A hierarchical bayesian model of human decision-making on an optimal stopping problem

We consider human performance on an optimal stopping problem where people are presented with a list of numbers independently chosen from a uniform distribution. People are told how many numbers are in the list, and how they were chosen. People are then shown the numbers one at a time, and are instructed to choose the maximum, subject to the constraint that they must choose a number at the time it is presented, and any choice below the maximum is incorrect. We present empirical evidence that suggests people use threshold-based models to make decisions, choosing the first currently maximal number that exceeds a fixed threshold for that position in the list. We then develop a hierarchical generative account of this model family, and use Bayesian methods to learn about the parameters of the generative process, making inferences about the threshold decision models people use. We discuss the interesting aspects of human performance on the task, including the lack of learning, and the presence of large individual differences, and consider the possibility of extending the modeling framework to account for individual differences. We also use the modeling results to discuss the merits of hierarchical, generative and Bayesian models of cognitive processes more generally.     

A two-stage model of visual search

A two-stage visual search model is described. Four experiments show that in a VM paradigm sequential presentation of the display leads to increases in accuracy and decreases in latency. Slower presentation rates allow for faster transfer of the target from iconic to short-term memory. When target and background items are dissimilar, transfer to short-term memory need not take place and decisions can be made on the basis of the Stage 1 analysis. These results are taken as confirming evidence for the proposed model.     

Delay reduction and optimal foraging: variable-ratio search in a foraging analogue.

The present study investigated conditions under which the conditioned reinforcement principles of delay-reduction theory and views based on simple maximization of reinforcement rate make ordinally opposing predictions with respect to foraging-related choice behavior. The use of variable-ratio schedules in the choice phase also represents an extension of delay-reduction theory to schedules that may better mimic the effort involved in searching. Pigeons responded on modified concurrent-chains schedules in which equal variable-ratio schedules led to unequal variable-interval outcomes and unequal reinforcer amounts. All 4 subjects completed a minimum of two replications of conditions for which the predictions of delay-reduction theory and a simple rate-maximizing theory were opposed. Results were consistent with delay reduction's ordinal predictions in 11 of 11 replications of the divergent predictions favoring the smaller, more immediate alternative. The predictions of rate maximization were upheld only when they were consistent with those of delay reduction. Results are discussed in terms of conditioned reinforcement, sensitivity to reductions in delay to food, and possible rules of thumb that may be useful in characterizing foraging.     

Guided Search 2.0 A revised model of visual search

An important component of routine visual behavior is the ability to find one item in a visual world filled with other, distracting items. This ability to performvisual search has been the subject of a large body of research in the past 15 years. This paper reviews the visual search literature and presents a model of human search behavior. Built upon the work of Neisser, Treisman, Julesz, and others, the model distinguishes between a preattentive, massively parallel stage that processes information about basic visual features (color, motion, various depth cues, etc.) across large portions of the visual field and a subsequent limited-capacity stage that performs other, more complex operations (e.g., face recognition, reading, object identification) over a limited portion of the visual field. The spatial deployment of the limited-capacity process is under attentional control. The heart of the guided search model is the idea that attentional deployment of limited resources isguided by the output of the earlier parallel processes. Guided Search 2.0 (GS2) is a revision of the model in which virtually all aspects of the model have been made more explicit and/or revised in light of new data. The paper is organized into four parts: Part 1 presents the model and the details of its computer simulation. Part 2 reviews the visual search literature on preattentive processing of basic features and shows how the GS2 simulation reproduces those results. Part 3 reviews the literature on the attentional deployment of limited-capacity processes in conjunction and serial searches and shows how the simulation handles those conditions. Finally, Part 4 deals with shortcomings of the model and unresolved issues.     

Fruitful visual search: Inhibition of return in a virtual foraging task

Inhibition of return (IOR) has long been viewed as a foraging facilitator in visual search. We investigated the contribution of IOR in a task that approximates natural foraging more closely than typical visual search tasks. Participants in a fully immersive virtual reality environment manually searched an array of leaves for a hidden piece of fruit, using a wand to select and examine each leaf location. Search was slower than in typical IOR paradigms, taking seconds instead of a few hundred milliseconds. Participants also made a speeded response when they detected a flashing leaf that either was or was not in a previously searched location. Responses were slower when the flashing leaf was in a previously searched location than when it was in an unvisited location. These results generalize IOR to an approximation of a naturalistic visual search setting and support the hypothesis that IOR can facilitate foraging. The experiment also constitutes the first use of a fully immersive virtual reality display in the study of IOR.     

A two-stage detection model applied to skilled visual search by radiologists

Harvard Medical School and Peter Bent Brigham Hospital, Boston, Massachusetts 02115 The model treats the detection of targets in a visual search task as a concatenation of two serial detection stages. Preattentive visual mechanisms in the initial stage function as a filter, selecting specific features of a visual pattern for the observer’s explicit attention and final cognitive evaluation. The model uses bivariate normal distributions to represent the decision variables for the two serial stages, assuming different parameters for the target and nontarget features in a test set. The model is applied to the detection performance of radiologists interpreting chest x-rays under various conditions of search. It accounts for the substantial improvement in radiologists’ ability to distinguish between target and nontarget test features when they had to search the x-ray images, compared to their performance without visual search. A change in the ROC curve between two different search tasks could be interpreted as a shift in the selection cutoff used by the preattentive filter.     

