Department of Psychology, Neuroscience & Behaviour
Neuroscience Graduate Program

An accessible introduction to constructing and interpreting Bayesian models of perceptual decision-making and action.
Many forms of perception and action can be mathematically modeled as probabilistic—or Bayesian—inference, a method used to draw conclusions from uncertain evidence. According to these models, the human mind behaves like a capable data scientist or crime scene investigator when dealing with noisy and ambiguous data. This textbook provides an approachable introduction to constructing and reasoning with probabilistic models of perceptual decision-making and action. Featuring extensive examples and illustrations, Bayesian Models of Perception and Action is the first textbook to teach this widely used computational framework to beginners.

Exploring the world through touch requires the integration of internal (e.g., anatomical) and external (e.g., spatial) reference frames — you only know what you touch when you know where your hands are in space. The deficit observed in tactile temporal-order judgements when the hands are crossed over the midline provides one tool to explore this integration. We used foot pedals and required participants to focus on either the hand that was stimulated first (an anatomical bias condition) or the location of the hand that was stimulated first (a spatiotopic bias condition). Spatiotopic-based responses produce a larger crossed-hands deficit, presumably by focusing observers on the external reference frame. In contrast, anatomical-based responses focus the observer on the internal reference frame and produce a smaller deficit. This manipulation thus provides evidence that observers can change the relative weight given to each reference frame. We quantify this effect using a probabilistic model that produces a population estimate of the relative weight given to each reference frame. We show that a spatiotopic bias can result in either a larger external weight (Experiment 1) or a smaller internal weight (Experiment 2) and provide an explanation of when each one would occur.

The ability to travel independently is crucial to an individual's quality of life but compromised by visual impairment. Several navigational aids have been developed for blind people to address this limitation. These devices typically employ auditory instructions to guide users to desired waypoints. Unfortunately, auditory instructions may interfere with users' awareness of environmental sounds that signal dangers or provide cues for spatial orientation. Accordingly, there is a need to explore the use of non-auditory modalities to convey information for safe and independent travel. Here, we explored the efficacy of a tactile navigational aid that provides turn signals via vibrations on a hip-worn belt. We compared the performance of 12 blind participants as they navigated a series of paths under the direction of the tactile belt or conventional auditory turn commands; furthermore, we assessed the effect of repeated testing, both in the presence and absence of simulated street sounds. A computer-controlled system triggered each turn command, measured participants’ time-to-path-completion, and detected major navigational errors. When participants navigated in a silent environment, they performed somewhat worse with the tactile belt than the auditory device, taking longer to complete each trial and committing more errors. When participants navigated in the presence of simulated street noises, the difference in completion time between auditory and tactile navigation diminished. These results suggest that tactile navigation holds promise as an effective method in everyday environments characterized by ambient noise such as street sounds.

Responses of auditory duration-tuned neurons (DTNs) are selective for stimulus duration. We used single-unit extracellular recording to investigate how the inferior colliculus (IC) encodes frequency-modulated (FM) sweeps in the big brown bat. It was unclear whether the responses of so-called “FM DTNs” encode signal duration, like classic pure-tone DTNs, or the FM sweep rate. Most FM cells had spiking responses selective for downward FM sweeps. We presented cells with linear FM sweeps whose center frequency (CEF) was set to the best excitatory frequency and whose bandwidth (BW) maximized the spike count. With these baseline parameters, we stimulated cells with linear FM sweeps randomly varied in duration to measure the range of excitatory FM durations and/or sweep rates. To separate FM rate and FM duration tuning, we doubled (and halved) the BW of the baseline FM stimulus while keeping the CEF constant and then recollected each cell’s FM duration tuning curve. If the cell was tuned to FM duration, then the best duration (or range of excitatory durations) should remain constant despite changes in signal BW; however, if the cell was tuned to the FM rate, then the best duration should covary with the same FM rate at each BW. A Bayesian model comparison revealed that the majority of neurons were tuned to the FM sweep rate, although a few cells showed tuning for FM duration. We conclude that the dominant parameter for temporal tuning of FM neurons in the IC is FM sweep rate and not FM duration.

