Decision rules of listeners in spectral-shape discrimination with or without signal-frequency uncertainty

On averaging multiple estimates of decision weights within or across listeners

As a practical guide, a formula is provided for averaging multiple estimates of decision weights, for the purpose of improving the accuracy and reliability of the final estimate of decision weights. The averaging over multiple weight estimates can take place either within or across listeners.

Dynamic Reweighting of Auditory Modulation Filters

Sound waveforms convey information largely via amplitude modulations (AM). A large body of experimental evidence has provided support for a modulation (bandpass) filterbank. Details of this model have varied over time partly reflecting different experimental conditions and diverse datasets from distinct task strategies, contributing uncertainty to the bandwidth measurements and leaving important issues unresolved. We adopt here a solely data-driven measurement approach in which we first demonstrate how different models can be subsumed within a common 'cascade' framework, and then proceed to characterize the cascade via system identification analysis using a single stimulus/task specification and hence stable task rules largely unconstrained by any model or parameters. Observers were required to detect a brief change in level superimposed onto random level changes that served as AM noise; the relationship between trial-by-trial noisy fluctuations and corresponding human responses enables targeted identification of distinct cascade elements. The resulting measurements exhibit a dynamic complex picture in which human perception of auditory modulations appears adaptive in nature, evolving from an initial lowpass to bandpass modes (with broad tuning, Q∼1) following repeated stimulus exposure.

The Elementary Operations of Human Vision Are Not Reducible to Template-Matching

It is generally acknowledged that biological vision presents nonlinear characteristics, yet linear filtering accounts of visual processing are ubiquitous. The template-matching operation implemented by the linear-nonlinear cascade (linear filter followed by static nonlinearity) is the most widely adopted computational tool in systems neuroscience. This simple model achieves remarkable explanatory power while retaining analytical tractability, potentially extending its reach to a wide range of systems and levels in sensory processing. The extent of its applicability to human behaviour, however, remains unclear. Because sensory stimuli possess multiple attributes (e.g. position, orientation, size), the issue of applicability may be asked by considering each attribute one at a time in relation to a family of linear-nonlinear models, or by considering all attributes collectively in relation to a specified implementation of the linear-nonlinear cascade. We demonstrate that human visual processing can operate under conditions that are indistinguishable from linear-nonlinear transduction with respect to substantially different stimulus attributes of a uniquely specified target signal with associated behavioural task. However, no specific implementation of a linear-nonlinear cascade is able to account for the entire collection of results across attributes; a satisfactory account at this level requires the introduction of a small gain-control circuit, resulting in a model that no longer belongs to the linear-nonlinear family. Our results inform and constrain efforts at obtaining and interpreting comprehensive characterizations of the human sensory process by demonstrating its inescapably nonlinear nature, even under conditions that have been painstakingly fine-tuned to facilitate template-matching behaviour and to produce results that, at some level of inspection, do conform to linear filtering predictions. They also suggest that compliance with linear transduction may be the targeted outcome of carefully crafted nonlinear circuits, rather than default behaviour exhibited by basic components.

A general formula for computing maximum proportion correct scores in various psychophysical paradigms with arbitrary probability distributions of stimulus observations

Proportion correct (Pc) is a fundamental measure of task performance in psychophysics. The maximum Pc score that can be achieved by an optimal (maximum-likelihood) observer in a given task is of both theoretical and practical importance, because it sets an upper limit on human performance. Within the framework of signal detection theory, analytical solutions for computing the maximum Pc score have been established for several common experimental paradigms under the assumption of Gaussian additive internal noise. However, as the scope of applications of psychophysical signal detection theory expands, the need is growing for psychophysicists to compute maximum Pc scores for situations involving non-Gaussian (internal or stimulus-induced) noise. In this article, we provide a general formula for computing the maximum Pc in various psychophysical experimental paradigms for arbitrary probability distributions of sensory activity. Moreover, easy-to-use MATLAB code implementing the formula is provided. Practical applications of the formula are illustrated, and its accuracy is evaluated, for two paradigms and two types of probability distributions (uniform and Gaussian). The results demonstrate that Pc scores computed using the formula remain accurate even for continuous probability distributions, as long as the conversion from continuous probability density functions to discrete probability mass functions is supported by a sufficiently high sampling resolution. We hope that the exposition in this article, and the freely available MATLAB code, facilitates calculations of maximum performance for a wider range of experimental situations, as well as explorations of the impact of different assumptions concerning internal-noise distributions on maximum performance in psychophysical experiments.

