On Holland's Dutch identity conjecture

The manifest probabilities of observed examinee response patterns resulting from marginalization with respect to the latent ability distribution produce the marginal likelihood function in item response theory. Under the conditions that the posterior distribution of examinee ability given some test response pattern is normal and the item logit functions are linear, Holland (1990a) gives a quadratic form for the log-manifest probabilities by using the Dutch Identity. Further, Holland conjectures that this special quadratic form is a limiting one for all smooth unidimensional item response models as test length tends to infinity. The purpose of this paper is to give three counterexamples to demonstrate that Holland's Dutch Identity conjecture does not hold in general. The counterexamples suggest that only under strong assumptions can it be true that the limits of log-manifest probabilities are quadratic. Three propositions giving sets of such strong conditions are given.     

Ordinal data,ordered scale points,and order statistics

This paper concerns ordinal responses. An ordered Dirichlet distribution describes prior and posterior beliefs about the cumulative probabilities of response categories. Associating the response categories with intervals of a latent random variable then induces a distribution on the order statistics of that variable. The psychometrician can use the asymptotic theory of order statistics to learn how distributional assumptions about the latent variable effect inference. An example relates the skewness of a latent variable to the proportional odds and proportional hazards models of McCullagh [1980].     

Chunking or not chunking? How do we find words in artificial language learning?

What is the nature of the representations acquired in implicit statistical learning? Recent results in the field of language learning have shown that adults and infants are able to find the words of an artificial language when exposed to a continuous auditory sequence consisting in a random ordering of these words. Such performance can only be based on processing the transitional probabilities between sequence elements. Two different kinds of mechanisms may account for these data: Participants may either parse the sequence into smaller chunks corresponding to the words of the artificial language, or they may become progressively sensitive to the actual values of the transitional probabilities between syllables. The two accounts are difficult to differentiate because they make similar predictions in comparable experimental settings. In this study, we present two experiments that aimed at contrasting these two theories. In these experiments, participants had to learn 2 sets of pseudo-linguistic regularities: Language 1 (L1) and Language 2 (L2) presented in the context of a serial reaction time task. L1 and L2 were either unrelated (none of the syllabic transitions of L1 were present in L2), or partly related (some of the intra-words transitions of L1 were used as inter-words transitions of L2). The two accounts make opposite predictions in these two settings. Our results indicate that the nature of the representations depends on the learning condition. When cues were presented to facilitate parsing of the sequence, participants learned the words of the artificial language. However, when no cues were provided, performance was strongly influenced by the employed transitional probabilities.     

What is learned about fragments in artificial grammar learning? A transitional probabilities approach

Learning local regularities in sequentially structured materials is typically assumed to be based on encoding of the frequencies of these regularities. We explore the view that transitional probabilities between elements of chunks, rather than frequencies of chunks, may be the primary factor in artificial grammar learning (AGL). The transitional probability model (TPM) that we propose is argued to provide an adaptive and parsimonious strategy for encoding local regularities in order to induce sequential structure from an input set of exemplars of the grammar. In a variant of the AGL procedure, in which participants estimated the frequencies of bigrams occurring in a set of exemplars they had been exposed to previously, participants were shown to be more sensitive to local transitional probability information than to mere pattern frequencies.     

Verbal probabilities: An alternative approach

Previous studies of verbal probabilities have tried to place expressions like a chance, possible, and certain on 0–1 numerical probability scales. We ask instead, out of a range of outcomes, which outcome a verbal probability suggests. When, for instance, a sample of laptop batteries lasts from 1.5 to 3.5 hours, what is a certain and what is a possible duration? Experiment 1 showed that speakers associate certain with low values and possible with (unlikely) high or maximal values. In Experiment 2, this methodology was applied to several positive and negative verbal probability phrases, showing a preference for high rather than low or middle values in a distribution. Experiment 3 showed that such maxima are not universally described by large numbers. For instance, maximum speed is often described in terms of a small number of time units. What can (possibly) happen is accordingly sometimes described with very low and sometimes with very high values, depending upon focus of interest. Finally, participants in Experiment 4 were given the role of hearers rather than speakers and were asked to infer outcome ranges from verbal probabilities. Hearers appeared to be partly aware of speakers' tendencies to describe outcomes at the top of the range.     

