Analyzing thresholds and efficiency with hierarchical Bayesian logistic regression

Bayesian hierarchical models and prior elicitation for fitting psychometric functions

Our previous articles demonstrated how to analyze psychophysical data from a group of participants using generalized linear mixed models (GLMM) and two-level methods. The aim of this article is to revisit hierarchical models in a Bayesian framework. Bayesian models have been previously discussed for the analysis of psychometric functions although this approach is still seldom applied. The main advantage of using Bayesian models is that if the prior is informative, the uncertainty of the parameters is reduced through the combination of prior knowledge and the experimental data. Here, we evaluate uncertainties between and within participants through posterior distributions. To demonstrate the Bayesian approach, we re-analyzed data from two of our previous studies on the tactile discrimination of speed. We considered different methods to include a priori knowledge in the prior distribution, not only from the literature but also from previous experiments. A special type of Bayesian model, the power prior distribution, allowed us to modulate the weight of the prior, constructed from a first set of data, and use it to fit a second one. Bayesian models estimated the probability distributions of the parameters of interest that convey information about the effects of the experimental variables, their uncertainty, and the reliability of individual participants. We implemented these models using the software Just Another Gibbs Sampler (JAGS) that we interfaced with R with the package rjags. The Bayesian hierarchical model will provide a promising and powerful method for the analysis of psychometric functions in psychophysical experiments.

Detection and discrimination of electrical stimuli from an upper limb cuff electrode inM. Mulatta

Objective.Peripheral nerve interfaces seek to restore nervous system function through electrical stimulation of peripheral nerves. In clinical use, these devices should function reliably for years or decades. In this study, we assessed evoked sensations from multi-channel cuff electrode stimulation in macaque monkeys up to 711 d post-implantation.Approach.Three trained macaque monkeys received multi-channel cuff electrode implants at the median or ulnar nerves in the upper arm. Electrical stimuli from the cuff interfaces evoked sensations, which we measured via standard psychophysical tasks. We adjusted pulse amplitude or pulse width for each block with various electrode channel configurations to examine the effects of stimulus parameterization on sensation. We measured detection thresholds and just-noticeable differences (JNDs) at irregular, near-daily intervals for several months using Bayesian inferencing from trial data. We examined data trends using classical models such as Weber's Law and the strength-duration relationship using linear regression.Main results.Detection thresholds were similar between blocks with pulse width modulation and blocks with pulse amplitude modulation when represented as charge per pulse, the product of the amplitude and the pulse width. Conversely, Weber fractions-calculated as the slope of the regression between JND charge values and reference stimulus charge-were significantly different between pulse width and pulse amplitude modulation blocks for the discrimination task.Significance.Weber fractions were lower in blocks with amplitude modulation than in blocks with pulse width modulation, suggesting that pulse amplitude modulation allows finer resolution of sensory encoding above threshold. Consequently, amplitude modulation may enable a greater dynamic range for sensory perception with neuroprosthetic devices.

Run and hide: visual performance in a brittle star

Spatial vision was recently reported in a brittle star, Ophiomastix wendtii, which lacks discrete eyes, but little is known about its visual ecology. Our aim was to better characterize the vision and visual ecology of this unusual visual system. We tested animal orientation relative to vertical bar stimuli at a range of angular widths and contrasts, to identify limits of angular and contrast detection. We also presented dynamic shadow stimuli, either looming towards or passing the animal overhead, to test for potential defensive responses. Finally, we presented animals lacking a single arm with a vertical bar stimulus known to elicit a response in intact animals. We found that O. wendtii orients to large (≥50 deg), high-contrast vertical bar stimuli, consistent with a shelter-seeking role and with photoreceptor acceptance angles estimated from morphology. We calculate poor optical sensitivity for individual photoreceptors, and predict dramatic oversampling for photoreceptor arrays. We also report responses to dark stimuli moving against a bright background - this is the first report of responses to moving stimuli in brittle stars and suggests additional defensive uses for vision in echinoderms. Finally, we found that animals missing a single arm orient less well to static stimuli, which requires further investigation.

Chicken colour discrimination depends on background colour

How well can a bird discriminate between two red berries on a green background? The absolute threshold of colour discrimination is set by photoreceptor noise, but animals do not perform at this threshold; their performance can depend on additional factors. In humans and zebra finches, discrimination thresholds for colour stimuli depend on background colour, and thus the adaptive state of the visual system. We have tested how well chickens can discriminate shades of orange or green presented on orange or green backgrounds. Chickens discriminated slightly smaller colour differences between two stimuli presented on a similarly coloured background, compared with a background of very different colour. The slope of the psychometric function was steeper when stimulus and background colours were similar but shallower when they differed markedly, indicating that background colour affects the certainty with which the animals discriminate the colours. The effect we find for chickens is smaller than that shown for zebra finches. We modelled the response to stimuli using Bayesian and maximum likelihood estimation and implemented the psychometric function to estimate the effect size. We found that the result is independent of the psychophysical method used to evaluate the effect of experimental conditions on choice performance.