Following focal sensory adaptation, the perceived separation between visual stimuli that straddle the adapted region is often exaggerated. For instance, in the tilt aftereffect illusion, adaptation to tilted lines causes subsequently viewed lines with nearby orientations to be perceptually repelled from the adapted orientation. Repulsion illusions in the nonvisual senses have been less studied. Here, we investigated whether adaptation induces a repulsion illusion in tactile spatial perception. In a two-interval forced-choice task, participants compared the perceived separation between two point-stimuli applied on the forearms successively. Separation distance was constant on one arm (the reference) and varied on the other arm (the comparison). In Experiment 1, we took three consecutive baseline measurements, verifying that in the absence of manipulation, participants' distance perception was unbiased across arms and stable across experimental blocks. In Experiment 2, we vibrated a region of skin on the reference arm, verifying that this focally reduced tactile sensitivity, as indicated by elevated monofilament detection thresholds. In Experiment 3, we applied vibration between the two reference points in our distance perception protocol and discovered that this caused an illusory increase in the separation between the points. We conclude that focal adaptation induces a repulsion aftereffect illusion in tactile spatial perception. The illusion provides clues as to how the tactile system represents spatial information. The analogous repulsion aftereffects caused by adaptation in different stimulus domains and sensory systems may point to fundamentally similar strategies for dynamic sensory coding.

To perceive, the brain must interpret stimulus-evoked neural activity. This is challenging: the stochastic nature of the neural response renders its interpretation inherently uncertain. Perception would be optimized if the brain used Bayesian inference to interpret inputs in light of expectations derived from experience. Bayesian inference would improve perception on average but cause illusions when stimuli violate expectation. Intriguingly, tactile, auditory, and visual perception are all prone to length contraction illusions, characterized by the dramatic underestimation of the distance between punctate stimuli delivered in rapid succession; the origin of these illusions has been mysterious. We previously proposed that length contraction illusions occur because the brain interprets punctate stimulus sequences using Bayesian inference with a low-velocity expectation. A novel prediction of our Bayesian observer model is that length contraction should intensify if stimuli are made more difficult to localize. Here, we report a tactile psychophysical study that tested this prediction. Twenty humans compared two distances on the forearm: a fixed reference distance defined by two taps with 1-s temporal separation, and an adjustable comparison distance defined by two taps with temporal separation t ≤ 1 s. We observed significant length contraction: as t was decreased, participants perceived the two distances as equal only when the comparison distance was made progressively greater than the reference distance. Furthermore, the use of weaker taps significantly enhanced participants' length contraction. These findings confirm the model's predictions, supporting the view that the spatiotemporal percept is a best estimate resulting from a Bayesian inference process. Keywords: cutaneous rabbit illusion, Bayesian inference, sensory saltation, somatosensory psychophysics, spatial illusion, uncertainty.

The ability to resolve the orientation of edges is crucial to daily tactile and sensorimotor function, yet the means by which edge perception occurs is not well understood. Primate cortical area 3b neurons have diverse receptive field (RF) spatial structures that may participate in edge orientation perception. We evaluated five candidate RF models for macaque area 3b neurons previously recorded while an oriented bar contacted the monkey's fingertip. We used a Bayesian classifier to assign each neuron a best-fit RF structure. We generated predictions for human performance by implementing an ideal observer that optimally decoded stimulus-evoked spike counts in the model neurons. The ideal observer predicted a saturating reduction in bar orientation discrimination threshold with increasing bar length. We tested 24 humans on an automated, precision-controlled bar orientation discrimination task and observed performance consistent with that predicted. We next queried the ideal observer to discover the RF structure and number of cortical neurons that best matched each participant's performance. Human perception was matched with a median of 24 model neurons firing throughout a 1 s period. The ten lowest-performing participants were fit with RFs lacking inhibitory sidebands, whereas 12 of the 14 higher-performing participants were fit with RFs containing inhibitory sidebands. Participants whose discrimination improved as bar length increased to 10 mm were fit with longer RFs; those who performed well on the 2 mm bar, with narrower RFs. These results suggest plausible RF features and computational strategies underlying tactile spatial perception and may have implications for perceptual learning. Keywords: Bayesian inference, cortex, linear filter, somatosensory, spatial acuity.

