Trial-by-trial updating of an internal reference in discrimination tasks: evidence from effects of stimulus order and trial sequence

Order effects in stimulus discrimination challenge established models of comparative judgement: A meta-analytic review of the Type B effect

This paper provides a comprehensive review of the Type B effect (TBE), a phenomenon reflected in the observation that discrimination sensitivity varies with the order of stimuli in comparative judgment tasks, such as the two-alternative forced-choice (2AFC) paradigm. Specifically, when the difference threshold is lower (higher) with the constant standard preceding rather than following the variable comparison, one speaks of a negative (positive) TBE. Importantly, prominent psychophysical difference models such as signal detection theory (Green & Swets, 1966) cannot easily account for the TBE, and are hence challenged by it. The present meta-analysis provides substantial evidence for the TBE across various stimulus attributes, suggesting that the TBE is a general feature of discrimination experiments when standard and comparison are presented successively. Thus, inconsistent with psychophysical difference models, subjective differences between stimuli are not merely a function of their physical differences but rather also depend on their temporal order. From the literature, we identify four classes of potential candidate theories explaining the origin of the TBE, namely (1) differential weighting of the stimulus magnitudes at the two positions (e.g., Hellström, Psychological Research, 39, 345-388 1977), (2) internal reference formation (e.g., Dyjas, Bausenhart, & Ulrich, Attention, Perception, & Psychophysics, 74, 1819-1841 2012), (3) Bayesian updating (e.g., de Jong, Akyürek, & van Rijn, Psychonomic Bulletin and Review, 28, 1183-1190 2021), and (4) biased threshold estimation (García-Pérez & Alcalá-Quintana, Attention, Perception & Psychophysics, 72, 1155-1178 2010). As these models, to some extent, make differential predictions about the direction of the TBE, investigating the respective boundary conditions of positive and negative TBEs might be a valuable perspective for diagnostic future research.

Alpha oscillations encode Bayesian belief updating underlying attentional allocation in dynamic environments

In a dynamic environment, expectations of the future constantly change based on updated evidence and affect the dynamic allocation of attention. To further investigate the neural mechanisms underlying attentional expectancies, we employed a modified Central Cue Posner Paradigm in which the probability of cues being valid (that is, accurately indicated the upcoming target location) was manipulated. Attentional deployment to the cued location (α), which was governed by precision of predictions on previous trials, was estimated using a hierarchical Bayesian model and was included as a regressor in the analyses of electrophysiological (EEG) data. Our results revealed that before the target appeared, alpha oscillations (8∼13 Hz) for high-predictability cues (88 % valid) were significantly predicted by precision-dependent attention (α). This relationship was not observed under low-predictability conditions (69 % and 50 % valid cues). After the target appeared, precision-dependent attention (α) correlated with alpha band oscillations only in the valid cue condition and not in the invalid condition. Further analysis under conditions of significant attentional modulation by precision suggested a separate effect of cue orientation. These results provide new insights on how trial-by-trial Bayesian belief updating relates to alpha band encoding of environmentally-sensitive allocation of visual spatial attention.

Serial dependence in timing at the perceptual level being modulated by working memory

Recent experiences bias the perception of following stimuli, as has been verified in various kinds of experiments in visual perception. This phenomenon, known as serial dependence, may reflect mechanisms to maintain perceptual stability. In the current study, we examined several key properties of serial dependence in temporal perception. Firstly, we examined the source of the serial dependence effect in temporal perception. We found that perception without motor reproduction is sufficient to induce the sequential effect; motor reproduction caused a stronger effect and is achieved by biasing the perception of the future target duration rather than directly influencing the subsequent movement. Secondly, we ask how working memory influences serial dependence in a temporal reproduction task. By varying the delay time between standard duration and the reproduction, we showed that the strength of serial dependence is enhanced as the delay increased. Those features of serial dependence are consistent with what has been observed in visual perceptual tasks, for example, orientation perception or location perception. The similarities between the visual and the timing tasks may suggest a similar neural coding mechanism of magnitude between the visual stimuli and the duration.

Influences of temporal order in temporal reproduction

Despite the crucial role of complex temporal sequences, such as speech and music, in our everyday lives, our ability to acquire and reproduce these patterns is prone to various contextual biases. In this study, we examined how the temporal order of auditory sequences affects temporal reproduction. Participants were asked to reproduce accelerating, decelerating or random sequences, each consisting of four intervals, by tapping their fingers. Our results showed that the reproduction and the reproduction variability were influenced by the sequential structure and interval orders. The mean reproduced interval was assimilated by the first interval of the sequence, with the lowest mean for decelerating and the highest for accelerating sequences. Additionally, the central tendency bias was affected by the volatility and the last interval of the sequence, resulting in a stronger central tendency in the random and decelerating sequences than the accelerating sequence. Using Bayesian integration between the ensemble mean of the sequence and individual durations and considering the perceptual uncertainty associated with the sequential structure and position, we were able to accurately predict the behavioral results. The findings highlight the critical role of the temporal order of a sequence in temporal pattern reproduction, with the first interval exerting greater influence on mean reproduction and the volatility and the last interval contributing to the perceptual uncertainty of individual intervals and the central tendency bias.

An Illusory Motion in Stationary Stimuli Alters Their Perceived Duration

Despite having equal duration, stimuli in physical motion are perceived to last longer than static ones. Here, we investigate whether illusory motion stimuli produce a time-dilation effect similar to physical motion. Participants performed a duration discrimination task that compared the perceived duration of static stimuli with and without illusory motion to a reference stimulus. In the first experiment, we observed a 4% increase in the number of "longer" responses for the illusory motion images than static stimuli with equal duration. The time-dilation effect, quantified as a shift in the Point of Subjective Equality (PSE), was approximately 55 ms for a 2-second stimulus. Although small, the effect was replicated in a second experiment in which the total number of standard-duration repetitions was reduced from 73 to 19. In the third experiment, we found a positive linear trend between the strength of the illusory motion and the magnitude of the time-dilation effect. These results demonstrate that, similar to physical motion stimuli, illusory motion stimuli are perceived to last longer than static stimuli. Furthermore, the strength of the illusion influences the extent of the lengthening of perceived duration.

