Journal of Mathematical Psychology最新文献

Visual perceptual decision-making involves multiple components including visual encoding, attention, accumulation of evidence, and motor execution. Recent research suggests that EEG signals can identify the time of encoding and the onset of evidence accumulation during perceptual decision-making. Although scientists show that spatial attention improves participant performance in decision making, little is known about how spatial attention influences the individual cognitive components that give rise to that improvement in performance. We found evidence in this work that both visual encoding time (VET) before evidence accumulation and other non-decision time processes after or during evidence accumulation are influenced by spatial top-down attention. Specifically, we used an open-source dataset in which participants were informed about the location of a target stimulus in the visual field on some trials during a face-car perceptual decision-making task. Fitting neural drift–diffusion models to response time, accuracy, and single-trial N200 latencies ($\sim$ 125 to 225 ms post-stimulus) of EEG allowed us to separate the processes of visual encoding and the decision process from other non-decision time processes such as motor execution. These models were fitted in a single step in a hierarchical Bayesian framework. Quantitative model comparison to simulation-based theories reveals that spatial attention manipulates both VET and other non-decision time processes. We discuss why spatial attention may affect other non-evidence accumulation processes, such as motor execution time (MET), and why this may seem unexpected given the literature. We provide recommendations for future work to deal with this topic by a combination of neuro-cognitive models and model simulations at the single-trial level.

Experiments where participants synchronise their taps to rhythmic cues are often used to study human perception and performance of rhythms. This experimental study is novel in two regards: The cyclic rhythms (non-isochronous patterns of cues) presented to participants were more challenging than usual (including many from unfamiliar time signatures), and we have modelled participants’ performance via a conditional point process. Point processes are well suited to describing partly random sequences of events, but have rarely been used previously to model tapping experiments, the only other study we know being Cannon (2021). Our model uses continuous functional parameters to describe participants’ responses to auditory stimuli with much finer temporal resolution than in previous studies. Taking account of both the clock and the dynamic attention theories of sensorimotor synchronisation, we assessed the time course of the propensity to tap within each cycle at a resolution of less than 13$\mathrm{ms}$, identifying the influence of cues on the tapping propensity and the progress of learning their rhythmic patterns. We also sought to determine the trajectory of the putative refractory period (feedback inhibition of tapping) after each tap, and assessed the distribution of tap-cue asynchronies in a more finely resolved manner than usual. Our models also indicated complex kinetics of the feedback over about 100$\mathrm{ms}$.

We propose a hierarchical Bayesian model for working memory updating. This model accounts for both the accuracy of the responses and the reaction times (RT) in the memory updating paradigm, which is a commonly used paradigm to measure working memory capacity. We adapt a mutual interference model from Oberauer and Kliegl (2006) to explain responses. Oberauer and Kliegl (2006) used a Boltzmann equation framework based on the activation levels of items stored in working memory to quantify the probability of correct response at the final recall step after memory updating. We expand the original framework with a Markov chain structure, so that the model accounts for the probabilities of all possible responses, correct or incorrect, at both the intermediate steps during memory updating and the final recall step after memory updating. We use a Wald diffusion process to characterize RT, where the drift rate parameters are associated with the activation levels of items in working memory. This model allows us to investigate the mechanisms underlying choices and RTs in the memory updating paradigm under a joint theoretical framework. A simulation study shows the effectiveness of this model, and posterior predictive distributions and out-of-sample validations show that this model gives a good account of empirical working memory updating findings. We apply the model to two published data sets. The first data set, from Oberauer and Kliegl (2001), examined age differences in working memory. Results from our model reveal an increased level of mutual interference, less use of memory trace information, and potentially less pre-activation of memorized items in older adults compared to younger adults. The second data set, from De Simoni and von Bastian (2018), investigated transfer effects of working memory training. Results from our model reveal a potential transfer effect in the speed of information accumulation, where training in one working memory task may improve the information processing speed in another.

Polytomous knowledge structure theory (abbr. polytomous KST) was introduced by Stefanutti et al. (2020) and further results on polytomous KST were obtained by Heller (2021). As the interesting work, this paper discusses Galois connections in polytomous KST. In this paper, two derivations between polytomous knowledge structures and polytomous attributions are presented. In addition, this paper gives an explicit characterization to introduce the completeness of polytomous attributions and defines the concept of a complete polytomous knowledge structure by the property that such a polytomous knowledge structure is derived from a complete polytomous attribution. This paper establishes a Galois connection between the collection $K$ of all polytomous knowledge structures and the collection $F$ of all polytomous attributions, where the closed elements are respectively in $K$ the complete polytomous knowledge structures, and in $F$ the complete polytomous attributions. Furthermore, this Galois connection induces a one-to-one correspondence between the two sets of closed elements. Moreover, this Galois connection can also induce a Galois connection between the collection of all granular polytomous knowledge structures and the collection of all granular polytomous attributions.

