Bayesian inference underlies the contraction bias in delayed comparison tasks

Delayed comparison tasks are widely used in the study of working memory and perception in psychology and neuroscience. It has long been known, however, that decisions in these tasks are biased. When the two stimuli in a delayed comparison trial are small in magnitude, subjects tend to report that the first stimulus is larger than the second stimulus. In contrast, subjects tend to report that the second stimulus is larger than the first when the stimuli are relatively large. Here we study the computational principles underlying this bias, also known as the contraction bias. We propose that the contraction bias results from a Bayesian computation in which a noisy representation of a magnitude is combined with a-priori information about the distribution of magnitudes to optimize performance. We test our hypothesis on choice behavior in a visual delayed comparison experiment by studying the effect of (i) changing the prior distribution and (ii) changing the uncertainty in the memorized stimulus. We show that choice behavior in both manipulations is consistent with the performance of an observer who uses a Bayesian inference in order to improve performance. Moreover, our results suggest that the contraction bias arises during memory retrieval/decision making and not during memory encoding. These results support the notion that the contraction bias illusion can be understood as resulting from optimality considerations.     

Bayesian natural selection and the evolution of perceptual systems

In recent years, there has been much interest in characterizing statistical properties of natural stimuli in order to better understand the design of perceptual systems. A fruitful approach has been to compare the processing of natural stimuli in real perceptual systems with that of ideal observers derived within the framework of Bayesian statistical decision theory. While this form of optimization theory has provided a deeper understanding of the information contained in natural stimuli as well as of the computational principles employed in perceptual systems, it does not directly consider the process of natural selection, which is ultimately responsible for design. Here we propose a formal framework for analysing how the statistics of natural stimuli and the process of natural selection interact to determine the design of perceptual systems. The framework consists of two complementary components. The first is a maximum fitness ideal observer, a standard Bayesian ideal observer with a utility function appropriate for natural selection. The second component is a formal version of natural selection based upon Bayesian statistical decision theory. Maximum fitness ideal observers and Bayesian natural selection are demonstrated in several examples. We suggest that the Bayesian approach is appropriate not only for the study of perceptual systems but also for the study of many other systems in biology.     

Naturalistic Stimulus Structure Determines the Integration of Audiovisual Looming Signals in Binocular Rivalry

Rapid integration of biologically relevant information is crucial for the survival of an organism. Most prominently, humans should be biased to attend and respond to looming stimuli that signal approaching danger (e.g. predator) and hence require rapid action. This psychophysics study used binocular rivalry to investigate the perceptual advantage of looming (relative to receding) visual signals (i.e. looming bias) and how this bias can be influenced by concurrent auditory looming/receding stimuli and the statistical structure of the auditory and visual signals.Subjects were dichoptically presented with looming/receding visual stimuli that were paired with looming or receding sounds. The visual signals conformed to two different statistical structures: (1) a ‘simple’ random-dot kinematogram showing a starfield and (2) a “naturalistic” visual Shepard stimulus. Likewise, the looming/receding sound was (1) a simple amplitude- and frequency-modulated (AM-FM) tone or (2) a complex Shepard tone. Our results show that the perceptual looming bias (i.e. the increase in dominance times for looming versus receding percepts) is amplified by looming sounds, yet reduced and even converted into a receding bias by receding sounds. Moreover, the influence of looming/receding sounds on the visual looming bias depends on the statistical structure of both the visual and auditory signals. It is enhanced when audiovisual signals are Shepard stimuli.In conclusion, visual perception prioritizes processing of biologically significant looming stimuli especially when paired with looming auditory signals. Critically, these audiovisual interactions are amplified for statistically complex signals that are more naturalistic and known to engage neural processing at multiple levels of the cortical hierarchy.     