Measuring decision weights in recognition experiments with multiple response alternatives: comparing the correlation and multinomial-logistic-regression methods

Psychophysical "reverse-correlation" methods allow researchers to gain insight into the perceptual representations and decision weighting strategies of individual subjects in perceptual tasks. Although these methods have gained momentum, until recently their development was limited to experiments involving only two response categories. Recently, two approaches for estimating decision weights in m-alternative experiments have been put forward. One approach extends the two-category correlation method to m > 2 alternatives; the second uses multinomial logistic regression (MLR). In this article, the relative merits of the two methods are discussed, and the issues of convergence and statistical efficiency of the methods are evaluated quantitatively using Monte Carlo simulations. The results indicate that, for a range of values of the number of trials, the estimated weighting patterns are closer to their asymptotic values for the correlation method than for the MLR method. Moreover, for the MLR method, weight estimates for different stimulus components can exhibit strong correlations, making the analysis and interpretation of measured weighting patterns less straightforward than for the correlation method. These and other advantages of the correlation method, which include computational simplicity and a close relationship to other well-established psychophysical reverse-correlation methods, make it an attractive tool to uncover decision strategies in m-alternative experiments.

Human pitch detectors are tuned on a fine scale, but are perceptually accessed on a coarse scale

Single neurons in auditory cortex display highly selective spectrotemporal properties: their receptive fields modulate over small fractions of an octave and integrate across temporal windows of 100-200 ms. We investigated how these characteristics impact auditory behavior. Human observers were asked to detect a specific sound frequency masked by broadband noise; we adopted an experimental design which required the engagement of frequency-selective mechanisms to perform above chance. We then applied psychophysical reverse correlation to derive spectrotemporal perceptual filters for the assigned task. We were able to expose signatures of neuronal-like spectrotemporal tuning on a scale of 1/10 octave and 50-100 ms, but detailed modeling of our results showed that observers were not able to rely on the explicit output of these channels. Instead, human observers pooled from a large bank of highly selective channels via a weighting envelope poorly tuned for frequency (on a scale of 1.5 octave) with sluggish temporal dynamics, followed by a highly nonlinear max-like operation. We conclude that human detection of specific frequencies embedded within complex sounds suffers from a high degree of intrinsic spectrotemporal uncertainty, resulting in low efficiency values (<1 %) for this perceptual ability. Signatures of the underlying neural circuitry can be exposed, but there does not appear to be a direct line for accessing individual neural channels on a fine scale.

Separating the contributions of primary and unwanted cues in psychophysical studies

A fundamental issue in the design and the interpretation of experimental studies of perception relates to the question of whether the participants in these experiments could perform the perceptual task assigned to them using another feature, or cue, than that intended by the experimenter. An approach frequently used by auditory- and visual-perception researchers to guard against this possibility involves applying random variations to the stimuli across presentations or trials so as to make the "unwanted" cue unreliable for the participants. However, the theoretical basis of this widespread practice is not well developed. In this article, we describe a 2-channel model based on general principles of psychophysical signal detection theory, which can be used to assess the respective contributions of the unwanted cue and of the primary cue to performance or thresholds measured in perceptual discrimination experiments involving stimulus randomization. Example applications of the model to the analysis of results obtained in representative studies from the auditory- and visual-perception literature are provided. In several cases, the results of the model-based analyses indicate that the effectiveness of the randomization procedure was less than originally assumed by the authors of these studies. These findings underscore the importance of quantifying the potential influence of unwanted cues on the results of psychophysical experiments, even when stimulus randomization is used.

