weak stochastic transitivity). The generality of this framework is demonstrated through empirical tests of 16 different axioms, including transitivity, consequence monotonicity, segregation, additivity of joint receipt, stochastic dominance, coalescing, restricted branch independence, double cancellation, triple cancellation, and the Thomsen condition. The model generalizes many previously proposed methods of axiom testing under measurement error, is analytically tractable, and provides a Bayesian framework for the random relation approach to probabilistic measurement (J. Math. Psychol. 40 (1996) 219). A hierarchical and nonparametric generalization of the model is discussed.     

The relationship between allocentric and egocentric frames of reference and categorical and coordinate spatial information processing

We report two experiments on the relationship between allocentric/egocentric frames of reference and categorical/coordinate spatial relations. Jager and Postma (2003) suggest two theoretical possibilities about their relationship: categorical judgements are better when combined with an allocentric reference frame and coordinate judgements with an egocentric reference frame (interaction hypothesis); allocentric/egocentric and categorical/coordinate form independent dimensions (independence hypothesis). Participants saw stimuli comprising two vertical bars (targets), one above and the other below a horizontal bar. They had to judge whether the targets appeared on the same side (categorical) or at the same distance (coordinate) with respect either to their body-midline (egocentric) or to the centre of the horizontal bar (allocentric). The results from Experiment 1 showed a facilitation in the allocentric and categorical conditions. In line with the independence hypothesis, no interaction effect emerged. To see whether the results were affected by the visual salience of the stimuli, in Experiment 2 the luminance of the horizontal bar was reduced. As a consequence, a significant interaction effect emerged indicating that categorical judgements were more accurate than coordinate ones, and especially so in the allocentric condition. Furthermore, egocentric judgements were as accurate as allocentric ones with a specific improvement when combined with coordinate spatial relations. The data from Experiment 2 showed that the visual salience of stimuli affected the relationship between allocentric/egocentric and categorical/coordinate dimensions. This suggests that the emergence of a selective interaction between the two dimensions may be modulated by the characteristics of the task.     

General recognition theory extended to include response times: Predictions for a class of parallel systems

General Recognition Theory (GRT; Ashby & Townsend, 1986) is a multidimensional theory of classification. Originally developed to study various types of perceptual independence, it has also been widely employed in diverse cognitive venues, such as categorization. The initial theory and applications have been static, that is, lacking a time variable and focusing on patterns of responses, such as confusion matrices. Ashby proposed a parallel, dynamic stochastic version of GRT with application to perceptual independence based on discrete linear systems theory with imposed noise (Ashby, 1989). The current study again focuses on cognitive/perceptual independence within an identification classification paradigm. We extend stochastic GRT and its implicated methodology for cognitive/perceptual independence, to an entire class of parallel systems. This goal is met in a distribution-free manner and includes all linear and non-linear systems satisfying very general conditions. A number of theorems are proven concerning stochastic forms of independence. However, the theorems all assume the stochastic version of decisional separability. A vital task remains to investigate the consequences of failures of stochastic decisional separability.     

PROBabilities from EXemplars (PROBEX): a “lazy” algorithm for probabilistic inference from generic knowledge

PROBEX (PROBabilities from EXemplars), a model of probabilistic inference and probability judgment based on generic knowledge is presented. Its properties are that: (a) it provides an exemplar model satisfying bounded rationality; (b) it is a “lazy” algorithm that presumes no pre‐computed abstractions; (c) it implements a hybrid‐representation, similarity‐graded probability. We investigate the ecological rationality of PROBEX and find that it compares favorably with Take‐The‐Best and multiple regression (Gigerenzer, Todd, & the ABC Research Group, 1999). PROBEX is fitted to the point estimates, decisions, and probability assessments by human participants. The best fit is obtained for a version that weights frequency heavily and retrieves only two exemplars. It is proposed that PROBEX implements speed and frugality in a psychologically plausible way.     

Probabilistic Logic Under Coherence, Conditional Interpretations, and Default Reasoning

We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability assessments. We also examine a property of strong satisfiability which is related to the notion of toleration well known in default reasoning. In our framework we give more general definitions of the notions of probabilistic consistency and probabilistic entailment of Adams. We also recall a notion of strict p-consistency and some related results. Moreover, we give new proofs of some results obtained in probabilistic default reasoning. Finally, we examine the relationships between conditional probability rankings and the notions of g-coherence and g-coherent entailment.     