Experimentally Derived δ13C and δ15N Discrimination Factors for Gray Wolves and the Impact of Prior Information in Bayesian Mixing Models

Stable isotope analysis of diet has become a common tool in conservation research. However, the multiple sources of uncertainty inherent in this analysis framework involve consequences that have not been thoroughly addressed. Uncertainty arises from the choice of trophic discrimination factors, and for Bayesian stable isotope mixing models (SIMMs), the specification of prior information; the combined effect of these aspects has not been explicitly tested. We used a captive feeding study of gray wolves (Canis lupus) to determine the first experimentally-derived trophic discrimination factors of C and N for this large carnivore of broad conservation interest. Using the estimated diet in our controlled system and data from a published study on wild wolves and their prey in Montana, USA, we then investigated the simultaneous effect of discrimination factors and prior information on diet reconstruction with Bayesian SIMMs. Discrimination factors for gray wolves and their prey were 1.97‰ for δ¹³C and 3.04‰ for δ¹⁵N. Specifying wolf discrimination factors, as opposed to the commonly used red fox (Vulpes vulpes) factors, made little practical difference to estimates of wolf diet, but prior information had a strong effect on bias, precision, and accuracy of posterior estimates. Without specifying prior information in our Bayesian SIMM, it was not possible to produce SIMM posteriors statistically similar to the estimated diet in our controlled study or the diet of wild wolves. Our study demonstrates the critical effect of prior information on estimates of animal diets using Bayesian SIMMs, and suggests species-specific trophic discrimination factors are of secondary importance. When using stable isotope analysis to inform conservation decisions researchers should understand the limits of their data. It may be difficult to obtain useful information from SIMMs if informative priors are omitted and species-specific discrimination factors are unavailable.     

Factors Limiting Performance in a Multitone Intensity-Discrimination Task: Disentangling Non-Optimal Decision Weights and Increased Internal Noise

To identify factors limiting performance in multitone intensity discrimination, we presented sequences of five pure tones alternating in level between loud (85 dB SPL) and soft (30, 55, or 80 dB SPL). In the “overall-intensity task”, listeners detected a level increment on all of the five tones. In the “masking task”, the level increment was imposed only on the soft tones, rendering the soft tones targets and loud tones task-irrelevant maskers. Decision weights quantifying the importance of the five tone levels for the decision were estimated using methods of molecular psychophysics. Compatible with previous studies, listeners placed higher weights on the loud tones than on the soft tones in the overall-intensity condition. In the masking task, the decisions were systematically influenced by the to-be-ignored loud tones (maskers). Using a maximum-likelihood technique, we estimated the internal noise variance and tested whether the internal noise was higher in the alternating-level five-tone sequences than in sequences presenting only the soft or only the loud tones. For the overall-intensity task, we found no evidence for increased internal noise, but listeners applied suboptimal decision weights. These results are compatible with the hypothesis that the presence of the loud tones does not impair the precision of the representation of the intensity of the soft tones available at the decision stage, but that this information is not used in an optimal fashion due to a difficulty in attending to the soft tones. For the masking task, in some cases our data indicated an increase in internal noise. Additionally, listeners applied suboptimal decision weights. The maximum-likelihood analyses we developed should also be useful for other tasks or other sensory modalities.     

Risk-Sensitivity in Bayesian Sensorimotor Integration

Information processing in the nervous system during sensorimotor tasks with inherent uncertainty has been shown to be consistent with Bayesian integration. Bayes optimal decision-makers are, however, risk-neutral in the sense that they weigh all possibilities based on prior expectation and sensory evidence when they choose the action with highest expected value. In contrast, risk-sensitive decision-makers are sensitive to model uncertainty and bias their decision-making processes when they do inference over unobserved variables. In particular, they allow deviations from their probabilistic model in cases where this model makes imprecise predictions. Here we test for risk-sensitivity in a sensorimotor integration task where subjects exhibit Bayesian information integration when they infer the position of a target from noisy sensory feedback. When introducing a cost associated with subjects'' response, we found that subjects exhibited a characteristic bias towards low cost responses when their uncertainty was high. This result is in accordance with risk-sensitive decision-making processes that allow for deviations from Bayes optimal decision-making in the face of uncertainty. Our results suggest that both Bayesian integration and risk-sensitivity are important factors to understand sensorimotor integration in a quantitative fashion.     