Neural Evidence for Boundary Updating as the Source of the Repulsive Bias in Classification

Binary classification, an act of sorting items into two classes by setting a boundary, is biased by recent history. One common form of such bias is repulsive bias, a tendency to sort an item into the class opposite to its preceding items. Sensory-adaptation and boundary-updating are considered as two contending sources of the repulsive bias, yet no neural support has been provided for either source. Here, we explored human brains of both men and women, using functional magnetic resonance imaging (fMRI), to find such support by relating the brain signals of sensory-adaptation and boundary-updating to human classification behavior. We found that the stimulus-encoding signal in the early visual cortex adapted to previous stimuli, yet its adaptation-related changes were dissociated from current choices. Contrastingly, the boundary-representing signals in the inferior-parietal and superior-temporal cortices shifted to previous stimuli and covaried with current choices. Our exploration points to boundary-updating, rather than sensory-adaptation, as the origin of the repulsive bias in binary classification.SIGNIFICANCE STATEMENT Many animal and human studies on perceptual decision-making have reported an intriguing history effect called "repulsive bias," a tendency to classify an item as the opposite class of its previous item. Regarding the origin of repulsive bias, two contending ideas have been proposed: "bias in stimulus representation because of sensory adaptation" versus "bias in class-boundary setting because of belief updating." By conducting model-based neuroimaging experiments, we verified their predictions about which brain signal should contribute to the trial-to-trial variability in choice behavior. We found that the brain signal of class boundary, but not stimulus representation, contributed to the choice variability associated with repulsive bias. Our study provides the first neural evidence supporting the boundary-based hypothesis of repulsive bias.

A unitary mechanism underlies adaptation to both local and global environmental statistics in time perception

Our duration estimation flexibly adapts to the statistical properties of the temporal context. Humans and non-human species exhibit a perceptual bias towards the mean of durations previously observed as well as serial dependence, a perceptual bias towards the duration of recently processed events. Here we asked whether those two phenomena arise from a unitary mechanism or reflect the operation of two distinct systems that adapt separately to the global and local statistics of the environment. We employed a set of duration reproduction tasks in which the target duration was sampled from distributions with different variances and means. The central tendency and serial dependence biases were jointly modulated by the range and the variance of the prior, and these effects were well-captured by a unitary mechanism model in which temporal expectancies are updated after each trial based on perceptual observations. Alternative models that assume separate mechanisms for global and local contextual effects failed to capture the empirical results.

Modality-specific sensory and decisional carryover effects in duration perception

BACKGROUND

The brain uses recent history when forming perceptual decisions. This results in carryover effects in perception. Although separate sensory and decisional carryover effects have been shown in many perceptual tasks, their existence and nature in temporal processing are unclear. Here, we investigated whether and how previous stimuli and previous choices affect subsequent duration perception, in vision and audition.

RESULTS

In a series of three experiments, participants were asked to classify visual or auditory stimuli into "shorter" or "longer" duration categories. In experiment 1, visual and auditory stimuli were presented in separate blocks. Results showed that current duration estimates were repelled away from the previous trial's stimulus duration, but attracted towards the previous choice, in both vision and audition. In experiment 2, visual and auditory stimuli were pseudorandomly presented in one block. We found that sensory and decisional carryover effects occurred only when previous and current stimuli were from the same modality. Experiment 3 further investigated the stimulus dependence of carryover effects within each modality. In this experiment, visual stimuli with different shape topologies (or auditory stimuli with different audio frequencies) were pseudorandomly presented in one visual (or auditory) block. Results demonstrated sensory carryover (within each modality) despite task-irrelevant differences in visual shape topology or audio frequency. By contrast, decisional carryover was reduced (but still present) across different visual topologies and completely absent across different audio frequencies.

CONCLUSIONS

These results suggest that serial dependence in duration perception is modality-specific. Moreover, repulsive sensory carryover effects generalize within each modality, whereas attractive decisional carryover effects are contingent on contextual details.

Duration discrimination: A diffusion decision modeling approach

The human ability to discriminate the duration of two subsequently presented stimuli is often studied with tasks that involve a comparison between a standard stimulus (with fixed duration) and comparison stimuli (with varying durations). The performance in such tasks is influenced by the presentation order of these successively presented stimuli. The so-called Type A effect refers to the impact of presentation order on the point of subjective equality. The Type B effect describes effects of presentation order on the just-noticeable-difference. Cognitive models that account for these context effects assume that participants' duration estimation is influenced by the history of previously encountered stimuli. For example, the internal reference model assumes that the magnitude of a "typical" stimulus is represented by an internal reference. This internal reference evolves throughout an experiment and is updated on every trial. Different recent models have in common that they describe how the internal reference is computed but are agnostic to the decision process itself. In this study, we develop a new model that incorporates the mechanisms of perceptual discrimination models into a diffusion model. The diffusion model focuses on the dynamics of the decision process itself and accounts for choice and response times based on a set of latent cognitive variables. We show that our model accurately predicts the accuracy and response time distribution in a classical duration discrimination task. Further, model parameters were sensitive to the Type A and B effect. The proposed model opens up new opportunities for studying human discrimination performance (e.g., individual differences).

A perceptual glitch in serial perception generates temporal distortions

Precisely estimating event timing is essential for survival, yet temporal distortions are ubiquitous in our daily sensory experience. Here, we tested whether the relative position, duration, and distance in time of two sequentially-organized events-standard S, with constant duration, and comparison C, with duration varying trial-by-trial-are causal factors in generating temporal distortions. We found that temporal distortions emerge when the first event is shorter than the second event. Importantly, a significant interaction suggests that a longer inter-stimulus interval (ISI) helps to counteract such serial distortion effect only when the constant S is in the first position, but not if the unpredictable C is in the first position. These results imply the existence of a perceptual bias in perceiving ordered event durations, mechanistically contributing to distortion in time perception. We simulated our behavioral results with a Bayesian model and replicated the finding that participants disproportionately expand first-position dynamic (unpredictable) short events. Our results clarify the mechanisms generating time distortions by identifying a hitherto unknown duration-dependent encoding inefficiency in human serial temporal perception, something akin to a strong prior that can be overridden for highly predictable sensory events but unfolds for unpredictable ones.

Individual beliefs about temporal continuity explain variation of perceptual biases

Perception of magnitudes such as duration or distance is often found to be systematically biased. The biases, which result from incorporating prior knowledge in the perceptual process, can vary considerably between individuals. The variations are commonly attributed to differences in sensory precision and reliance on priors. However, another factor not considered so far is the implicit belief about how successive sensory stimuli are generated: independently from each other or with certain temporal continuity. The main types of explanatory models proposed so far-static or iterative-mirror this distinction but cannot adequately explain individual biases. Here we propose a new unifying model that explains individual variation as combination of sensory precision and beliefs about temporal continuity and predicts the experimentally found changes in biases when altering temporal continuity. Thus, according to the model, individual differences in perception depend on beliefs about how stimuli are generated in the world.

Implicit Versus Explicit Timing-Separate or Shared Mechanisms?