The sure thing principle,dilations, and objective probabilities

The common theme that unites the four sections is STP, the sure thing principle. But the paper can be divided neatly into two parts. The first, consisting of the first two sections, contains an analysis of STP as it figures in Savage?s system and proposals of changes to that system. Also possibilities for partially ordered acts are considered. The second, consisting of the last two sections, is about imprecise probabilities, dilations and objective probabilities. Variants of STP are considered but this part is self-contained and can be read separately. The main claim there is that dilations, which can have extremely counterintuitive consequences, can be eliminated by a more careful analysis of the phenomenon. It outlines a proposal of how to do it. Here the concept of objective probabilities plays a crucial role.     

What is learned from experience in a probabilistic environment?

Three experiments explored what is learned from experience in a probabilistic environment. The task was a simulated medical decision‐making task with each patient having one of two test results and one of two diseases. The test result was highly predictive of the disease for all participants. The base rate of the test result was varied between participants to produce different inverse conditional probabilities of the test result given the disease across conditions. Participants trained using feedback to predict a patient's disease from a test result showed the classic confusion of the inverse error, substituting the forward conditional probability for the inverse conditional probability when tested on it. Additional training on the base rate of the test result did little to improve performance. Training on the joint probabilities, however, produced good performance on either conditional probability. The pattern of results demonstrated that experience with the environment is not always sufficient for good performance. That natural sampling leads to good performance was not supported. Further, because participants not trained on joint probabilities did, however, know them but still committed the confusion of the inverse error, the hypothesis that having joint probabilities would facilitate performance was not supported. The pattern of results supported the conclusion that people learn all the necessary information from experience in a probabilistic environment, but depending upon what the experience was, it may interfere with their ability to recall to memory the appropriate sample set necessary for estimating or using the inverse conditional probability. Copyright © 2004 John Wiley & Sons, Ltd.     

Infants’ statistical word segmentation in an artificial language is linked to both parental speech input and reported production abilities

Individual variability in infant's language processing is partly explained by environmental factors, like the quantity of parental speech input, as well as by infant‐specific factors, like speech production. Here, we explore how these factors affect infant word segmentation. We used an artificial language to ensure that only statistical regularities (like transitional probabilities between syllables) could cue word boundaries, and then asked how the quantity of parental speech input and infants’ babbling repertoire predict infants’ abilities to use these statistical cues. We replicated prior reports showing that 8‐month‐old infants use statistical cues to segment words, with a preference for part‐words over words (a novelty effect). Crucially, 8‐month‐olds with larger novelty effects had received more speech input at 4 months and had greater production abilities at 8 months. These findings establish for the first time that the ability to extract statistical information from speech correlates with individual factors in infancy, like early speech experience and language production. Implications of these findings for understanding individual variability in early language acquisition are discussed.     

转换概率和词长期待对语音统计学习的影响

语音统计学习指个体在加工人工语言过程中, 可以追踪音节间的转换概率实现切分语流、提取词(语)的过程。本研究采用2(转换概率：高转换概率、低转换概率) × 2(词长期待：两音节、三音节)的混合实验设计来考察转换概率和词长期待对语音统计学习的影响, 转换概率是被试间变量, 词长期待是被试内变量。事后检验发现, 仅在低转换概率人工语言的三音节迫选条件下, 被试没有表现出显著的学习效果。事先对比发现, 在学习低转换概率的人工语言后, 被试完成三音节迫选试次的成绩显著低于两音节迫选试次; 在三音节迫选试次中, 学习低转换概率人工语言被试的成绩也显著低于学习高转换概率被试的成绩。以上结果说明, 转换概率和词长期待共同影响个体语音统计学习的效果。     

More than 50% or Less than 70% Chance: Pragmatic Implications of Single‐Bound Probability Estimates

Probability estimates can be given as ranges or uncertainty intervals, where often only one of the interval bounds (lower or upper) is specified. For instance, a climate forecast can describe La Niña as having “more than 70% chance” or “less than 90% chance” of occurring. In three experiments, we studied how research participants perceived climate‐related forecasts expressed with lower‐bound (“over X% chance”) or upper‐bound (“under Y% chance”) probability statements. Results indicate that such single‐bound statements give pragmatic information in addition to the numeric probabilities they convey. First, the studies show that these statements are directional, leading the listeners' attention in opposite directions. “Over” statements guide attention towards the possible occurrence of the event and are explained by reasons for why it might happen, while “under” statements direct attention to its possible non‐occurrence and are more often explained by reasons for why the target event might not appear, corresponding to positive (it is possible) versus negative (it is uncertain) verbal probabilities. Second, boundaries were found to reveal the forecaster's beliefs and could be perceived as indicative of an increasing or a decreasing trend. Single‐bound probability estimates are therefore not neutral communications of probability level but might “leak” information about the speaker's expectations and about past and future developments of the forecast. Copyright © 2017 John Wiley & Sons, Ltd.