Lost in the Forest,Stuck in the Trees: Dispositional Global/Local Bias Is Resistant to Exposure to High and Low Spatial Frequencies

Visual stimuli can be perceived at a broad, “global” level, or at a more focused, “local” level. While research has shown that many individuals demonstrate a preference for global information, there are large individual differences in the degree of global/local bias, such that some individuals show a large global bias, some show a large local bias, and others show no bias. The main purpose of the current study was to examine whether these dispositional differences in global/local bias could be altered through various manipulations of high/low spatial frequency. Through 5 experiments, we examined various measures of dispositional global/local bias and whether performance on these measures could be altered by manipulating previous exposure to high or low spatial frequency information (with high/low spatial frequency faces, gratings, and Navon letters). Ultimately, there was little evidence of change from pre-to-post manipulation on the dispositional measures, and dispositional global/local bias was highly reliable pre- to post-manipulation. The results provide evidence that individual differences in global/local bias or preference are relatively resistant to exposure to spatial frequency information, and suggest that the processing mechanisms underlying high/low spatial frequency use and global/local bias may be more independent than previously thought.     

A new perceptual bias reveals suboptimal population decoding of sensory responses

Several studies have reported optimal population decoding of sensory responses in two-alternative visual discrimination tasks. Such decoding involves integrating noisy neural responses into a more reliable representation of the likelihood that the stimuli under consideration evoked the observed responses. Importantly, an ideal observer must be able to evaluate likelihood with high precision and only consider the likelihood of the two relevant stimuli involved in the discrimination task. We report a new perceptual bias suggesting that observers read out the likelihood representation with remarkably low precision when discriminating grating spatial frequencies. Using spectrally filtered noise, we induced an asymmetry in the likelihood function of spatial frequency. This manipulation mainly affects the likelihood of spatial frequencies that are irrelevant to the task at hand. Nevertheless, we find a significant shift in perceived grating frequency, indicating that observers evaluate likelihoods of a broad range of irrelevant frequencies and discard prior knowledge of stimulus alternatives when performing two-alternative discrimination.     

An initial ‘snapshot’ of sensory information biases the likelihood and speed of subsequent changes of mind

We often need to rapidly change our mind about perceptual decisions in order to account for new information and correct mistakes. One fundamental, unresolved question is whether information processed prior to a decision being made (‘pre-decisional information’) has any influence on the likelihood and speed with which that decision is reversed. We investigated this using a luminance discrimination task in which participants indicated which of two flickering greyscale squares was brightest. Following an initial decision, the stimuli briefly remained on screen, and participants could change their response. Using psychophysical reverse correlation, we examined how moment-to-moment fluctuations in stimulus luminance affected participants’ decisions. This revealed that the strength of even the very earliest (pre-decisional) evidence was associated with the likelihood and speed of later changes of mind. To account for this effect, we propose an extended diffusion model in which an initial ‘snapshot’ of sensory information biases ongoing evidence accumulation.     

Phonotaxis in flying crickets

The effects of two-tone stimuli on the high frequency bat-avoidance steering behavior of flying crickets (Teleogryllus oceanicus) were studied during tethered flight. Similarly, the effects of two-tone stimuli on the ultrasound sensitive auditory interneuron, Int-1, which elicits this behavior, were studied using intracellular staining and recording techniques. When a low frequency tone (3-8 kHz) was presented simultaneously with an aversive high frequency tone (in a two-tone stimulus paradigm), the high frequency avoidance steering behavior was suppressed. Suppression was optimal when the low frequency tone was between 4 and 5 kHz and about 10-15 dB louder than the high frequency tone (Figs. 2, 3). Best suppression occurred when the low frequency tone-pulse just preceded or overlapped the high frequency tone-pulse, indicating that the suppressive effects of 5 kHz could last for up to 70 ms (Fig. 4). The threshold for avoidance of the bat-like stimulus was elevated when model bat biosonar (30 kHz) was presented while the animal was performing positive phonotaxis toward 5 kHz model calling song, but only if the calling song intensity was relatively high (greater than 70-80 dB SPL) (Fig. 1). However, avoidance steering could always be elicited as long as the calling song was not more than 10 dB louder than the ultrasound (Fig. 1). This suppressive effect did not require performance of positive phonotaxis to the calling song (Fig. 2) and was probably due to the persistence of the suppressive effects of the 5 kHz model calling song (Fig. 4). The requirement for relatively high intensities of calling song suggest that the suppression of bat-avoidance by the calling song is not likely to be of great significance in nature. The high frequency harmonics of the male cricket's natural calling song overlap the lower frequency range used by insectivorous bats (10-20 kHz) and are loud enough to elicit avoidance behavior in a flying female as she closely approaches a singing male (Fig. 5). The high frequency 'harmonics' of a model calling song were aversive even if presented with a normally attractive temporal pattern (pulse repetition rate of 16 pps) (Fig. 6A). When the 5 kHz 'fundamental' was added to one of the high frequency 'harmonics', in a two-tone stimulus paradigm, this complex model calling song was attractive; the high frequency 'harmonic' no longer elicited the avoidance behavior (Fig. 6) and the animals steered toward the model CS. Thus, addition of 5 kHz to a high frequency harmonic of the calling song 'masked' the aversive nature of this stimulus.(ABSTRACT TRUNCATED AT 400 WORDS)     