Harmonic pitch: dependence on resolved partials, spectral edges, and combination tones

Perceptual weights were estimated in a pitch-comparison experiment to assess the relative influences of individual partial tones on listeners' pitch judgments. The stimuli were harmonic sounds (F0=200 Hz) with partials up to the 12th. Low-numbered partials were removed step-by-step, so that the remaining higher-numbered partials would have a better chance of showing any effect. The individual frequencies of the partials were perturbed randomly on each stimulus presentation, and weights were estimated as the correlation coefficients between the frequency perturbations and the listeners' responses. When the harmonic sounds contained all twelve partials, the listeners depended mostly on the low-numbered, resolved partials within the well-established dominance region. As the low-numbered partials were taken out of the dominance region, the listeners mostly listened to the lowest and highest partials at the spectral edges. For one listener, such an edge-listening strategy took the form of relying on nonlinear combination tones. Overall, there was no indication of any influence on pitch from unresolved partials, thus no evidence of contribution to pitch from temporal cues carried by this group of partials. The estimated patterns of weights were well described by the predictions of Goldstein's optimal-processor model. The predicted weights were inversely proportional to the amount of error for estimating the individual frequencies of the partials. The agreement between the predicted and measured weights suggests that, for harmonic sounds, partials whose frequencies are perceived with the best precision will likely have the greatest influence on perceived pitch.

Psychophysical reverse correlation with multiple response alternatives

Psychophysical reverse-correlation methods such as the "classification image" technique provide a unique tool to uncover the internal representations and decision strategies of individual participants in perceptual tasks. Over the past 30 years, these techniques have gained increasing popularity among both visual and auditory psychophysicists. However, thus far, principled applications of the psychophysical reverse-correlation approach have been almost exclusively limited to two-alternative decision (detection or discrimination) tasks. Whether and how reverse-correlation methods can be applied to uncover perceptual templates and decision strategies in situations involving more than just two response alternatives remain largely unclear. Here, the authors consider the problem of estimating perceptual templates and decision strategies in stimulus identification tasks with multiple response alternatives. They describe a modified correlational approach, which can be used to solve this problem. The approach is evaluated under a variety of simulated conditions, including different ratios of internal-to-external noise, different degrees of correlations between the sensory observations, and various statistical distributions of stimulus perturbations. The results indicate that the proposed approach is reasonably robust, suggesting that it could be used in future empirical studies.

The decision process in forward-masked intensity discrimination: evidence from molecular analyses

In a two-interval forced-choice intensity discrimination task presenting a fixed increment, the level of the forward masker in interval 1 and interval 2 was sampled independently from the same normal distribution on each trial. Mean and standard deviation of the distribution were varied. Correlational analyses of the trial-by-trial data revealed different decision strategies depending on the relation between mean masker level and standard level. If the two levels were identical, listeners tended to select the interval containing the higher-level masker, behaving like an energy detector at the output of a temporal window of integration. For mean masker level higher than the standard level, most listeners showed a negative correlation between the masker level in a given interval and the probability of selecting this interval, indicating a strategy of comparing the masker loudness and the target loudness in each of the two observation intervals, and voting for the interval where the loudness difference was smaller. Implications for models of forward-masked intensity discrimination and differences from decision strategies reported for forward-masked detection tasks [Jesteadt et al., (2005). "Effect of variability in level on forward masking and on increment detection," J. Acoust. Soc. Am. 118, 325-337] are discussed.

Low-level information and high-level perception: the case of speech in noise

Auditory information is processed in a fine-to-crude hierarchical scheme, from low-level acoustic information to high-level abstract representations, such as phonological labels. We now ask whether fine acoustic information, which is not retained at high levels, can still be used to extract speech from noise. Previous theories suggested either full availability of low-level information or availability that is limited by task difficulty. We propose a third alternative, based on the Reverse Hierarchy Theory (RHT), originally derived to describe the relations between the processing hierarchy and visual perception. RHT asserts that only the higher levels of the hierarchy are immediately available for perception. Direct access to low-level information requires specific conditions, and can be achieved only at the cost of concurrent comprehension. We tested the predictions of these three views in a series of experiments in which we measured the benefits from utilizing low-level binaural information for speech perception, and compared it to that predicted from a model of the early auditory system. Only auditory RHT could account for the full pattern of the results, suggesting that similar defaults and tradeoffs underlie the relations between hierarchical processing and perception in the visual and auditory modalities.