Time implicitly shapes cognition, but time is also explicitly represented, for instance, in the form of durations. Parsimoniously, the brain could use the same mechanisms for implicit and explicit timing. Yet, the evidence has been equivocal, revealing both joint versus separate signatures of timing. Here, we directly compared implicit and explicit timing using magnetoencephalography, whose temporal resolution allows investigating the different stages of the timing processes. Implicit temporal predictability was induced in an auditory paradigm by a manipulation of the foreperiod. Participants received two consecutive task instructions: discriminate pitch (indirect measure of implicit timing) or duration (direct measure of explicit timing). The results show that the human brain efficiently extracts implicit temporal statistics of sensory environments, to enhance the behavioral and neural responses to auditory stimuli, but that those temporal predictions did not improve explicit timing. In both tasks, attentional orienting in time during predictive foreperiods was indexed by an increase in alpha power over visual and parietal areas. Furthermore, pretarget induced beta power in sensorimotor and parietal areas increased during implicit compared to explicit timing, in line with the suggested role for beta oscillations in temporal prediction. Interestingly, no distinct neural dynamics emerged when participants explicitly paid attention to time, compared to implicit timing. Our work thus indicates that implicit timing shapes the behavioral and sensory response in an automatic way and is reflected in oscillatory neural dynamics, whereas the translation of implicit temporal statistics to explicit durations remains somewhat inconclusive, possibly because of the more abstract nature of this task.

Two attentive strategies reducing subjective distortions in serial duration perception

Humans tend to perceptually distort (dilate/shrink) the duration of brief stimuli presented in a sequence when discriminating the duration of a second stimulus (Comparison) from the duration of a first stimulus (Standard). This type of distortion, termed “Time order error” (TOE), is an important window into the determinants of subjective perception. We hypothesized that stimulus durations would be optimally processed, suppressing subjective distortions in serial perception, if the events to be compared fell within the boundaries of rhythmic attentive sampling (4–8 Hz, theta band). We used a two-interval forced choice (2IFC) experimental design, and in three separate experiments tested different Standard durations: 120-ms, corresponding to an 8.33 Hz rhythmic attentive window; 160 ms, corresponding to a 6.25 Hz window; and 200 ms, for a 5 Hz window. We found that TOE, as measured by the Constant Error metric, is sizeable for a 120-ms Standard, is reduced for a 160-ms Standard, and statistically disappears for 200-ms Standard events, confirming our hypothesis. For 120- and 160-ms Standard events, to reduce TOEs it was necessary to increase the interval between the Standard and the Comparison event from sub-second (400, 800 ms) to supra-second (1600, 2000 ms) lags, suggesting that the orienting of attention in time waiting for the Comparison event to onset may work as a back-up strategy to optimize its encoding. Our results highlight the flexible use of two different attentive strategies to optimize subjective time perception.

Time changes: Timing contexts support event segmentation in associative memory

We tend to mentally segment a series of events according to perceptual contextual changes, such that items from a shared context are more strongly associated in memory than items from different contexts. It is also known that timing context provides a scaffold to structure experiences in memory, but its role in event segmentation has not been investigated. We adapted a previous paradigm, which was used to investigate event segmentation using visual contexts, to study the effects of changes in timing contexts on event segmentation in associative memory. In two experiments, we presented lists of 36 items in which the interstimulus intervals (ISIs) changed after a series of six items ranging between 0.5 and 4 s in 0.5 s steps. After each list, participants judged which one of two test items were shown first (temporal order judgment) for items that were either drawn from the same context (within an ISI) or from consecutive contexts (across ISIs). Further, participants judged from memory whether the ISI associated to an item lasted longer than a standard interval (2.25 s) that was not previously shown (temporal source memory). Experiment 2 further included a time-item encoding task. Results revealed an effect of timing context changes in temporal order judgments, with faster responses (Experiment 1) or higher accuracy (Experiment 2) when items were drawn from the same context, as opposed to items drawn from across contexts. Further, in both experiments, we found that participants were well able to provide temporal source memory judgments based on recalled durations. Finally, replicated across experiments, we found subjective duration bias, as estimated by psychometric curve fitting parameters of the recalled durations, correlated negatively with within-context temporal order judgments. These findings show that changes in timing context support event segmentation in associative memory.

Duration Comparisons for Vision and Touch Are Dependent on Presentation Order and Temporal Context

Integrating visual and tactile information in the temporal domain is critical for active perception. To accomplish this, coordinated timing is required. Here, we study perceived duration within and across these two modalities. Specifically, we examined how duration comparisons within and across vision and touch were influenced by temporal context and presentation order using a two-interval forced choice task. We asked participants to compare the duration of two temporal intervals defined by tactile or visual events. Two constant standard durations (700 ms and 1,000 ms in 'shorter' sessions; 1,000 ms and 1,500 ms in 'longer' sessions) were compared to variable comparison durations in different sessions. In crossmodal trials, standard and comparison durations were presented in different modalities, whereas in the intramodal trials, the two durations were presented in the same modality. The standard duration was either presented first (<sc>) or followed the comparison duration (<cs>). In both crossmodal and intramodal conditions, we found that the longer standard duration was overestimated in <cs> trials and underestimated in <sc> trials whereas the estimation of shorter standard duration was unbiased. Importantly, the estimation of 1,000ms was biased when it was the longer standard duration within the shorter sessions but not when it was the shorter standard duration within the longer sessions, indicating an effect of temporal context. The effects of presentation order can be explained by a central tendency effect applied in different ways to different presentation orders. Both crossmodal and intramodal conditions showed better discrimination performance for <sc> trials than <cs> trials, supporting the Type B effect for both crossmodal and intramodal duration comparison. Moreover, these results were not dependent on whether the standard duration was defined using tactile or visual stimuli. Overall, our results indicate that duration comparison between vision and touch is dependent on presentation order and temporal context, but not modality.

The origin of Vierordt's law: The experimental protocol matters

In 1868, Karl Vierordt discovered one type of errors in time perception-an overestimation of short duration and underestimation of long durations, known as Vierordt's law. Here we reviewed the original study in its historical context and asked whether Vierordt's law is a result of an unnatural experimental randomization protocol. Using iterative Bayesian updating, we simulated the original results with high accuracy. Importantly, the model also predicted that a slowly changing random-walk sequence produces less central tendency than a random sequence with the same durations. This was validated by a duration reproduction experiment from two sequences (random and random walk) with the same sampled distribution. The results showed that trial-wise variation influenced the magnitude of Vierordt's law. We concluded that Vierordt's law is caused by an unnatural yet widely used experimental protocol.