Tactile acuity is known to decline with age in adults, possibly as the result of receptor loss, but less is understood about how tactile acuity changes during childhood. Previous research from our laboratory has shown that fingertip size influences tactile spatial acuity in young adults: those with larger fingers tend to have poorer acuity, possibly because mechanoreceptors are more sparsely distributed in larger fingers. We hypothesized that a similar relationship would hold among children. If so, children's tactile spatial acuity might be expected to worsen as their fingertips grow. However, concomitant CNS maturation might result in more efficient perceptual processing, counteracting the effect of fingertip growth on tactile acuity. To investigate, we conducted a cross-sectional study, testing 116 participants ranging in age from 6 to 16 years on a precision-controlled tactile grating orientation task. We measured each participant's grating orientation threshold on the dominant index finger, along with physical properties of the fingertip: surface area, volume, sweat-pore spacing, and temperature. We found that, as in adults, children with larger fingertips (at a given age) had significantly poorer acuity, yet paradoxically acuity did not worsen significantly with age. We propose that finger growth during development results in a gradual decline in innervation density as receptive fields reposition to cover an expanding skin surface. At the same time, central maturation presumably enhances perceptual processing.

Two-point discrimination is widely used to measure tactile spatial acuity. The validity of the two-point threshold as a spatial acuity measure rests on the assumption that two points can be distinguished from one only when the two points are sufficiently separated to evoke spatially distinguishable foci of neural activity. However, some previous research has challenged this view, suggesting instead that two-point task performance benefits from an unintended non-spatial cue, allowing spuriously good performance at small tip separations. We compared the traditional two-point task to an equally convenient alternative task in which participants attempt to discern the orientation (vertical or horizontal) of two points of contact. We used precision digital readout calipers to administer two-interval forced-choice versions of both tasks to 24 neurologically healthy adults, on the fingertip, finger base, palm, and forearm. We used Bayesian adaptive testing to estimate the participants' psychometric functions on the two tasks. Traditional two-point performance remained significantly above chance levels even at zero point separation. In contrast, two-point orientation discrimination approached chance as point separation approached zero, as expected for a valid measure of tactile spatial acuity. Traditional two-point performance was so inflated at small point separations that 75%-correct thresholds could be determined on all tested sites for fewer than half of participants. The 95%-correct thresholds on the two tasks were similar, and correlated with receptive field spacing. In keeping with previous critiques, we conclude that the traditional two-point task provides an unintended non-spatial cue, resulting in spuriously good performance at small spatial separations. Unlike two-point discrimination, two-point orientation discrimination rigorously measures tactile spatial acuity. We recommend the use of two-point orientation discrimination for neurological assessment. Keywords: tactile perception, somatosensory discrimination, reliability and validity, neurological examination, psychophysics, sensory testing, spatial acuity.

In touch as in vision, perceptual acuity improves with training to an extent that differs greatly across people: even individuals with similar initial acuity may undergo markedly different improvement with training. What accounts for this variability in perceptual learning? We hypothesized that a simple physical characteristic -- fingertip surface area -- might constrain tactile learning, because previous research suggests that larger fingers have more widely spaced mechanoreceptors. To test our hypothesis, we trained 10 human participants intensively on a tactile spatial acuity task. During four days, participants completed 1900 training trials (38 50-trial blocks) in which they discriminated the orientation of square-wave gratings pressed onto the stationary index or ring finger, with auditory feedback provided to signal correct and incorrect responses. We progressively increased task difficulty by shifting to thinner groove widths whenever participants achieved ≥ 90%-correct block performance. We took optical scans to measure surface area from the distal inter-phalangeal crease to the tip of the finger. Participants' acuity improved markedly on the trained finger, and to a lesser extent on the untrained finger. Crucially, we found that participants' tactile spatial acuity improved towards a theoretical optimum set by their finger size: participants with worse initial performance, relative to their finger size, improved more with training, and post-training performance correlated better than did pre-training performance with finger size. These results strongly support the hypothesis that tactile perceptual learning is limited by finger size. We suspect that analogous physical constraints on perceptual learning will be found in other sensory modalities.