Variation in spectral-shape discrimination weighting functions at different stimulus levels and signal strengths

This study evaluated whether weights for spectral-shape discrimination depend on overall stimulus level and signal strength (the degree of spectral-shape change between two stimuli). Five listeners discriminated between standard stimuli that were the sum of six equal-amplitude tones and signal stimuli created by decreasing the amplitudes of three low-frequency components and increasing the amplitudes of three high-frequency components. Weighting functions were influenced by stimulus level in that the relative contribution of the low-frequency (decremented) components to the high-frequency (incremented) components decreased with increasing stimulus level. Although individual variability was present, a follow-up experiment suggested that the level dependence was due to greater reliance on high-frequency components rather than incremented components. Excitation-pattern analyses indicated that the level dependence is primarily, but not solely, driven by cochlear factors. In general, different signal strengths had no effect on the weighting functions (when normalized), but two of the five listeners showed variability in the shape of the weighting function across signal strengths. Results suggest that the effects of stimulus level on weighting functions and individual variability in the shapes of the weighting functions should be considered when comparing weighting functions across conditions and groups that might require different stimulus levels and signal strengths.

Molecular analysis of the effect of relative tone level on multitone pattern discrimination

Molecular psychophysics attempts to model the observer's response to stimuli as they vary from trial to trial. The approach has gained popularity in multitone pattern discrimination studies as a means of estimating the relative reliance or decision weight listeners give to different tones in the pattern. Various factors affecting decision weights have been examined, but one largely ignored is the relative level of tones in the pattern. In the present study listeners detected a level-increment in a sequence of 5, 100-ms, 2.0-kHz tone bursts alternating in level between 40 and 80 dB SPL. The level increment was made largest on the 40-dB tones, yet despite this all four highly-practiced listeners gave near exclusive weight to the 80-dB tones. The effect was the same when the tones were replaced by bursts of broadband Gaussian noise alternating in level. It was reduced only when the level differences were made <10 dB, and it was entirely reversed only when the low-level tones alternated with louder bursts of Gaussian noise. The results are discussed in terms of the effects of both sensory and perceptual factors on estimates of decision weights.

Estimates of effective frequency selectivity based on the detection of a tone added to complex maskers

In Experiment 1, the validity of parameters associated with the roex(p, r) auditory filter shape was examined for three different types of maskers: (a) A noise masker, (b) a random 12-tone masker whose frequencies varied on a burst-by-burst basis [multiple-burst different (MBD)], and (c) a random 12-tone masker whose frequencies were the same across bursts [multiple-burst same (MBS)]. First, the power spectrum model of masking was used to estimate auditory filter shapes for four observers. Second, the resulting auditory filter shapes were used in a computer simulation that provided an estimate of internal noise for each observer. Third, relative weights across frequency were estimated for each observer and each masker type. For the noise masker, these analyses provided predictions and relative weights that were consistent across the three analyses. For the MBD and MBS maskers, there was little consistency; neither the estimated internal noise nor the estimated relative weights reliably supported a single-filter model of detection. In Experiment 2, the time course for the detection of a tone added to an MBD masker was evaluated by estimating relative weights jointly in time and frequency. The relative weights at the signal frequency formed a rough inverse "U" across time.

A molecular description of profile analysis: decision weights and internal noise

Systematic inefficiencies and internal noise in a spectral profile discrimination task were investigated. Listeners detected a 1000-Hz sinusoid added in-phase to the central component of a complex consisting of 11 equal-intensity sinusoids. Parameters for a channel model that employs decision weights and internal noise were estimated with molecular psychophysical techniques. Maximum likelihood predictions of the model were generally within a few decibels of observed thresholds. The degree to which an assumption of ideal weights leads to overestimation of internal noise was also assessed.