Temporal Context Actively Shapes EEG Signatures of Time Perception

Our subjective perception of time is optimized to temporal regularities in the environment. This is illustrated by the central tendency effect: When estimating a range of intervals, short intervals are overestimated, whereas long intervals are underestimated to reduce the overall estimation error. Most models of interval timing ascribe this effect to the weighting of the current interval with previous memory traces after the interval has been perceived. Alternatively, the perception of the duration could already be flexibly tuned to its temporal context. We investigated this hypothesis using an interval reproduction task in which human participants (both sexes) reproduced a shorter and longer interval range. As expected, reproductions were biased toward the subjective mean of each presented range. EEG analyses showed that temporal context indeed affected neural dynamics during the perception phase. Specifically, longer previous durations decreased contingent negative variation and P2 amplitude and increased beta power. In addition, multivariate pattern analysis showed that it is possible to decode context from the transient EEG signal quickly after both onset and offset of the perception phase. Together, these results suggest that temporal context creates dynamic expectations which actively affect the perception of duration.SIGNIFICANCE STATEMENT The subjective sense of duration does not arise in isolation, but is informed by previous experiences. This is demonstrated by abundant evidence showing that the production of duration estimates is biased toward previously experienced time intervals. However, it is yet unknown whether this temporal context actively affects perception or only asserts its influence in later, postperceptual stages as proposed by most current formal models of this task. Using an interval reproduction task, we show that EEG signatures flexibly adapt to the temporal context during perceptual encoding. Furthermore, interval history can be decoded from the transient EEG signal even when the current duration was identical. Thus, our results demonstrate that context actively influences perception.

Perceptual timing precision with vibrotactile, auditory, and multisensory stimuli

The growing use of vibrotactile signaling devices makes it important to understand the perceptual limits on vibrotactile information processing. To promote that understanding, we carried out a pair of experiments on vibrotactile, auditory, and bimodal (synchronous vibrotactile and auditory) temporal acuity. On each trial, subjects experienced a set of isochronous, standard intervals (400 ms each), followed by one interval of variable duration (400 ± 1-80 ms). Intervals were demarcated by short vibrotactile, auditory, or bimodal pulses. Subjects categorized the timing of the last interval by describing the final pulse as either "early" or "late" relative to its predecessors. In Experiment 1, each trial contained three isochronous standard intervals, followed by an interval of variable length. In Experiment 2, the number of isochronous standard intervals per trial varied, from one to four. Psychometric modeling revealed that vibrotactile stimulation produced poorer temporal discrimination than either auditory or bimodal stimulation. Moreover, auditory signals dominated bimodal sensitivity, and inter-individual differences in temporal discriminability were reduced with bimodal stimulation. Additionally, varying the number of isochronous intervals in a trial failed to improve temporal sensitivity in either modality, suggesting that memory played a key role in judgments of interval duration.

A common dynamic prior for time in duration discrimination

Estimation of time depends heavily on both global and local statistical context. Durations that are short relative to the global distribution are systematically overestimated; durations that are locally preceded by long durations are also overestimated. Context effects are prominent in duration discrimination tasks, where a standard duration and a comparison duration are presented on each trial. In this study, we compare and test two models that posit a dynamically updating internal reference that biases time estimation on global and local scales in duration discrimination tasks. The internal reference model suggests that the internal reference operates during postperceptual stages and only interacts with the first presented duration. In contrast, a Bayesian account of time estimation implies that any perceived duration updates the internal reference and therefore interacts with both the first and second presented duration. We implemented both models and tested their predictions in a duration discrimination task where the standard duration varied from trial to trial. Our results are in line with a Bayesian perspective on time estimation. First, the standard systematically biased estimation of the comparison, such that shorter standards increased the likelihood of reporting that the comparison was shorter. Second, both the previous standard and comparison systematically biased time estimation of subsequent trials in the same direction. Third, more precise observers showed smaller biases. In sum, our findings suggest a common dynamic prior for time that is updated by each perceived duration and where the relative weighting of old and new observations is determined by their relative precision.

Order effects in two-alternative forced-choice tasks invalidate adaptive threshold estimates

Adaptive psychophysical methods are widely used for the quick estimation of percentage points (thresholds) on psychometric functions for two-alternative forced-choice (2AFC) tasks. The use of adaptive methods is supported by numerous simulation studies documenting their performance, which have shown that thresholds can be reasonably estimated with them when their founding assumptions hold. One of these assumptions is that the psychometric function is invariant, but empirical evidence is mounting that human performance in 2AFC tasks needs to be described by two different psychometric functions, one that holds when the test stimulus is presented first in the 2AFC trial and a different one that holds when the test is presented second. The same holds when presentations are instead simultaneous at two spatial locations rather than sequential. We re-evaluated the performance of adaptive methods in the presence of these order effects via simulation studies and an empirical study with human observers. The simulation study showed that thresholds are severely overestimated by adaptive methods in these conditions, and the empirical study corroborated these findings. These results question the validity of threshold estimates obtained with adaptive methods that incorrectly assume the psychometric function to be invariant with presentation order. Alternative ways in which thresholds can be accurately estimated in the presence of order effects are discussed.

Perceptual inference is impaired in individuals with ASD and intact in individuals who have lost the autism diagnosis

Beyond the symptoms which characterize their diagnoses, individuals with autism spectrum disorder (ASD) show enhanced performance in simple perceptual discrimination tasks. Often attributed to superior sensory sensitivities, enhanced performance may also reflect a weaker bias towards previously perceived stimuli. This study probes perceptual inference in a group of individuals who have lost the autism diagnosis (LAD); that is, they were diagnosed with ASD in early childhood but have no current ASD symptoms. Groups of LAD, current ASD, and typically developing (TD) participants completed an auditory discrimination task. Individuals with TD showed a bias towards previously perceived stimuli-a perceptual process called "contraction bias"; that is, their representation of a given tone was contracted towards the preceding trial stimulus in a manner that is Bayesian optimal. Similarly, individuals in the LAD group showed a contraction bias. In contrast, individuals with current ASD showed a weaker contraction bias, suggesting reduced perceptual inferencing. These findings suggest that changes that characterize LAD extend beyond the social and communicative symptoms of ASD, impacting perceptual domains. Measuring perceptual processing earlier in development in ASD will tap the causality between changes in perceptual and symptomatological domains. Further, the characterization of perceptual inference could reveal meaningful individual differences in complex high-level behaviors.