Illusions provide a window into the brain's perceptual strategies. In certain illusions, an ostensibly task-irrelevant variable influences perception. For example, in touch as in audition and vision, the perceived distance between successive punctate stimuli reflects not only the actual distance but curiously the inter-stimulus time. Stimuli presented at different positions in rapid succession are drawn perceptually towards one another. This effect manifests in several illusions, among them the startling cutaneous rabbit, in which taps delivered to as few as two skin positions appear to hop progressively from one position to the next, landing in the process on intervening areas that were never stimulated. Here we provide an accessible step-by-step exposition of a Bayesian perceptual model that replicates the rabbit and related illusions. The Bayesian observer optimally joins uncertain estimates of spatial location with the expectation that stimuli tend to move slowly. We speculate that this expectation -- a Bayesian prior -- represents the statistics of naturally occurring stimuli, learned by humans through sensory experience. In its simplest form, the model contains a single free parameter, tau: a time constant for space perception. We show that the Bayesian observer incorporates both pre- and post-dictive inference. Directed spatial attention affects the prediction-postdiction balance, shifting the model's percept towards the attended location, as observed experimentally in humans. Applying the model to the perception of multi-tap sequences, we show that the low-speed prior fits perception better than an alternative, low-acceleration prior. We discuss the applicability of our model to related tactile, visual, and auditory illusions. To facilitate future model-driven experimental studies, we present a convenient freeware computer program that implements the Bayesian observer; we invite investigators to use this program to create their own testable predictions. Keywords: probabilistic inference, sensory saltation, motion illusions, tactile spatial attention, optimal percepts, Kalman smoothing, somatosensory spatiotemporal perception, sensory uncertainty.

Peterson and Salvagio (2008) demonstrated convexity context effects in figure-ground perception: subjects shown displays consisting of unfamiliar alternating convex and concave regions identified the convex regions as foreground objects progressively more frequently as the number of regions increased; this occurred only when the concave regions were homogeneously colored. The origins of these effects have been unclear. Here, we present a two-free-parameter Bayesian observer that replicates convexity context effects. The Bayesian observer incorporates two plausible expectations regarding three-dimensional scenes: 1) objects tend to be convex rather than concave, and 2) backgrounds tend (more than foreground objects) to be homogeneously colored. The Bayesian observer estimates the probability that a depicted scene is three-dimensional, and that the convex regions are figures. It responds stochastically by sampling from its posterior distributions. Like human observers, the Bayesian observer shows convexity context effects only for images with homogeneously colored concave regions. With optimal parameter settings, it performs similarly to the average human subject on the four display types tested. We propose that object convexity and background color homogeneity are environmental regularities exploited by human visual perception; vision achieves figure-ground perception by interpreting ambiguous images in light of these and other expected regularities in natural scenes. Keywords: figure-ground, scene segregation, object convexity, configural cue, Gestalt principles, natural scene statistics, Bayesian inference, computational model.