Eye movements in active visual search: A computable phenomenological model

We present a computational model and corresponding computer simulations that mimic phenomenologically the eye movement trajectories observed in a conjunctive visual search task. The element of randomness is captured in the model through a Monte Carlo selection of a particular eye movement based on its probability, which depends on three factors, adjusted to match to the observed saccade amplitude distribution, forward bias in consecutive saccades, and return rates. Memory is assumed to operate through tagging of objects already recognized as nontargets, which, in turn, requires their processing within the attentional area of conspicuity (AC). That AC is adjusted so that computer simulations optimally reproduce the distribution of the number of saccades, the failure rate for capturing the target, and the return rate to previously inspected locations. For their viability, computer simulations critically depend on memory’s being long-ranged. In turn, the simulations confirm the formation of circulating or spiraling patterns in the observed eye trajectories. We also relate consistently the average number of saccades per trial to the saccade amplitude distribution by modeling analytically the combined roles of the AC in attention and memory. The full Supplemental Appendix A for this article may be downloaded from http:// app.psychonomic-journals.org/content/supplemental.     

A diffusion model of early visual search: Theoretical analysis and experimental results

Summary Meinecke (1989, Exp. 1, cond. HO) showed that the detectability of a visual target embedded in a linear noise array decreases with increasing retinal eccentricity, while the reaction time (RT) of the hits increases. One of the most interesting features of her results was that the RT of the correct rejections is consistently larger than the RT for signals presented near the fovea. This finding suggests that initially visual attention is concentrated near the fixation point and then diffuses across the stimulus array to perform a serial, exhaustive search. We present a diffusion model of early visual-search processes that quantitatively describes this evolution of attention in time and space; in contrast to most previous conceptions, it is based on a genuine relation between the spatial and temporal dimensions of the search processes performed. The model predicts quantitatively both detection performance and RT. We conducted an experiment similar to that of Meinecke (1989), but with an additional variation of the presentation time. All the main features of the 189 predictions could be explained by the model. The interpretation of the four model's parameters is discussed in some detail and compared with previous estimates of the microscopic search speed derived from alternative models. Finally, we consider some possible modifications related to results of Kehrer (1987, 1989), and some generalizations to multi target detection and two-dimensional stimulus arrays.     

Guided search: an alternative to the feature integration model for visual search

Subjects searched sets of items for targets defined by conjunctions of color and form, color and orientation, or color and size. Set size was varied and reaction times (RT) were measured. For many unpracticed subjects, the slopes of the resulting RT X Set Size functions are too shallow to be consistent with Treisman's feature integration model, which proposes serial, self-terminating search for conjunctions. Searches for triple conjunctions (Color X Size X Form) are easier than searches for standard conjunctions and can be independent of set size. A guided search model similar to Hoffman's (1979) two-stage model can account for these data. In the model, parallel processes use information about simple features to guide attention in the search for conjunctions. Triple conjunctions are found more efficiently than standard conjunctions because three parallel processes can guide attention more effectively than two.     

Global and local covert visual attention: Evidence from a bayesian hidden markov model

Psychological, psychophysical and physiological research indicates that people switch between two covert attention states, local and global attention, while visually exploring complex scenes. The focus in the local attention state is on specific aspects and details of the scene, and on examining its content with greater visual detail. The focus in the global attention state is on exploring the informative and perceptually salient areas of the scene, and possibly on integrating the information contained therein. The existence of these two visual attention states, their relative prevalence and sequence in time has remained empirically untested to date. To fill this gap, we develop a psychometric model of visual covert attention that extends recent work on hidden Markov models, and we test it using eye-movement data. The model aims to describe the observed time series of saccades typically collected in eye-movement research by assuming a latent Markov process, indicative of the brain switching between global and local covert attention. We allow subjects to be in either state while exploring a stimulus visually, and to switch between them an arbitrary number of times. We relax the no-memory-property of the Markov chain. The model that we develop is estimated with MCMC methodology and calibrated on eye-movement data collected in a study of consumers' attention to print advertisements in magazines.We thank Dominique Claessens of Verify International for making the data available to us.     

A developmental study of visual search behavior

Children in second, fourth and sixth grades and college sophomores were compared on a visual search and scanning task under three experimental condilions. In Condition I, a single target letter was sought in a list of letters of low visual confusability. In Condition II, two target letters were sought but only one appeared in a given list. In Condition III, a single target letter was sought in a list of letters of high confusability. Search time decreased with age in all three tasks. Searching for two targets was no harder than searching for one. A highly confusable visual context increased search time at all age levels.     