The relationship between allocentric and egocentric frames of reference and categorical and coordinate spatial information processing

We report two experiments on the relationship between allocentric/egocentric frames of reference and categorical/coordinate spatial relations. Jager and Postma (2003) suggest two theoretical possibilities about their relationship: categorical judgements are better when combined with an allocentric reference frame and coordinate judgements with an egocentric reference frame (interaction hypothesis); allocentric/egocentric and categorical/coordinate form independent dimensions (independence hypothesis). Participants saw stimuli comprising two vertical bars (targets), one above and the other below a horizontal bar. They had to judge whether the targets appeared on the same side (categorical) or at the same distance (coordinate) with respect either to their body-midline (egocentric) or to the centre of the horizontal bar (allocentric). The results from Experiment 1 showed a facilitation in the allocentric and categorical conditions. In line with the independence hypothesis, no interaction effect emerged. To see whether the results were affected by the visual salience of the stimuli, in Experiment 2 the luminance of the horizontal bar was reduced. As a consequence, a significant interaction effect emerged indicating that categorical judgements were more accurate than coordinate ones, and especially so in the allocentric condition. Furthermore, egocentric judgements were as accurate as allocentric ones with a specific improvement when combined with coordinate spatial relations. The data from Experiment 2 showed that the visual salience of stimuli affected the relationship between allocentric/egocentric and categorical/coordinate dimensions. This suggests that the emergence of a selective interaction between the two dimensions may be modulated by the characteristics of the task.     

New aspects of the probabilistic evaluation of hypotheses and experience

The probabilistic corroboration of two or more hypotheses or series of observations may be performed additively or multiplicatively . For additive corroboration (e.g. by Laplace's rule of succession), stochastic independence is needed. Inferences, based on overwhelming numbers of observations without unexplained counterinstances permit hyperinduction , whereby extremely high probabilities, bordering on certainty for all practical purposes may be achieved. For multiplicative corroboration, the error probabilities (1 - Pr) of two (or more) hypotheses are multiplied. The probabilities, obtained by reconverting the product, are valid for both of the hypotheses and indicate the gain by corroboration.. This method is mathematically correct, no probabilities > 1 can result (as in some conventional methods) and high probabilities with fewer observations may be obtained, however, semantical independence is a prerequisite. The combined method consists of (1) the additive computation of the error probabilities (1 - Pr) of two or more single hypotheses, whereby arbitrariness is avoided or at least reduced and (2) the multiplicative procedure . The high reliability of Empirical Counterfactual Statements is explained by the possibility of multiplicative corroboration of “all-no” statements due to their strict semantical independence.     

‘The Queen Mother and I’: assimilation,contrast, and attitudes toward social groups

We examined whether social group attitudes are subject to context effects. It was hypothesised that manipulating the context in which a group exemplar was rendered accessible would produce different effects when subjects were subsequently asked to evaluate the exemplar's group. In our study, all subjects first expressed their opinion about the (popular) Queen Mother before indicating their attitude toward the British Royal Family. In the ‘non‐redundant’ condition, the two questions were structured such that the Queen Mother was expected to be included in individuals' representation of the Royal Family, leading to a high correlation between the two judgements and a favourable evaluation of the group. Conversely, in the ‘redundant’ condition, the questions were structured such that the Queen Mother was expected to be excluded from individuals' representation of the Royal Family, leading to a lower correlation between the judgements and a less favourable evaluation of the group. The results supported the hypothesis, and are consistent with the Schwarz and Bless (1992a,b) inclusion/exclusion model of assimilation and contrast. Copyright © 1999 John Wiley & Sons, Ltd.     

用不同外部表征方式集中呈现信息条件下的因果力判断

在分别用文字陈述、表格和图形三种外部表征方式集中呈现因果信息的条件下,用直接估计因果力大小的实验范式考察单一因果关系因果力估计的特点,检验概率对比模型,效力PC理论和pCI规则。让287名大学生被试估计不同化学药物影响动物基因变异的能力。结果发现,对单一因果关系因果力估计具有以下4个特点：⑴不对称性：在预防原因条件下的因果力估计较多符合效力PC理论,而在产生原因条件下的因果力估计一般符合概率对比模型;⑵文字陈述、表格和图形三种信息外部表征方式,不影响产生原因条件下的因果力估计,但影响预防原因条件下的因果力估计。在预防原因条件下,与文字陈述和表格表征相比,图形表征会促使更多被试按效力PC理论来做因果力估计;⑶没有被试使用pCI规则;⑷被试估计因果力所使用的规则存在明显的个体差异。     

Morgenbesser’s Coin, Counterfactuals, and Causal Versus Probabilistic Independence

It is widely held that, as Morgenbesser’s case is usually taken to show, considerations of causal or probabilistic dependence should enter into the evaluation of counterfactuals. This paper challenges that idea. I present a modified version of Morgenbesser’s case and show how probabilistic approaches to counterfactuals are in serious trouble. Specifically, I show how probabilistic approaches run into a dilemma in characterizing probabilistic independence. The modified case also illustrates a difficulty in defining causal independence. I close with a suggestion for a strategy to handle this difficulty.     