Task-induced neural covariability as a signature of approximate Bayesian learning and inference

Perception is often characterized computationally as an inference process in which uncertain or ambiguous sensory inputs are combined with prior expectations. Although behavioral studies have shown that observers can change their prior expectations in the context of a task, robust neural signatures of task-specific priors have been elusive. Here, we analytically derive such signatures under the general assumption that the responses of sensory neurons encode posterior beliefs that combine sensory inputs with task-specific expectations. Specifically, we derive predictions for the task-dependence of correlated neural variability and decision-related signals in sensory neurons. The qualitative aspects of our results are parameter-free and specific to the statistics of each task. The predictions for correlated variability also differ from predictions of classic feedforward models of sensory processing and are therefore a strong test of theories of hierarchical Bayesian inference in the brain. Importantly, we find that Bayesian learning predicts an increase in so-called “differential correlations” as the observer’s internal model learns the stimulus distribution, and the observer’s behavioral performance improves. This stands in contrast to classic feedforward encoding/decoding models of sensory processing, since such correlations are fundamentally information-limiting. We find support for our predictions in data from existing neurophysiological studies across a variety of tasks and brain areas. Finally, we show in simulation how measurements of sensory neural responses can reveal information about a subject’s internal beliefs about the task. Taken together, our results reinterpret task-dependent sources of neural covariability as signatures of Bayesian inference and provide new insights into their cause and their function.     

Characterizing the Impact of Category Uncertainty on Human Auditory Categorization Behavior

Categorization is an important cognitive process. However, the correct categorization of a stimulus is often challenging because categories can have overlapping boundaries. Whereas perceptual categorization has been extensively studied in vision, the analogous phenomenon in audition has yet to be systematically explored. Here, we test whether and how human subjects learn to use category distributions and prior probabilities, as well as whether subjects employ an optimal decision strategy when making auditory-category decisions. We asked subjects to classify the frequency of a tone burst into one of two overlapping, uniform categories according to the perceived tone frequency. We systematically varied the prior probability of presenting a tone burst with a frequency originating from one versus the other category. Most subjects learned these changes in prior probabilities early in testing and used this information to influence categorization. We also measured each subject''s frequency-discrimination thresholds (i.e., their sensory uncertainty levels). We tested each subject''s average behavior against variations of a Bayesian model that either led to optimal or sub-optimal decision behavior (i.e. probability matching). In both predicting and fitting each subject''s average behavior, we found that probability matching provided a better account of human decision behavior. The model fits confirmed that subjects were able to learn category prior probabilities and approximate forms of the category distributions. Finally, we systematically explored the potential ways that additional noise sources could influence categorization behavior. We found that an optimal decision strategy can produce probability-matching behavior if it utilized non-stationary category distributions and prior probabilities formed over a short stimulus history. Our work extends previous findings into the auditory domain and reformulates the issue of categorization in a manner that can help to interpret the results of previous research within a generative framework.     

