Visual statistical decisions

To identify variables that underlie intuitive judgments about the sizes of groups of similar objects, we asked people to judge the relative heights of vertical bars briefly shown, two groups at a time, on a computer display. Randomly selected normal deviates determined individual bar height. Average differences in height and group sizes were also randomly varied. Twenty-eight participants judged 250 differences each, which were then submitted to multiple regression analysis and psychophysical inspection. The total number of bars sharpened discrimination, whereas variance dulled it. Critical ratio (CR), the forerunner to the modern t test, emerged as the most important predictor; little additional variance was explained by other factors. The difference in the number of bars was a reliable factor, favoring the greater number of bars. Confidence limits around thresholds, defined as CRs needed to say “possibly greater,” surrounded 1.65; as a z value, this corresponded to a one-tailed probability of .05. Judgments about noisy stimuli thus seem to be based on a statistical process and to employ a probability criterion similar to that used in the formal statistical evaluation of experimental findings—namely, p<.05.     

Effects of signal uncertainty on statistical decisions

The experimental task involved statistical judgements about parameters of a random sample of dots displayed sequentially from a ‘signal’ or ‘noise’ distribution. Signal uncertainty was introduced by presenting small signal subsets of dots within larger observation sequences. Observer detection performance was adversely affected by this kind of signal uncertainty, but in the same way and to similar extent as that expected on the basis of ‘ideal’ and ‘independent’ statistical decision strategies.     

Visual comparison processes: Identity and similarity decisions

In the first experiment, in which two successively presented free-form visual patterns varied in their similarity to each other, subjects had to decide, in one condition, if the patterns were “identical” and in two other conditions if the patterns were “similar.” Qualitative individual differences in the effect of similarity on the time required to make a decision were found in the “identity” condition, and these differences interacted with the “similarity” conditions. The individual differences and the experimental effects are interpreted in terms of a two-process model of the visual comparison process—a holistic matching process that is sometimes accompanied by an analytic difference detection process. In the second experiment, the same subjects repeatedly categorized subsets of the free-form visual patterns on the basis of similarity. There appeared to be no individual differences in the subjects’ perceptions of similarity, but subjects’ perceptions did differ from the assumptions made by the experimenters when they established the response criteria for the first experiment.     

Context-gated statistical learning and its role in visual-saccadic decisions

Adaptive behavior in a nonstationary world requires humans to learn and track the statistics of the environment. We examined the mechanisms of adaptation in a nonstationary environment in the context of visual-saccadic inhibition of return (IOR). IOR is adapted to the likelihood that return locations will be refixated in the near future. We examined 2 potential learning mechanisms underlying adaptation: (a) a local tracking or priming mechanism that facilitates behavior that is consistent with recent experience and (b) a mechanism that supports retrieval of knowledge of the environmental statistics based on the contextual features of the environment. Participants generated sequences of 2 saccadic eye movements in conditions where the probability that the 2nd saccade was directed back to the previously fixated location varied from low (.17) to high (.50). In some conditions, the contingency was signaled by a contextual cue (the shape of the movement cue). Adaptation occurred in the absence of contextual signals but was more pronounced in the presence of contextual cues. Adaptation even occurred when different contingencies were randomly intermixed, showing the parallel formation of multiple associations between context and statistics. These findings are accounted for by an evidence accumulation framework in which the resting baseline of decision alternatives is adjusted on a trial-by-trial basis. This baseline tracks the subjective prior beliefs about the behavioral relevance of the different alternatives and is updated on the basis of the history of recent events and the contextual features of the current environment.     

Visual statistical learning in the newborn infant

Statistical learning – implicit learning of statistical regularities within sensory input – is a way of acquiring structure within continuous sensory environments. Statistics computation, initially shown to be involved in word segmentation, has been demonstrated to be a general mechanism that operates across domains, across time and space, and across species. Recently, statistical leaning has been reported to be present even at birth when newborns were tested with a speech stream. The aim of the present study was to extend this finding, by investigating whether newborns’ ability to extract statistics operates in multiple modalities, as found for older infants and adults. Using the habituation procedure, two experiments were carried out in which visual sequences were presented. Results demonstrate that statistical learning is a general mechanism that extracts statistics across domain since the onset of sensory experience. Intriguingly, present data reveal that newborn learner’s limited cognitive resources constrain the functioning of statistical learning, narrowing the range of what can be learned.     

Visual attention and coactivation of response decisions for features from different dimensions

The role of visual attention in task performance has been extensively debated. On the basis of the dimensional-action model, we hypothesized that a major role of attention is to transfer response decisions from targets on which it is focused to high-level centers dealing with response execution. This hypothesis predicts that response decisions for two targets will interact only when attention is focused on both targets, and only when the response to the targets is defined by different dimensions. Three experiments, using the redundancy-gain paradigm, tested and confirmed this prediction. Experiment 1 showed that coactivation of two cross-dimensional targets occurred only when the targets were positioned in the same location, not when they were in separate locations. Experiment 2 manipulated the focus of attention and showed that coactivation can occur even for targets positioned in different locations if they are both within the attentional focus. Experiment 3 showed that this attention-induced coactivation does not occur for targets from the same dimensional module. These results suggest that a major role of attention is postperceptual and involves gating of selected responses to executive functions.     