Perspectival representation and fallacies in metaethics

Abstract

The prevailing theoretical framework for theorising about representation construes all representation as involving objective representational contents. This classic framework has tended to drive philosophers either to claim that evaluative judgements are representations and therefore objective, or else to claim that evaluative judgements are not really representations, because they are not objective. However, a more general, already well-explored framework is available, which will allow theorists to treat evaluative judgements as full-fledged representations (thus doing justice to their representational aspects) while leaving open whether they are objective. Such a more general conception of representational content is exemplified, e.g. by Lewis’s ‘centred contents’ and Gibbard’s framework of ‘contents of judgement’, thus it is not new. I shall start in §1 by introducing the more general framework of perspectival contents and then illustrate in §2 how awareness of it can help expose the fallaciousness of certain widely used forms of argumentation in metaethics.     

Learning Orthographic Structure With Sequential Generative Neural Networks

Learning the structure of event sequences is a ubiquitous problem in cognition and particularly in language. One possible solution is to learn a probabilistic generative model of sequences that allows making predictions about upcoming events. Though appealing from a neurobiological standpoint, this approach is typically not pursued in connectionist modeling. Here, we investigated a sequential version of the restricted Boltzmann machine (RBM), a stochastic recurrent neural network that extracts high‐order structure from sensory data through unsupervised generative learning and can encode contextual information in the form of internal, distributed representations. We assessed whether this type of network can extract the orthographic structure of English monosyllables by learning a generative model of the letter sequences forming a word training corpus. We show that the network learned an accurate probabilistic model of English graphotactics, which can be used to make predictions about the letter following a given context as well as to autonomously generate high‐quality pseudowords. The model was compared to an extended version of simple recurrent networks, augmented with a stochastic process that allows autonomous generation of sequences, and to non‐connectionist probabilistic models (n‐grams and hidden Markov models). We conclude that sequential RBMs and stochastic simple recurrent networks are promising candidates for modeling cognition in the temporal domain.     

Subjective probability and everyday life

Abstract.— Recent research on probability judgement indicates that people's ability to estimate probabilities is very limited. It is argued that people may lack the cognitive apparatus necessary for processing probabilistic information, in so far as probability judgements play an unimportant role in everyday life. When probability judgements occasionally are made in everyday life it is argued that they are not based on frequency data but on some more or less well grounded theory.     

The role of colour in categorial judgements

Two experiments are reported that extend the findings of Ostergaard and Davidoff (1985) on the role of colour in object processing. Two types of categorial judgements were investigated from pictorial stimuli: size judgement and living/non-living classifications. The effect of real size on size judgements (Paivio, 1975) was replicated. It was found that colour did not affect either of the categorial judgements, but the facilitation occurring in object naming tasks was confirmed. It is argued that semantic judgements can precede name retrieval, that physical colour input does not enter the semantic system, and that the representation of object colour information in the semantic system may be largely verbal.     

Unmasking the Truth Beneath the Beauty: Why the Supposed Aesthetic Judgements Made in Science May Not Be Aesthetic at All

In this article I examine the status of putative aesthetic judgements in science and mathematics. I argue that if the judgements at issue are taken to be genuinely aesthetic they can be divided into two types, positing either a disjunction or connection between aesthetic and epistemic criteria in theory/proof assessment. I show that both types of claim face serious difficulties in explaining the purported role of aesthetic judgements in these areas. I claim that the best current explanation of this role, McAllister's ‘aesthetic induction’ model, fails to demonstrate that the judgements at issue are genuinely aesthetic. I argue that, in light of these considerations, there are strong reasons for suspecting that many, and perhaps all, of the supposedly aesthetic claims are not genuinely aesthetic but are in fact ‘masked’ epistemic assessments.     

Extending the Basic Local Independence Model to Polytomous Data

Psychometrika - A probabilistic framework for the polytomous extension of knowledge space theory (KST) is proposed. It consists in a probabilistic model, called polytomous local independence model,...