Sensation weighting in duration discrimination: A univariate, multivariate, and varied-design study of presentation-order effects

Stimulus discriminability is often assessed by comparisons of two successive stimuli: a fixed standard (St) and a varied comparison stimulus (Co). Hellström's sensation weighting (SW) model describes the subjective difference between St and Co as a difference between two weighted compounds, each comprising a stimulus and its internal reference level (ReL). The presentation order of St and Co has two important effects: Relative overestimation of one stimulus is caused by perceptual time-order errors (TOEs), as well as by judgment biases. Also, sensitivity to changes in Co tends to differ between orders StCo and CoSt: the Type B effect. In three duration discrimination experiments, difference limens (DLs) were estimated by an adaptive staircase method. The SW model was adapted for modeling of DLs generated with this method. In Experiments 1 and 2, St durations were 100, 215, 464, and 1,000 ms in separate blocks. TOEs and Type B effects were assessed with univariate and multivariate analyses, and were well accounted for by the SW model, suggesting that the two effects are closely related, as this model predicts. With short St durations, lower DLs were found with the order CoSt than with StCo, challenging alternative models. In Experiment 3, St durations of 100 and 215 ms, or 464 and 1,000 ms, were intermixed within a block. From the SW model this was predicted to shift the ReL for the first-presented interval, thereby also shifting the TOE. This prediction was confirmed, strengthening the SW model's account of the comparison of stimulus magnitudes.

Local context effects in the magnitude-duration illusion: Size but not numerical value sequentially alters perceived duration

Many aspects of an event can change perceived duration. A common example of this is the magnitude-duration illusion, in which a high magnitude (e.g. large or high value) stimulus will be perceived to last longer than a low magnitude stimulus. The effects of magnitude on perceived duration are normally considered in terms of global context effects; what is large depends on the stimuli used throughout the experiment. In the current article, we examine local context effects in the magnitude-duration illusion, how trial-by-trial changes in magnitude affect the subjective duration of an event. We performed two experiments in which numerical magnitude and stimulus size were varied within either the example phase or reproduction phase of a temporal reproduction task. We showed that in the current trial the combined value-size magnitude presented in the example phase affected subsequent reproductions, while the magnitude presented in the reproduction phase did not. The size magnitude presented in the reproduction phase also affected the reproduction in the following trial, such that a larger stimulus in the current reproduction phase resulted in shorter reproductions in the next reproduction phase. This indicates that low level stimulus properties (i.e. size) can act to contextualize subsequent stimulus properties, which in turn affect perceived duration. The findings of our experiments add local, low-level, context effects to the known modifiers of perceived duration, as well as provide evidence with regards to the role of magnitude in interval timing.

The Do's and Don'ts of Psychophysical Methods for Interpretability of Psychometric Functions and Their Descriptors

Many areas of research require measuring psychometric functions or their descriptors (thresholds, slopes, etc.). Data for this purpose are collected with psychophysical methods of various types and justification for the interpretation of results arises from a model of performance grounded in signal detection theory. Decades of research have shown that psychophysical data display features that are incompatible with such framework, questioning the validity of interpretations obtained under it and revealing that psychophysical performance is more complex than this framework entertains. This paper describes the assumptions and formulation of the conventional framework for the two major classes of psychophysical methods (single- and dual-presentation methods) and presents various lines of empirical evidence that the framework is inconsistent with. An alternative framework is then described and shown to account for all the characteristics that the conventional framework regards as anomalies. This alternative process model explicitly separates the sensory, decisional, and response components of performance and represents them via parameters whose estimation characterizes the corresponding processes. Retrospective and prospective evidence of the validity of the alternative framework is also presented. A formal analysis also reveals that some psychophysical methods and response formats are unsuitable for separation of the three components of observed performance. Recommendations are thus given regarding practices that should be avoided and those that should be followed to ensure interpretability of the psychometric function, or descriptors (detection threshold, difference limen, point of subjective equality, etc.) obtained with shortcut methods that do not require estimation of psychometric functions.

Having your cake and eating it: Faster responses with reduced muscular activation while learning a temporal interval

We examined how motor responses to a stimulus evolve as individuals learn to predict when a stimulus will appear, by comparing responses to a regular versus irregular stimulus train. The study was conducted with two groups of adults - one responded to the regular appearance of a visual stimulus every 3 s (R group) and the second responded to the irregular presentation of the same stimulus (IR group) at intervals varying between 2 and 4 s. Participants responded to the appearance of the stimulus by bending over to press a button that was slightly out of reach. This whole body reach requires muscular activation at the ankles. Over the course of 50 consecutive responses, the response times in the R group were found to decrease more than those for participants in the IR group. The electromyographs (EMGs) of two ankle antagonist muscles, the anterior tibialis and soleus were also modified as participants progressively learnt the temporal regularity of a sequence. Tibialis onset times for the R group were found to decrease faster. A less predictable observation was the faster reduction in post stimulus activation of the tibialis muscle for the R group. Soleus muscle deactivation is an indicator of movement preparation. EMG integrals for this muscle a little before stimulus onset showed a trend for greater decrease in the R group. In summary, our study shows that temporal expectations over repeated stimulus presentation permit the dynamic optimization of motor activity with progressively faster response times, muscle activation onset times and lower muscle activation amplitudes.

Integration of audiovisual spatial signals is not consistent with maximum likelihood estimation

Multisensory perception is regarded as one of the most prominent examples where human behaviour conforms to the computational principles of maximum likelihood estimation (MLE). In particular, observers are thought to integrate auditory and visual spatial cues weighted in proportion to their relative sensory reliabilities into the most reliable and unbiased percept consistent with MLE. Yet, evidence to date has been inconsistent. The current pre-registered, large-scale (N = 36) replication study investigated the extent to which human behaviour for audiovisual localization is in line with maximum likelihood estimation. The acquired psychophysics data show that while observers were able to reduce their multisensory variance relative to the unisensory variances in accordance with MLE, they weighed the visual signals significantly stronger than predicted by MLE. Simulations show that this dissociation can be explained by a greater sensitivity of standard estimation procedures to detect deviations from MLE predictions for sensory weights than for audiovisual variances. Our results therefore suggest that observers did not integrate audiovisual spatial signals weighted exactly in proportion to their relative reliabilities for localization. These small deviations from the predictions of maximum likelihood estimation may be explained by observers' uncertainty about the world's causal structure as accounted for by Bayesian causal inference.

