任务情境和证据信息对青少年贝叶斯推理的影响研究

采用生活情境测查任务和经典测查任务探讨了任务情境对青少年贝叶斯推理的影响,以及生活情境测查任务中不同证据信息对青少年贝叶斯判断的影响作用.结果表明:(1)在生活情境测查任务中,从小学六年级到大学二年级,被试的贝叶斯推理能力稳步缓慢提升(相邻的两个被试组之间差异不显著,而不相邻的两个被试组之间差异更容易达到显著水平),发展没有出现加速期,而经典测查任务情境下没有表现出年龄差异;(2)贝叶斯推理作为条件概率的判断不仅受任务情境的影响,而且同一任务情境中不同证据信息也会影响贝叶斯判断.当证据信息与先验信念一致时,被试可以充分利用线索进行推理.     

A new formulation of the Principle of Indifference

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for.     

Bets and Boundaries: Assigning Probabilities to Imprecisely Specified Events

Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imprecision by rough sets over an approximation space presents an especially tractable case to help get one’s bearings. Two solutions present themselves: the first takes as upper and lower probabilities of the event X the (exact) probabilities assigned X’s upper and lower rough-set approximations; the second, motivated both by formal considerations and by a simple betting argument, is to treat X’s rough-set approximation as a conditional event and assign to it a point-valued (conditional) probability. With rough sets over an approximation space we get a lot of good behaviour. For example, in the first construction mentioned the lower probabilities are n-monotone, for every . When we examine other models of approximation/imprecision/vagueness, and in particular, proximity spaces, we lose a lot of that good behaviour. In the literature there is not (even) agreement on the definition of upper and lower approximations for events (subsets) in the underlying domain. Betting considerations suggest one choice and, again, ways to assign upper and lower and point-valued probabilities, but nothing works well. Special Issue on Vagueness Edited by Rosanna Keefe and Libor Bêhounek     

What determines creative association? Revealing two factors which separately influence the creative process when solving the Remote Associates Test

The Remote Associates Test is a well‐established measure, frequently used to assess individuals’ creative abilities, as a function of the ability to elicit remote associates. The nature of the involved associative processes is still poorly understood. This hampers a deeper understanding of the creative process, rendering it difficult to determine what factors are controlled for, when the RAT is employed. We report an experiment that sheds further light on the nature of the associative process by manipulating (a) the frequency with which a pair of items are associated as associative strength, and (b) the probability of reaching the answer given the strength and the spread. Experimental results indicate a clear and surprisingly separate influence of frequency and probability on accuracy and response times. Frequency and probability both are thus factors that need to be included in the modeling process and controlled for when using the RAT to assess creativity.     

Rank‐permutation tests for behavior analysis,and a test for trend allowing unequal data numbers for each subject

We advocate for rank‐permutation tests as the best choice for null‐hypothesis significance testing of behavioral data, because these tests require neither distributional assumptions about the populations from which our data were drawn nor the measurement assumption that our data are measured on an interval scale. We provide an algorithm that enables exact‐probability versions of such tests without recourse to either large‐sample approximation or resampling approaches. We particularly consider a rank‐permutation test for monotonic trend, and provide an extension of this test that allows unequal number of data points, or observations, for each subject. We provide an extended table of critical values of the test statistic for this test, and both a spreadsheet implementation and an Oracle® Java Web Start application to generate other critical values at https://sites.google.com/a/eastbayspecialists.co.nz/rank-permutation/ .     

Interpretation bias and social anxiety: does interpretation bias mediate the relationship between trait social anxiety and state anxiety responses?

Two studies aimed to examine whether high socially anxious individuals are more likely to negatively interpret ambiguous social scenarios and facial expressions compared to low socially anxious individuals. We also examined whether interpretation bias serves as a mediator of the relationship between trait social anxiety and state anxiety responses, in particular current state anxiety, bodily sensations, and perceived probability and cost of negative evaluation pertaining to a speech task. Study 1 used ambiguous social scenarios and Study 2 used ambiguous facial expressions as stimuli to objectively assess interpretation bias. Undergraduate students with high and low social anxiety completed measures of state anxiety responses at three time points: baseline, after the interpretation bias task, and after the preparation for an impromptu speech. Results showed that high socially anxious individuals were more likely to endorse threat interpretations for ambiguous social scenarios and to interpret ambiguous faces as negative than low socially anxious individuals. Furthermore, negative interpretations mediated the relationship between trait social anxiety and perceived probability of negative evaluation pertaining to the speech task in Study 1 but not Study 2. The present studies provide new insight into the role of interpretation bias in social anxiety.     

从贝叶斯主义的视角看迪昂问题

对于迪昂问题,贝叶斯主义有着独特的视角。本文主要通过介绍多林与斯特雷文斯各自运用贝叶斯方法解决迪昂问题的两个方案,试图说明迪昂问题在贝叶斯机制中的处理方式,并且对这两个方案作出比较,认为斯特雷文斯的方案更为客观与合理。     

The reference class problem is your problem too

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains.     

A Note on Binary Inductive Logic

We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.     

The Logic of Theory Assessment

This paper starts by indicating the analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper consists in working out the claim that one can have Hempel’s cake and eat it too — in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, α is an acceptable theory for evidence β if and only if α is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, 1988) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, 2000) as well as to nonmonotonic consequence relations (Kraus et al., 1990). It concludes by relating the plausibility-informativeness approach to Carnap’s positive relevance account, thereby shedding new light on Carnap’s analysis as well as solving another problem of confirmation theory. A precursor of this paper has appeared as “The Logic of Confirmation and Theory Assessment” in L. Běhounek & M. Bílková (eds.), The Logica Yearbook 2004, Prague: Filosofia, 2005, 161–176.