Neural networks simulating the frequency discrimination of hearing for non-stationary short tone stimuli

This paper addresses the question of frequency discrimination of hearing for non-stationary (short) tone stimuli (duration 125 ms). Shortening of the stimulus duration leads to widening of the frequency spectrum of the tone. It can be shown that for hearing no acoustical uncertainty relation holds and thus some nonlinear elements must be present in hearing physiology. We present neurophysiological and psychoacoustical findings supporting the hypothesis that frequency discrimination of non-stationary short tone stimuli is performed in neural networks of the auditory system. Neural network architectures that could process the temporal and place excitation patterns originating in the cochlea are suggested. We show how these networks (temporal coincidence network processing the temporal code and lateral inhibition network processing the place code) can be combined to show performance consistent with auditory physiology. They might explain the frequency discrimination of hearing for non-stationary short tone stimuli. We show the fitting of psychophysical relations based on these networks with the experimentally determined data.     

Dynamic integration of reward and stimulus information in perceptual decision-making

In perceptual decision-making, ideal decision-makers should bias their choices toward alternatives associated with larger rewards, and the extent of the bias should decrease as stimulus sensitivity increases. When responses must be made at different times after stimulus onset, stimulus sensitivity grows with time from zero to a final asymptotic level. Are decision makers able to produce responses that are more biased if they are made soon after stimulus onset, but less biased if they are made after more evidence has been accumulated? If so, how close to optimal can they come in doing this, and how might their performance be achieved mechanistically? We report an experiment in which the payoff for each alternative is indicated before stimulus onset. Processing time is controlled by a “go” cue occurring at different times post stimulus onset, requiring a response within msec. Reward bias does start high when processing time is short and decreases as sensitivity increases, leveling off at a non-zero value. However, the degree of bias is sub-optimal for shorter processing times. We present a mechanistic account of participants'' performance within the framework of the leaky competing accumulator model [1], in which accumulators for each alternative accumulate noisy information subject to leakage and mutual inhibition. The leveling off of accuracy is attributed to mutual inhibition between the accumulators, allowing the accumulator that gathers the most evidence early in a trial to suppress the alternative. Three ways reward might affect decision making in this framework are considered. One of the three, in which reward affects the starting point of the evidence accumulation process, is consistent with the qualitative pattern of the observed reward bias effect, while the other two are not. Incorporating this assumption into the leaky competing accumulator model, we are able to provide close quantitative fits to individual participant data.     

Using Bayes' Rule to Define the Value of Evidence from Syndromic Surveillance

In this work we propose the adoption of a statistical framework used in the evaluation of forensic evidence as a tool for evaluating and presenting circumstantial “evidence” of a disease outbreak from syndromic surveillance. The basic idea is to exploit the predicted distributions of reported cases to calculate the ratio of the likelihood of observing n cases given an ongoing outbreak over the likelihood of observing n cases given no outbreak. The likelihood ratio defines the Value of Evidence (V). Using Bayes'' rule, the prior odds for an ongoing outbreak are multiplied by V to obtain the posterior odds. This approach was applied to time series on the number of horses showing clinical respiratory symptoms or neurological symptoms. The separation between prior beliefs about the probability of an outbreak and the strength of evidence from syndromic surveillance offers a transparent reasoning process suitable for supporting decision makers. The value of evidence can be translated into a verbal statement, as often done in forensics or used for the production of risk maps. Furthermore, a Bayesian approach offers seamless integration of data from syndromic surveillance with results from predictive modeling and with information from other sources such as disease introduction risk assessments.     

Deep Cerebellar Nuclei Play an Important Role in Two-Tone Discrimination on Delay Eyeblink Conditioning in C57BL/6 Mice

Previous studies have shown that deep cerebellar nuclei (DCN)-lesioned mice develop conditioned responses (CR) on delay eyeblink conditioning when a salient tone conditioned stimulus (CS) is used, which suggests that the cerebellum potentially plays a role in more complicated cognitive functions. In the present study, we examined the role of DCN in tone frequency discrimination in the delay eyeblink-conditioning paradigm. In the first experiment, DCN-lesioned and sham-operated mice were subjected to standard simple eyeblink conditioning under low-frequency tone CS (LCS: 1 kHz, 80 dB) or high-frequency tone CS (HCS: 10 kHz, 70 dB) conditions. DCN-lesioned mice developed CR in both CS conditions as well as sham-operated mice. In the second experiment, DCN-lesioned and sham-operated mice were subjected to two-tone discrimination tasks, with LCS+ (or HCS+) paired with unconditioned stimulus (US), and HCS− (or LCS−) without US. CR% in sham-operated mice increased in LCS+ (or HCS+) trials, regardless of tone frequency of CS, but not in HCS− (or LCS−) trials. The results indicate that sham-operated mice can discriminate between LCS+ and HCS− (or HCS+ and LCS−). In contrast, DCN-lesioned mice showed high CR% in not only LCS+ (or HCS+) trials but also HCS− (or LCS−) trials. The results indicate that DCN lesions impair the discrimination between tone frequency in eyeblink conditioning. Our results suggest that the cerebellum plays a pivotal role in the discrimination of tone frequency.     