A developmental study of visual search behavior

Children in second, fourth and sixth grades and college sophomores were compared on a visual search and scanning task under three experimental conditions. In Condition I, a single target letter was sought in a list of letters of low visual confusability. In Condition II, two target letters were sought but only one appeared in a given list. In Condition III, a single target letter was sought in a list of letters of high confusability. Search time decreased with age in all three tasks. Searching for two targets was no harder than searching for one. A highly confusable visual context increased search time at all age levels.     

自我相关信息对视觉搜索主动抑制的易化作用

工作记忆表征会以自上而下的方式调控注意选择过程, 其中一种表现就是能够对储存的干扰物表征产生注意的主动抑制, 进而提高对目标的搜索效率。另一方面, 凸显性刺激也会以自下而上的方式优先捕获注意。那么, 当保持在工作记忆中的干扰物为更具社会凸显性特征的刺激(如与自己有关的信息)时, 会对视觉搜索过程中的注意抑制产生怎样的影响, 目前尚不清楚。本研究采用短暂联结任务和工作记忆引导的视觉搜索任务范式, 探讨了自我凸显性对注意主动抑制的影响。结果发现, 相比他人和中性条件, 当工作记忆表征为自我联结刺激时, 目标搜索反应更快。本研究从行为层面为自我相关信息能够易化主动抑制过程提供了证据。     

The dynamics of infant visual foraging

Human infants actively forage for visual information from the moment of birth onward. Although we know a great deal about how stimulus characteristics influence looking behavior in the first few postnatal weeks, we know much less about the intrinsic dynamics of the behavior. Here we show that a simple stochastic dynamical system acts quantitatively like 4-week-old infants on a range of measures if there is hysteresis in the transitions between looking and looking away in the model system. The success of this simple three-parameter model suggests that visual foraging in the first few weeks after birth may be influenced more by noise and hysteresis in underlying neural mechanisms than by how infants process visual information after a look begins.     

Visual search and foraging compared in a large-scale search task

It has been argued that visual search is a valid model for human foraging. However, the two tasks differ greatly in terms of the coding of space and the effort required to search. Here we describe a direct comparison between visually guided searches (as studied in visual search tasks) and foraging that is not based upon a visually distinct target, within the same context. The experiment was conducted in a novel apparatus, where search locations were indicated by an array of lights embedded in the floor. In visually guided conditions participants searched for a target defined by the presence of a feature (red target amongst green distractors) or the absence of a feature (green target amongst red and green distractors). Despite the expanded search scale and the different response requirements, these conditions followed the pattern found in conventional visual search paradigms: feature-present search latencies were not linearly related to display size, whereas feature-absent searches were longer as the number of distractors increased. In a non-visually guided foraging condition, participants searched for a target that was only visible once the switch was activated. This resulted in far longer latencies that rose markedly with display size. Compared to eye-movements in previous visual search studies, there were few revisit errors to previously inspected locations in this condition. This demonstrates the important distinction between visually guided and non-visually guided foraging processes, and shows that the visual search paradigm is an equivocal model for general search in any context. We suggest a comprehensive model of human spatial search behaviour needs to include search at a small and large scale as well as visually guided and non-visually guided search.     

A taxonomy of errors in multiple-target visual search

Multiple-target visual searches are especially error prone; once one target is found, additional targets are likely to be missed. This phenomenon, often called satisfaction of search (which we refer to here as subsequent search misses; SSMs), is well known in radiology, despite no existing consensus about the underlying cause(s). Taking a cognitive laboratory approach, we propose that there are multiple causes of SSMs and present a taxonomy of SSMs based on searchers' eye movements during a multiple-target search task, including both previously identified and novel sources of SSMs. The types and distributions of SSMs revealed effects of working memory load, search strategy, and additional causal factors, suggesting that there is no single cause of SSMs. A multifaceted approach is likely needed to understand the psychological causes of SSMs and then to mitigate them in applied settings such as radiology and baggage screening.     

A conjunctive feature similarity effect for visual search

Traditional models of visual search assume interitem similarity effects arise from within each feature dimension independently of other dimensions. In the present study, we examine whether distractor–distractor effects also depend on feature conjunctions (i.e., whether feature conjunctions form a separate “feature” dimension that influences interitem similarity). Spatial frequency and orientation feature dimensions were used to generate distractors. In the bound condition, the number of distractors sharing the same conjunction of features was higher than that in the unbound condition, but the sharing of features within frequency and orientation dimensions was the same across conditions. The results showed that the target was found more efficiently in the bound than in the unbound condition, indicating that distractor–distractor similarity is also influenced by conjunctive representations.     

A conjunctive feature similarity effect for visual search

Traditional models of visual search assume interitem similarity effects arise from within each feature dimension independently of other dimensions. In the present study, we examine whether distractor-distractor effects also depend on feature conjunctions (i.e., whether feature conjunctions form a separate “feature” dimension that influences interitem similarity). Spatial frequency and orientation feature dimensions were used to generate distractors. In the bound condition, the number of distractors sharing the same conjunction of features was higher than that in the unbound condition, but the sharing of features within frequency and orientation dimensions was the same across conditions. The results showed that the target was found more efficiently in the bound than in the unbound condition, indicating that distractor-distractor similarity is also influenced by conjunctive representations.