Perceived Duration: The Interplay of Top-Down Attention and Task-Relevant Information

Perception of time is susceptible to distortions; among other factors, it has been suggested that the perceived duration of a stimulus is affected by the observer’s expectations. It has been hypothesized that the duration of an oddball stimulus is overestimated because it is unexpected, whereas repeated stimuli have a shorter perceived duration because they are expected. However, recent findings suggest instead that fulfilled expectations about a stimulus elicit an increase in perceived duration, and that the oddball effect occurs because the oddball is a target stimulus, not because it is unexpected. Therefore, it has been suggested that top-down attention is sometimes sufficient to explain this effect, and sometimes only necessary, with an additional contribution from saliency. However, how the expectedness of a target stimulus and its salient features affect its perceived duration is still an open question. In the present study, participants’ expectations about and the saliency of target stimuli were orthogonally manipulated with stimuli presented on a short (Experiment 1) or long (Experiment 2) temporal scale. Four repetitive standard stimuli preceded each target stimulus in a task in which participants judged whether the target was longer or shorter in duration than the standards. Engagement of top-down attention to target stimuli increased their perceived duration to the same extent irrespective of their expectedness. A small but significant additional contribution to this effect from the saliency of target stimuli was dependent on the temporal scale of stimulus presentation. In Experiment 1, saliency only significantly increased perceived duration in the case of expected target stimuli. In contrast, in Experiment 2, saliency exerted a significant effect on the overestimation elicited by unexpected target stimuli, but the contribution of this variable was eliminated in the case of expected target stimuli. These findings point to top-down attention as the primary cognitive mechanism underlying the perceptual extraction and processing of task-relevant information, which may be strongly correlated with perceived duration. Furthermore, the scalar properties of timing were observed, favoring the pacemaker-accumulator model of timing as the underlying timing mechanism.

Laws of concatenated perception: Vision goes for novelty, decisions for perseverance

Every instant of perception depends on a cascade of brain processes calibrated to the history of sensory and decisional events. In the present work, we show that human visual perception is constantly shaped by two contrasting forces exerted by sensory adaptation and past decisions. In a series of experiments, we used multilevel modeling and cross-validation approaches to investigate the impact of previous stimuli and decisions on behavioral reports during adjustment and forced-choice tasks. Our results revealed that each perceptual report is permeated by opposite biases from a hierarchy of serially dependent processes: Low-level adaptation repels perception away from previous stimuli, whereas decisional traces attract perceptual reports toward the recent past. In this hierarchy of serial dependence, "continuity fields" arise from the inertia of decisional templates and not from low-level sensory processes. This finding is consistent with a Two-process model of serial dependence in which the persistence of readout weights in a decision unit compensates for sensory adaptation, leading to attractive biases in sequential perception. We propose a unified account of serial dependence in which functionally distinct mechanisms, operating at different stages, promote the differentiation and integration of visual information over time.

Age-Related Effects on Cross-Modal Duration Perception

Reliable duration perception of external events is necessary to coordinate perception with action, precisely discriminate speech, and for other daily functions. Visual duration perception can be heavily influenced by concurrent auditory signals; however, age-related effects on this process have received minimal attention. In the present study, we examined the effect of aging on duration perception by quantifying (1) duration discrimination thresholds, (2) auditory temporal dominance, and (3) visual duration expansion/compression percepts induced by an accompanying auditory stimulus of longer/shorter duration. Duration discrimination thresholds were significantly greater for visual than auditory tasks in both age groups, however there was no effect of age. While the auditory modality retained dominance in duration perception with age, older adults still performed worse than young adults when comparing durations of two target stimuli (e.g., visual) in the presence of distractors from the other modality (e.g., auditory). Finally, both age groups perceived similar visual duration compression, whereas older adults exhibited visual duration expansion over a wider range of auditory durations compared to their younger counterparts. Results are discussed in terms of multisensory integration and possible decision strategies that change with age.

The dynamic effect of context on interval timing in children and adults

Human reproductions of time intervals are often biased toward previously perceived durations, resulting in a central tendency effect. The aim of the current study was to compare this effect of temporal context on time reproductions within children and adults. Children aged from 5 to 7 years, as well as adults, performed a ready-set-go reproduction task with a short and a long duration distribution. A central tendency effect was observed both in children and adults, with no age-difference in the effect of global context on temporal performance. However, the analysis of the effect of local context (trial-by-trial) indicated that younger children relied more on the duration (objective duration) presented in the most recent trial than adults. In addition, statistical analyses of the influence on temporal performance of recently reproduced durations by subjects (subjective duration) revealed that temporal reproductions in adults were influenced by performance drifts, i.e., their evaluation of their temporal error, while children simply relied on the value of reproduced durations on the recent trials. We argue that the central tendency effect was larger in young children due to their noisier internal representation of durations: A noisy system led participants to base their estimation on experienced duration rather than on the evaluation of their judgment.

1-s Productions: A Validation of an Efficient Measure of Clock Variability

Objective: Clock variance is an important statistic in many clinical and developmental studies. Existing methods require a large number of trials for accurate clock variability assessment, which is problematic in studies using clinical or either young or aged participants. Furthermore, these existing methods often implicitly convolute clock and memory processes, making it difficult to disentangle whether the clock or memory system are driving the observed deviations. Here we assessed whether 20 repeated productions of a well-engrained interval (1 s), a task that does not incorporate memory updating nor the processing of feedback, could provide an accurate assessment of clock variability.

Method: Sixty-eight undergraduate students completed two tasks: a 1-s production task in which they were asked to produce a 1-s duration by ending a tone by a keypress, and a multi-duration reproduction task. Durations presented in the reproduction task were tones lasting 1.17, 1.4 and 1.68 s. No feedback was presented in either task, and the order of presentation was counterbalanced between participants.

Results: The observed central tendency in the reproduction task was better explained by models including the measures of clock variability derived from the 1-s production task than by models without it. Three clock variability measures were calculated for each participant [standard deviation, root mean squared residuals (RMSRs) from an estimated linear slope, and RMSR scaled by mean production duration]. The model including the scaled RMSR was preferred over the alternative models, and no notable effects of the order of task presentation were observed. These results suggest that: (1) measures of variability should account for drift; (2) the presentation of another timing task before a 1-s production task did not influence the assessment of the clock variability; and (3) the observed variability adheres to the scalar property and predicts temporal performance, and is thus a usable index of clock variability.

Conclusion: This study shows that just 20 repeated productions of 1 s provide a reliable index of clock variability. As administering this task is fast and easy, it could prove to be useful in a large variety of developmental and clinical populations.