Visual acuity and egg spatial chromatic contrast predict egg rejection behavior of American robins

Color and spatial vision is critical for recognition and discrimination tasks affecting fitness, including finding food and mates, and recognizing offspring. For example, as a counter defense to avoid the cost of raising the unrelated offspring of obligate interspecific avian brood parasites, many host species routinely view, recognize and remove the foreign egg(s) from their nests. Recent research has shown that host species visually attend to both chromatic and spatial pattern features of eggs; yet how hosts simultaneously integrate these features together when recognizing eggs remains an open question. Here, we tested egg rejection responses of American robins (Turdus migratorius) using a range of 3D-printed model eggs covered with blue and yellow checkered patterns differing in relative square sizes. We predicted that robins would reject a model egg if they could visually resolve the blue and yellow squares as separate features, or accept it if the squares blended together and appeared similar in color to the natural blue-green color of robin eggs as perceived by the avian visual system. As predicted, the probability of robins rejecting a model egg increased with greater sizes of its blue and yellow squares. Our results suggest that chromatic visual acuity and viewing distance have the potential to limit the ability of a bird to recognize a foreign egg in its nest, thus providing a limitation to host egg recognition that obligate interspecific avian brood parasites may exploit.

Auditory and auditory-visual frequency-band importance functions for consonant recognition

The relative importance of individual frequency regions for speech intelligibility has been firmly established for broadband auditory-only (AO) conditions. Yet, speech communication often takes place face-to-face. This study tested the hypothesis that under auditory-visual (AV) conditions, where visual information is redundant with high-frequency auditory cues, lower frequency regions will increase in relative importance compared to AO conditions. Frequency band-importance functions for consonants were measured for eight hearing-impaired and four normal-hearing listeners. Speech was filtered into four 1/3-octave bands each separated by an octave to minimize energetic masking. On each trial, the signal-to-noise ratio (SNR) in each band was selected randomly from a 10-dB range. AO and AV band-importance functions were estimated using three logistic-regression analyses: a primary model relating performance to the four independent SNRs; a control model that also included band-interaction terms; and a different set of four control models, each examining one band at a time. For both listener groups, the relative importance of the low-frequency bands increased under AV conditions, consistent with earlier studies using isolated speech bands. All three analyses showed similar results, indicating the absence of cross-band interactions. These results suggest that accurate prediction of AV speech intelligibility may require different frequency-importance functions than for AO conditions.

A millipede compound eye mediating low-resolution vision

Millipedes are a species-rich and ancient arthropod clade which typically bear a pair of lateral compound eyes with a small number of large facets. To understand the visual tasks that underlie the evolution of millipede eyes, their spatial resolving performance is of key importance. We here investigate the spatial resolution of the millipede Cylindroiulus punctatus using behavioural assays. Individual animals were placed in the centre of a cylindrical arena under bright downwelling light, with dark stimuli of varying angular dimensions placed on the arena wall. We used continuous isoluminant stimuli based on a difference of Gaussians signal to test for orientation to the dark target via object taxis. Headings of individual animals were tracked in relation to the stimuli to determine whether the animals oriented towards the stimulus. We implemented a multilevel logistic regression model to identify the arc width of the stimulus that animals could resolve. We then modelled the angular sensitivity needed to identify this. We also related the visual performance to the 3D anatomy of the eye. We found that C. punctatus can resolve a stimulus of 56° period (sufficient to detect a 20° dark target). Assuming a contrast threshold of 10%, this requires a receptor acceptance angle of 72° or narrower. Spatial resolving power this low would only suffice for the simplest visual tasks, such as shelter-seeking.

Orienting to polarized light at night - matching lunar skylight to performance in a nocturnal beetle

For polarized light to inform behaviour, the typical range of degrees of polarization observable in the animal's natural environment must be above the threshold for detection and interpretation. Here, we present the first investigation of the degree of linear polarization threshold for orientation behaviour in a nocturnal species, with specific reference to the range of degrees of polarization measured in the night sky. An effect of lunar phase on the degree of polarization of skylight was found, with smaller illuminated fractions of the moon's surface corresponding to lower degrees of polarization in the night sky. We found that the South African dung beetle Escarabaeus satyrus can orient to polarized light for a range of degrees of polarization similar to that observed in diurnal insects, reaching a lower threshold between 0.04 and 0.32, possibly as low as 0.11. For degrees of polarization lower than 0.23, as measured on a crescent moon night, orientation performance was considerably weaker than that observed for completely linearly polarized stimuli, but was nonetheless stronger than in the absence of polarized light.