Within- and Cross-Modal Distance Information Disambiguate Visual Size-Change Perception

Perception is fundamentally underconstrained because different combinations of object properties can generate the same sensory information. To disambiguate sensory information into estimates of scene properties, our brains incorporate prior knowledge and additional “auxiliary” (i.e., not directly relevant to desired scene property) sensory information to constrain perceptual interpretations. For example, knowing the distance to an object helps in perceiving its size. The literature contains few demonstrations of the use of prior knowledge and auxiliary information in combined visual and haptic disambiguation and almost no examination of haptic disambiguation of vision beyond “bistable” stimuli. Previous studies have reported humans integrate multiple unambiguous sensations to perceive single, continuous object properties, like size or position. Here we test whether humans use visual and haptic information, individually and jointly, to disambiguate size from distance. We presented participants with a ball moving in depth with a changing diameter. Because no unambiguous distance information is available under monocular viewing, participants rely on prior assumptions about the ball''s distance to disambiguate their -size percept. Presenting auxiliary binocular and/or haptic distance information augments participants'' prior distance assumptions and improves their size judgment accuracy—though binocular cues were trusted more than haptic. Our results suggest both visual and haptic distance information disambiguate size perception, and we interpret these results in the context of probabilistic perceptual reasoning.     

Incorporating prior beliefs about selection bias into the analysis of randomized trials with missing outcomes

In randomized studies with missing outcomes, non-identifiable assumptions are required to hold for valid data analysis. As a result, statisticians have been advocating the use of sensitivity analysis to evaluate the effect of varying assumptions on study conclusions. While this approach may be useful in assessing the sensitivity of treatment comparisons to missing data assumptions, it may be dissatisfying to some researchers/decision makers because a single summary is not provided. In this paper, we present a fully Bayesian methodology that allows the investigator to draw a 'single' conclusion by formally incorporating prior beliefs about non-identifiable, yet interpretable, selection bias parameters. Our Bayesian model provides robustness to prior specification of the distributional form of the continuous outcomes.     

Visual Mislocalization of Moving Objects in an Audiovisual Event

The present study investigated the influence of an auditory tone on the localization of visual objects in the stream/bounce display (SBD). In this display, two identical visual objects move toward each other, overlap, and then return to their original positions. These objects can be perceived as either streaming through or bouncing off each other. In this study, the closest distance between object centers on opposing trajectories and tone presentation timing (none, 0 ms, ± 90 ms, and ± 390 ms relative to the instant for the closest distance) were manipulated. Observers were asked to judge whether the two objects overlapped with each other and whether the objects appeared to stream through, bounce off each other, or reverse their direction of motion. A tone presented at or around the instant of the objects’ closest distance biased judgments toward “non-overlapping,” and observers overestimated the physical distance between objects. A similar bias toward direction change judgments (bounce and reverse, not stream judgments) was also observed, which was always stronger than the non-overlapping bias. Thus, these two types of judgments were not always identical. Moreover, another experiment showed that it was unlikely that this observed mislocalization could be explained by other previously known mislocalization phenomena (i.e., representational momentum, the Fröhlich effect, and a turn-point shift). These findings indicate a new example of crossmodal mislocalization, which can be obtained without temporal offsets between audiovisual stimuli. The mislocalization effect is also specific to a more complex stimulus configuration of objects on opposing trajectories, with a tone that is presented simultaneously. The present study promotes an understanding of relatively complex audiovisual interactions beyond simple one-to-one audiovisual stimuli used in previous studies.