An important unresolved question in sensory neuroscience is whether, and if so with what time course, tactile perception is enhanced by visual deprivation. In three experiments involving 158 normally sighted human participants, we assessed whether tactile spatial acuity improves with short-term visual deprivation over periods ranging from under 10 to over 110 minutes. We used an automated, precisely controlled two-interval forced-choice grating orientation task to assess each participant's ability to discern the orientation of square-wave gratings pressed against the stationary index finger pad of the dominant hand. A two-down one-up staircase (Experiment 1) or a Bayesian adaptive procedure (Experiments 2 and 3) was used to determine the groove width of the grating whose orientation each participant could reliably discriminate. The experiments consistently showed that tactile grating orientation discrimination does not improve with short-term visual deprivation. In fact, we found that tactile performance degraded slightly but significantly upon a brief period of visual deprivation (Experiment 1) and did not improve over periods of up to 110 minutes of deprivation (Experiments 2 and 3). The results additionally showed that grating orientation discrimination tends to improve upon repeated testing, and confirmed that women significantly outperform men on the grating orientation task. We conclude that, contrary to two recent reports but consistent with an earlier literature, passive tactile spatial acuity is not enhanced by short-term visual deprivation. Our findings have important theoretical and practical implications. On the theoretical side, the findings set limits on the time course over which neural mechanisms such as crossmodal plasticity may operate to drive sensory changes; on the practical side, the findings suggest that researchers who compare tactile acuity of blind and sighted participants should not blindfold the sighted participants.

Tactile spatial acuity is enhanced in blindness, according to several studies, but the cause of this enhancement has been controversial. Two competing hypotheses are the tactile experience hypothesis (reliance on the sense of touch drives tactile-acuity enhancement) and the visual deprivation hypothesis (the absence of vision itself drives tactile-acuity enhancement). Here, we performed experiments to distinguish between these two hypotheses. We used force-controlled grating orientation tasks to compare the passive (finger stationary) tactile spatial acuity of 28 profoundly blind and 55 normally sighted humans on the index, middle, and ring fingers of each hand, and on the lips. The tactile experience hypothesis predicted that blind participants would outperform the sighted on the fingers, and that Braille reading would correlate with tactile acuity. The visual deprivation hypothesis predicted that blind participants would outperform the sighted on fingers and lips. Consistent with the tactile experience hypothesis, the blind significantly outperformed the sighted on all fingers, but not on the lips. Additionally, among blind participants, proficient Braille readers on their preferred reading index finger outperformed nonreaders. Finally, proficient Braille readers performed better with their preferred reading index finger than with the opposite index finger, and their acuity on the preferred reading finger correlated with their weekly reading time. These results clearly implicate reliance on the sense of touch as the trigger for tactile spatial acuity enhancement in the blind, and suggest the action of underlying experience-dependent neural mechanisms such as somatosensory and/or cross-modal cortical plasticity.

Braille reading is a demanding task that requires the identification of rapidly varying tactile patterns. During proficient reading, neighboring characters impact the fingertip at 100 ms intervals, and adjacent raised dots within a character at 50 ms intervals. Because the brain requires time to interpret afferent sensorineural activity, among other reasons, tactile stimuli separated by such short temporal intervals pose a challenge to perception. How, then, do proficient Braille readers successfully interpret inputs arising from their fingertips at such rapid rates? We hypothesized that somatosensory perceptual consolidation occurs more rapidly in proficient Braille readers. If so, Braille readers should outperform sighted participants on masking tasks, which demand rapid perceptual processing, but would not necessarily outperform the sighted on tests of simple vibrotactile sensitivity. To investigate, we conducted two-interval forced-choice vibrotactile detection, amplitude discrimination, and masking tasks on the index fingertips of 89 sighted and 57 profoundly blind humans. Sighted and blind participants had similar unmasked detection (25 ms target tap) and amplitude discrimination (compared with 100 µm reference tap) thresholds, but congenitally blind Braille readers, the fastest readers among the blind participants, exhibited significantly less masking than the sighted (masker, 50 Hz, 50 µm; target-masker delays, ±50 and ±100 ms). Indeed, Braille reading speed correlated significantly and specifically with masking task performance, and in particular with the backward masking decay time constant. We conclude that vibrotactile sensitivity is unchanged but that perceptual processing is accelerated in congenitally blind Braille readers. Supplemental Information (PDF).