How language and event recall can shape memory for time

How do we represent the duration of past events that we have conceptualized through language? Prior research suggests that memory for duration depends on the segmental structure perceived at encoding. However, it remains unclear why duration memory displays characteristic distortions and whether language-mediated encoding can further distort duration memory. Here we examine these questions and specifically ask whether the amount of event information recalled relative to the stimulus duration explains temporal distortions. In several studies, participants first studied animated stimuli described by phrases implying either fast or slow motion (e.g., a mule vs car going up a road). They then mentally reproduced the stimuli from memory (as if replaying them in their minds) and verbally recalled them. We manipulated the amount of stimulus study and the type of recall cue (visual vs linguistic) to assess the role of language and information recalled on the length of mental reproductions. Results indicated that the density of the information recalled (number of details recalled per second) explained temporal distortions: higher density events were lengthened and lower density events were shortened. Moreover, language additionally lengthened or shortened duration reproductions when phrases cued the task, suggesting that episodic details and verbal conceptual features were combined during recollection rather than encoding. These results suggest that the density of the details recalled and language-mediated recollection shape memory for event duration. We argue that temporal memory distortions stem from event encoding and retrieval mechanisms. Implications of these findings for theories of time, memory and language are discussed.

Decay of internal reference information in duration discrimination: Intertrial interval modulates the Type B effect

Psychophysical evidence suggests that human perception of a stimulus is assimilated towards previous stimuli. The internal reference model (IRM) explains such assimilation through an internal reference (IR), which integrates past and present stimulus representations and thus might be conceived as a form of perceptual memory. In this study, we investigated whether the IR decays with time, as previously shown for perceptual memory representations in general. One specific prediction of IRM is higher discrimination sensitivity when a constant standard precedes rather than follows a variable comparison in a two-alternative forced-choice (2AFC) discrimination task. Furthermore, the magnitude of this so-called negative Type B effect should decrease with decreasing weighting of past stimulus information in the integration process. Therefore, decay of the IR should result in a reduced Type B effect. To examine this prediction, we carried out a 2AFC duration discrimination experiment with a short (1,600 ms) and a long (3,200 ms) intertrial interval (ITI). As expected, a reduced negative Type B effect was observed at the long compared with the short ITI, consistent with the idea that humans rely on the immediate past when evaluating current sensory input, however, less so when the IR incorporating the perceptual short-term memory representation of these past stimuli has already decayed.

Performance-informed EEG analysis reveals mixed evidence for EEG signatures unique to the processing of time

Certain EEG components (e.g., the contingent negative variation, CNV, or beta oscillations) have been linked to the perception of temporal magnitudes specifically. However, it is as of yet unclear whether these EEG components are really unique to time perception or reflect the perception of magnitudes in general. In the current study we recorded EEG while participants had to make judgments about duration (time condition) or numerosity (number condition) in a comparison task. This design allowed us to directly compare EEG signals between the processing of time and number. Stimuli consisted of a series of blue dots appearing and disappearing dynamically on a black screen. Each stimulus was characterized by its duration and the total number of dots that it consisted of. Because it is known that tasks like these elicit perceptual interference effects that we used a maximum-likelihood estimation (MLE) procedure to determine, for each participant and dimension separately, to what extent time and numerosity information were taken into account when making a judgement in an extensive post hoc analysis. This approach enabled us to capture individual differences in behavioral performance and, based on the MLE estimates, to select a subset of participants who suppressed task-irrelevant information. Even for this subset of participants, who showed no or only small interference effects and thus were thought to truly process temporal information in the time condition and numerosity information in the number condition, we found CNV patterns in the time-domain EEG signals for both tasks that was more pronounced in the time-task. We found no substantial evidence for differences between the processing of temporal and numerical information in the time–frequency domain.

Short-term effects on temporal judgement: Sequential drivers of interval bisection and reproduction

Our prior experiences provide the background with which we judge subsequent events. In the time perception literature one common finding is that providing participants with a higher percentage of a particular interval can skew judgment; intervals will appear longer if the distribution of intervals contains more short experiences. However, changing the distribution of intervals that participants witness also changes the short-term, interval-to-interval, sequence that participants experience. In the experiment presented here, we kept the overall distribution of intervals constant while manipulating the immediately-prior experience of participants. In temporal bisection, this created a noted assimilation effect; participants judged intervals as shorter given an immediately preceding short interval. In interval reproduction, there was no effect of the immediately prior interval length unless the prior interval had a linked motor command. We thus proposed that the immediately prior interval provided a context by which a subsequent interval is judged. However, in the case of reproduction, where a subsequent interval is reproduced, rather than seen, the effects of contextualization are attenuated.

Temporal Context Influences the Perceived Duration of Everyday Actions: Assessing the Ecological Validity of Lab-Based Timing Phenomena

Timing is key to accurate performance, for example when learning a new complex sequence by mimicry. However, most timing research utilizes artificial tasks and simple stimuli with clearly marked onset and offset cues. Here we address the question whether existing interval timing findings generalize to real-world timing tasks. In this study, animated video clips of a person performing different everyday actions were presented and participants had to reproduce the main action's duration. Although reproduced durations are more variable then observed in laboratory studies, the data adheres to two interval timing laws: Relative timing sensitivity is constant across durations (scalar property), and the subjective duration of a previous action influenced the current action's perceived duration (temporal context effect). Taken together, this demonstrates that laboratory findings generalize, and paves the way for studying interval timing as a component of complex, everyday cognitive performance.

Temporal discrimination of one's own reaction times in dual-task performance: Context effects and methodological constraints

In this study we used the method of constant stimuli to investigate introspective reaction times in the psychological refractory period (PRP) paradigm under different temporal contexts. Previous introspective PRP studies have mostly used visual analogue scales to assess introspective reaction times and found that participants were largely unaware of the typical dual-task costs that arise in this paradigm (PRP effect). This apparent limitation of introspection has been taken as evidence for a serial processing bottleneck that encompasses response selection as well as conscious perception. In our study, in each trial participants first performed the PRP task and were then presented with a comparison interval that they had to compare with their reaction time to the second task (RT2). Across three experiments, we observed that the subjective estimates of RT2 (i.e., the points of subjective equality) did not reflect the objective pattern but were almost completely biased toward the center of the comparison intervals (asymmetry effect). In a control experiment in which participants discriminated RT2s of other participants without performing the PRP task, this bias was largely reduced. We interpret these results as indicating that in dual-task performance participants acquire only poor temporal representations of their own reaction times, and the apparent unawareness of the PRP effect may reflect disturbed timing abilities rather than a conscious perception bottleneck.