Visual statistical learning at basic and subordinate category levels in real-world images

Visual statistical learning (VSL) has been proposed as a powerful mechanism underlying the striking ability of human observers to handle complex visual environments. Previous studies have shown that VSL can occur when statistical information is embedded at multiple levels of abstraction, such as at semantically different category levels. In the present study, we further examined whether statistical regularities at a basic category level (e.g., a regular sequence of a bird, then a car, and then a dog) could influence the ability to extract statistical regularities at the subordinate level (e.g., a regular sequence of a parrot, then a sports car, and then an Eskimo dog). In the familiarization phase, participants were exposed to a stream of real-world images whose semantic categories had temporal regularities. Importantly, the temporal regularities existed at both the basic and subordinate levels, or the regularities existed at only the subordinate level, depending on the experimental condition. After completing the familiarization, participants performed a surprise two-alternative forced choice (2AFC) task for a familiarity judgment between two triplets in which the temporal regularities were either preserved or not preserved. Our results showed that the existence of statistical regularities at the basic level did not influence VSL at the subordinate level. The subsequent experiments showed these results consistently even when the basic-level categories had to be explicitly recognized and when the stimuli were not easily categorized at their subordinate level. Our results suggest that VSL is constrained to learn a particular level of patterns when patterns are presented across multiple levels.     

Visual statistical learning in infancy: evidence for a domain general learning mechanism

The rapidity with which infants come to understand language and events in their surroundings has prompted speculation concerning innate knowledge structures that guide language acquisition and object knowledge. Recently, however, evidence has emerged that by 8 months, infants can extract statistical patterns in auditory input that are based on transitional probabilities defining the sequencing of the input's components (Science 274 (1996) 1926). This finding suggests powerful learning mechanisms that are functional in infancy, and raises questions about the domain generality of such mechanisms. We habituated 2-, 5-, and 8-month-old infants to sequences of discrete visual stimuli whose ordering followed a statistically predictable pattern. The infants subsequently viewed the familiar pattern alternating with a novel sequence of identical stimulus components, and exhibited significantly greater interest in the novel sequence at all ages. These results provide support for the likelihood of domain general statistical learning in infancy, and imply that mechanisms designed to detect structure inherent in the environment may play an important role in cognitive development.     

Surreal decisions

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives.     

Memories of real-life decisions

Three studies investigated decision makers' memory representations of choice alternatives in most important real-life decisions. In Study 1, each participant recalled the most important decision that she or he had ever made and rated to what degree a number of characteristics could describe the decisions. In Study 2, the participants were asked to think about an important decision that they had made during the last 7-10 days. In Study 3, the memory representations of decisions of a group of action-oriented participants were compared with those of a group of state-oriented participants (Kuhl, 1983). Characteristics related to standard decision theory, like consequences, values, and likelihood, had high ratings of applicability as well as affect/feeling. When testing the applicability of a circumplex model, the fuzzy-trace theory of memory, and differences between state- and action-oriented decision makers, we found (1) that there was no support for the circumplex model of emotions. Instead, an important decision problem was characterised by both positive and negative affect/emotion and thus, a bipolar mapping was found inadequate; (2) that a comparison of abstract and concrete aspects showed that the abstract characteristics scored higher, thereby supporting the fuzzy-trace theory; and (3) that the prediction that action-oriented participants would score higher than state-oriented participants on the characteristic of activity was not supported. However, state-oriented decision makers rated passivity higher than action-oriented decision makers for the important decision of leaving a partner. State-oriented decision makers used perceptual/cognitive scenario representations to a greater extent than action-oriented participants. Finally, it was stressed that in the development of decision theories it is essential to find theoretical representations as close as possible to how decision makers themselves represent the decisions. The method used in this contribution is focused on the role of memory in decision making and gives further insights into how important real-life decisions are represented by different decision makers.     

Rapid decisions from experience

In many everyday decisions, people quickly integrate noisy samples of information to form a preference among alternatives that offer uncertain rewards. Here, we investigated this decision process using the Flash Gambling Task (FGT), in which participants made a series of choices between a certain payoff and an uncertain alternative that produced a normal distribution of payoffs. For each choice, participants experienced the distribution of payoffs via rapid samples updated every 50 ms. We show that people can make these rapid decisions from experience and that the decision process is consistent with a sequential sampling process. Results also reveal a dissociation between these preferential decisions and equivalent perceptual decisions where participants had to determine which alternatives contained more dots on average. To account for this dissociation, we developed a sequential sampling rank-dependent utility model, which showed that participants in the FGT attended more to larger potential payoffs than participants in the perceptual task despite being given equivalent information. We discuss the implications of these findings in terms of computational models of preferential choice and a more complete understanding of experience-based decision making.     

Mutual interference between statistical summary perception and statistical learning

The visual system is an efficient statistician, extracting statistical summaries over sets of objects (statistical summary perception) and statistical regularities among individual objects (statistical learning). Although these two kinds of statistical processing have been studied extensively in isolation, their relationship is not yet understood. We first examined how statistical summary perception influences statistical learning by manipulating the task that participants performed over sets of objects containing statistical regularities (Experiment 1). Participants who performed a summary task showed no statistical learning of the regularities, whereas those who performed control tasks showed robust learning. We then examined how statistical learning influences statistical summary perception by manipulating whether the sets being summarized contained regularities (Experiment 2) and whether such regularities had already been learned (Experiment 3). The accuracy of summary judgments improved when regularities were removed and when learning had occurred in advance. In sum, calculating summary statistics impeded statistical learning, and extracting statistical regularities impeded statistical summary perception. This mutual interference suggests that statistical summary perception and statistical learning are fundamentally related.