We have observed that passive tactile spatial acuity, the ability to resolve the spatial structure of surfaces pressed upon the skin, differs subtly but consistently between the sexes, with women able to perceive finer surface detail than men. Eschewing complex central explanations, we hypothesized that this sex difference in somatosensory perception might result from simple physical differences between the fingers of women and men.  To investigate, we tested 50 women and 50 men on a tactile grating orientation task, and measured the surface area of the participants' index fingertips.  In subsets of participants, we additionally measured finger skin compliance and optically imaged the fingerprint microstructure to count sweat pores.  We show here that tactile perception improves with decreasing finger size, and that this correlation fully explains the better perception of women, who on average have smaller fingers than men. Indeed, when sex and finger size are both considered in statistical analyses, only finger size predicts tactile acuity. Thus, a man and a woman with fingers of equal size will, on average, enjoy equal tactile acuity.  We further show that sweat pores, and presumably the Merkel receptors beneath them, are packed more densely in smaller fingers. Supplemental information (PDF)

Although tactile spatial acuity tests are used in both neuroscience research and clinical assessment, few automated devices exist for delivering controlled spatially structured stimuli to the skin. Consequently, investigators often apply tactile stimuli manually. Manual stimulus application is time consuming, requires great care and concentration on the part of the investigator, and leaves many stimulus parameters uncontrolled. We describe here a computer-controlled tactile stimulus system, the Tactile Automated Passive-finger Stimulator (TAPS), that applies spatially structured stimuli to the skin, controlling for onset velocity, contact force, and contact duration. TAPS is a versatile, programmable system, capable of efficiently conducting a variety of psychophysical procedures. We describe the components of TAPS, and show how TAPS is used to administer a two-interval forced-choice tactile grating orientation test.

When brief stimuli contact the skin in rapid succession at two or more locations, perception strikingly shrinks the intervening distance, and expands the elapsed time, between consecutive events. The origins of these perceptual space-time distortions are unknown. Here I show that these illusory effects, which I term perceptual length contraction and time dilation, are emergent properties of a Bayesian observer model that incorporates prior expectation for speed. Rapidly moving stimuli violate expectation, provoking perceptual length contraction and time dilation. The Bayesian observer replicates the cutaneous rabbit illusion, the tau effect, the kappa effect, and other spatiotemporal illusions. Additionally, it shows realistic tactile temporal order judgment and spatial attention effects. The remarkable explanatory power of this simple model supports the hypothesis, first proposed by Helmholtz, that the brain biases perception in favor of expectation. Specifically, the results suggest that the brain automatically incorporates prior expectation for speed in order to overcome spatial and temporal imprecision inherent in the sensorineural signal.

We compared the abilities of blind and sighted humans to distinguish grooved from smooth surfaces pressed against the stationary index fingertip. Ranging in age from 20 to 72 years, 37 blind and 47 sighted subjects participated in an automated two-alternative forced-choice tactile grating detection task. The tactile acuity of blind and sighted subjects declined with age at equivalent rates (0.011-mm threshold increase per year), but the blind subjects were able to perceive significantly thinner grooves than were their sighted peers (the average difference between blind and sighted subjects of the same age and gender was 0.267 mm). The blind Braille readers performed no better than the blind nonreaders, and the congenitally blind subjects performed equivalently to those with adult-onset blindness. The superior tactile acuity of blind persons may result from the involvement of normally visually responsive cerebrocortical areas in tactile processing, as shown by functional imaging studies.

Functional imaging studies in blind subjects have shown tactile activation of cortical areas that normally subserve vision, but whether blind people have enhanced tactile acuity has long been controversial. We compared the passive tactile acuity of blind and sighted subjects on a fully automated grating orientation task and used multivariate Bayesian data analysis to determine predictors of acuity. Acuity was significantly superior in blind subjects, independently of the degree of childhood vision, light perception level, or Braille reading. Acuity was strongly dependent on the force of contact between the stimulus surface and the skin, declined with subject age, and was better in women than in men. Despite large intragroup variability, the difference between blind and sighted subjects was highly significant: the average blind subject had the acuity of an average sighted subject of the same gender but 23 years younger. The results suggest that crossmodal plasticity may underlie tactile acuity enhancement in blindness. Keywords: tactile acuity, crossmodal plasticity, blind, Braille, grating orientation, somatosensory psychophysics, sensory compensation.

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