Evidence for different processes involved in the effects of nontemporal stimulus size and numerical digit value on duration judgments

Perceived duration has been shown to be positively related to task-irrelevant, nontemporal stimulus magnitude. To account for this finding, Walsh's (2003) A Theory of Magnitude (ATOM) model suggests that magnitude of time is not differentiated from magnitude of other nontemporal stimulus characteristics and collectively processed by a generalized magnitude system. In Experiment 1, we investigated the combined effects of stimulus size and numerical quantity, as two nontemporal stimulus dimensions covered by the ATOM model, on duration judgments. Participants were required to reproduce the duration of target intervals marked by Arabic digits varying in physical size and numerical value. While the effect of stimulus size was effectively moderated by target duration, the effect of numerical value appeared to require attentional resources directed to the numerical value in order to become effective. Experiment 2 was designed to further elucidate the mediating influence of attention on the effect of numerical value on duration judgments. An effect of numerical value was only observed when participants' attention was directed to digit value, but not when participants were required to pay special attention to digit parity. While the ATOM model implies a common metrics and generalized magnitude processing for time, size, and quantity, the present findings provided converging evidence for the notion of two qualitatively different mechanisms underlying the effects of nontemporal stimulus size and numerical value on duration judgments. Furthermore, our data challenge the implicit common assumption that the effect of numerical value on duration judgments represents a continuously increasing function of digit magnitude.

The Indecision Model of Psychophysical Performance in Dual-Presentation Tasks: Parameter Estimation and Comparative Analysis of Response Formats

Psychophysical data from dual-presentation tasks are often collected with the two-alternative forced-choice (2AFC) response format, asking observers to guess when uncertain. For an analytical description of performance, psychometric functions are then fitted to data aggregated across the two orders/positions in which stimuli were presented. Yet, order effects make aggregated data uninterpretable, and the bias with which observers guess when uncertain precludes separating sensory from decisional components of performance. A ternary response format in which observers are also allowed to report indecision should fix these problems, but a comparative analysis with the 2AFC format has never been conducted. In addition, fitting ternary data separated by presentation order poses serious challenges. To address these issues, we extended the indecision model of psychophysical performance to accommodate the ternary, 2AFC, and same-different response formats in detection and discrimination tasks. Relevant issues for parameter estimation are also discussed along with simulation results that document the superiority of the ternary format. These advantages are demonstrated by fitting the indecision model to published detection and discrimination data collected with the ternary, 2AFC, or same-different formats, which had been analyzed differently in the sources. These examples also show that 2AFC data are unsuitable for testing certain types of hypotheses. matlab and R routines written for our purposes are available as Supplementary Material, which should help spread the use of the ternary format for dependable collection and interpretation of psychophysical data.

Time-order-errors and duration ranges in the Episodic Temporal Generalization task

The current model of the Episodic Temporal Generalization task, where subjects have to judge whether pairs of auditory stimuli are equal in duration, predicts that results are scale-free and unaffected by the presentation order of the stimuli. To test these predictions, we conducted three experiments assessing sub- and supra-second standards and taking presentation order into account. Proportions were spaced linearly in Experiments 1 and 2 and logarithmically in Experiment 3. Critically, we found effects of duration range and presentation order with both spacing schemes. Our results constitute the first report of presentation order effects in the Episodic Temporal Generalization task and demonstrate that future studies should always consider duration range, number of trials and presentation order as crucial factors modulating performance.

Duration Aftereffect Depends on the Duration of Adaptation

It has been widely demonstrated that a prolonged adaptation to a relatively long or short stimulus leads to a robust repulsive duration aftereffect. However, little is known about the rapid adaptation to stimulus duration. In this study, we investigated whether the duration aftereffect could also be induced by short-term adaptation to stimuli of both sub- and supra-second durations. To control for the internal reference for duration judgment, participants were adapted to a stimulus of medium duration, and then tested with both longer and shorter stimuli. We found that the duration aftereffect was only observed after long-term adaptation to stimuli of both sub- and supra-second durations, which suggests that the exposure time to the adaptor is a fundamental factor in determining the duration aftereffect. Our findings offer further evidence of the duration aftereffect, which in this study was dissociated from the anchor effect and high-level aftereffects.

Learned interval time facilitates associate memory retrieval

The extent to which time is represented in memory remains underinvestigated. We designed a time paired associate task (TPAT) in which participants implicitly learned cue-time-target associations between cue-target pairs and specific cue-target intervals. During subsequent memory testing, participants showed increased accuracy of identifying matching cue-target pairs if the time interval during testing matched the implicitly learned interval. A control experiment showed that participants had no explicit knowledge about the cue-time associations. We suggest that "elapsed time" can act as a temporal mnemonic associate that can facilitate retrieval of events associated in memory.

For the Last Time: Temporal Sensitivity and Perceived Timing of the Final Stimulus in an Isochronous Sequence

An isochronous sequence is a series of repeating events with the same inter-onset-interval. A common finding is that as the length of a sequence increases, so does temporal sensitivity to irregularities — that is, the detection of deviations from isochrony is better with a longer sequence. Several theoretical accounts exist in the literature as to how the brain processes sequences for the detection of irregularities, yet there remains to be a systematic comparison of the predictions that such accounts make. To compare the predictions of these accounts, we asked participants to report whether the last stimulus of a regularly-timed sequence appeared ‘earlier’ or ‘later’ than expected. Such task allowed us to separately analyse bias and performance. Sequences lengths (3, 4, 5 or 6 beeps) were either randomly interleaved or presented in separate blocks. We replicate previous findings showing that temporal sensitivity increases with longer sequence in the interleaved condition but not in the blocked condition (where performance is higher overall). Results also indicate that there is a consistent bias in reporting whether the last stimulus is isochronous (irrespectively of how many stimuli the sequence is composed of). Such result is consistent with a perceptual acceleration of stimuli embedded in isochronous sequences. From the comparison of the models’ predictions we determine that the improvement in sensitivity is best captured by an averaging of successive estimates, but with an element that limits performance improvement below statistical optimality. None of the models considered, however, provides an exhaustive explanation for the pattern of results found.

Magnitude Estimation with Noisy Integrators Linked by an Adaptive Reference

Judgments of physical stimuli show characteristic biases; relatively small stimuli are overestimated whereas relatively large stimuli are underestimated (regression effect). Such biases likely result from a strategy that seeks to minimize errors given noisy estimates about stimuli that itself are drawn from a distribution, i.e., the statistics of the environment. While being conceptually well described, it is unclear how such a strategy could be implemented neurally. The present paper aims toward answering this question. A theoretical approach is introduced that describes magnitude estimation as two successive stages of noisy (neural) integration. Both stages are linked by a reference memory that is updated with every new stimulus. The model reproduces the behavioral characteristics of magnitude estimation and makes several experimentally testable predictions. Moreover, the model identifies the regression effect as a means of minimizing estimation errors and explains how this optimality strategy depends on the subject's discrimination abilities and on the stimulus statistics. The latter influence predicts another property of magnitude estimation, the so-called range effect. Beyond being successful in describing decision-making, the present work suggests that noisy integration may also be important in processing magnitudes.