Research on advice utilization often operationalizes the construct via Judge Advisor Systems (JAS), where a judge’s belief is elicited, they are provided advice, and given an opportunity to revise their belief. Belief change, or weight of advice (WOA), is measured as the shift in the judge’s belief proportional to the difference between their original belief and the advice. Several JAS studies have found WOA typically takes on a trimodal distribution, with inflation at the boundary values of 0 (indicating a judge declined advice) and 1 (adoption of advice). A dual hurdle beta model is proposed to account for these inflations. In addition to being an innovative computational model to address this methodological challenge, it also serves as a descriptive theoretical model which posits that the decision process happens in two stages: an initial discrete “choosing” stage, where the judge opts to either decline, adopt, or compromise with advice; and a subsequent continuous “averaging” stage, which occurs only if the judge opts to compromise. The approach was assessed via reanalysis of three recent JAS studies reflective of popular topics in the literature, such as algorithmic advice utilization, egocentric discounting effects, and judgmental forecasting. In each case new results were uncovered about how different correlates of advice utilization influence the decision process at either or both of the discrete and continuous stages, often in quite different ways, providing support for the descriptive theoretical model. A Bayesian graphical analysis framework is provided that can be applied to future research on advice utilization.

Stevens’ idea of “direct measurement” of stimulus magnitude is extended to the direct measurement of stimulus differences. An important extension of Wave Theory provides predictions of response probabilities from single direct measures of comparative difference. As an illustration of the method, in an experiment 20 university students compared, only once, each of 16 job pairs, judging which has the larger salary and creating the size of salary differences. The correlation between a theoretical measure of the size of perceived salary difference and the direct measures of perceived salary difference is 0.99. The probability of correctly predicting individual binary choices between jobs, based on the students’ generated measures of perceived stimulus difference, ranges to 1.00 from 0.935. This new theory draws together Stevens and Fechner by showing that they perceived the same underlying psychological events through perfectly related measures of subjective experience.

In this note the property of complementary symmetry is shown to imply the following consequence: If $x_{p}y$ is a binary prospect to win $x$ with probability $p$ and otherwise receive $y$, then the difference between the selling and buying prices of $x_{p}y$ will be equal to the difference between the selling and buying prices of the complement of this prospect, $y_{p}x$.

Surprising events trigger measurable brain activity and influence human behavior by affecting learning, memory, and decision-making. Currently there is, however, no consensus on the definition of surprise. Here we identify 18 mathematical definitions of surprise in a unifying framework. We first propose a technical classification of these definitions into three groups based on their dependence on an agent’s belief, show how they relate to each other, and prove under what conditions they are indistinguishable. Going beyond this technical analysis, we propose a taxonomy of surprise definitions and classify them into four conceptual categories based on the quantity they measure: (i) ‘prediction surprise’ measures a mismatch between a prediction and an observation; (ii) ‘change-point detection surprise’ measures the probability of a change in the environment; (iii) ‘confidence-corrected surprise’ explicitly accounts for the effect of confidence; and (iv) ‘information gain surprise’ measures the belief-update upon a new observation. The taxonomy poses the foundation for principled studies of the functional roles and physiological signatures of surprise in the brain.

We prove that every system of binary probabilities satisfying the triangle inequalities is induced by a regular system of choice probabilities.

In this article, we develop a new general inference method for selecting learning models. The method relies upon a specific hold-out cross-validation, which takes into account the dependency within the data. This allows us to retrieve the model that best fits the learning strategy of a single individual. The novelty of our approach lies on the choice of the testing set, both in the experimental design and in the data analysis. This individual approach is then applied to two category learning models (ALCOVE and Component-cue) on data-sets manipulating presentation order, after verification of the reliability of our method. We found that both models performed equally well during transfer, but Component-cue best fits the majority of participants during learning. To further analyze these models, we also investigated a potential relation between the underlying mechanisms of the models and the actual types of presentation order assigned to participants.