A measure of internal noise based on sample discrimination

Internal noise is often inferred from the difference between observed performance and optimum performance in detection and discrimination tasks. It can be measured directly in some cases by observing the extent to which a change in external variability impacts performance. In the studies reported here, external variability was added to an intensity discrimination task by adding a Gaussian random variable with zero mean to the overall level presented in each interval of a two-interval forced-choice task. The standard deviation of the random variable was set to half the mean difference between the levels in the two intervals, resulting in d'(ideal) = 2. As the mean difference and the corresponding standard deviation of the random variable decreased in size, performance was increasingly limited by internal noise, permitting a reliable estimate of internal noise to be obtained. This can be viewed as a sample discrimination task, with one component per sample. In the first study, performance was measured using 2-kHz tones presented at an average level of 70 dB SPL, with mean differences between distributions ranging from 0.1 to 2.2 dB in steps of 0.3 dB. The distributions were either Gaussian in level or in power. Conditions with no external variability were used to obtain a psychometric function. In the second study, performance was measured using 2-kHz tones presented at average levels of 50 and 90 dB SPL, with mean differences ranging from 0.4 to 2.2 dB in steps of 0.6 dB. In both studies, the measure of internal noise was highly reliable and in good agreement with the intensity difference limen (DL) estimated from the psychometric function. Analyses suggest that this measure could be used to estimate the mean difference between the decision distributions as well as the amount of internal noise in cases where the mean difference between the distributions is unknown.

Spectral shape discrimination by hearing-impaired and normal-hearing listeners

The ability to discriminate between sounds with different spectral shapes was evaluated for normal-hearing and hearing-impaired listeners. Listeners discriminated between a standard stimulus and a signal stimulus in which half of the standard components were decreased in level and half were increased in level. In one condition, the standard stimulus was the sum of six equal-amplitude tones (equal-SPL), and in another the standard stimulus was the sum of six tones at equal sensation levels re: audiometric thresholds for individual subjects (equal-SL). Spectral weights were estimated in conditions where the amplitudes of the individual tones were perturbed slightly on every presentation. Sensitivity was similar in all conditions for normal-hearing and hearing-impaired listeners. The presence of perturbation and equal-SL components increased thresholds for both groups, but only small differences in weighting strategy were measured between the groups depending on whether the equal-SPL or equal-SL condition was tested. The average data suggest that normal-hearing listeners may rely more on the central components of the spectrum whereas hearing-impaired listeners may have been more likely to use the edges. However, individual weighting functions were quite variable, especially for the HI listeners, perhaps reflecting difficulty in processing changes in spectral shape due to hearing loss. Differences in weighting strategy without changes in sensitivity suggest that factors other than spectral weights, such as internal noise or difficulty encoding a reference stimulus, also may dominate performance.

Decision strategies of hearing-impaired listeners in spectral shape discrimination

The ability to discriminate between sounds with different spectral shapes was evaluated for normal-hearing and hearing-impaired listeners. Listeners detected a 920-Hz tone added in phase to a single component of a standard consisting of the sum of five tones spaced equally on a logarithmic frequency scale ranging from 200 to 4200 Hz. An overall level randomization of 10 dB was either present or absent. In one subset of conditions, the no-perturbation conditions, the standard stimulus was the sum of equal-amplitude tones. In the perturbation conditions, the amplitudes of the components within a stimulus were randomly altered on every presentation. For both perturbation and no-perturbation conditions, thresholds for the detection of the 920-Hz tone were measured to compare sensitivity to changes in spectral shape between normal-hearing and hearing-impaired listeners. To assess whether hearing-impaired listeners relied on different regions of the spectrum to discriminate between sounds, spectral weights were estimated from the perturbed standards by correlating the listener's responses with the level differences per component across two intervals of a two-alternative forced-choice task. Results showed that hearing-impaired and normal-hearing listeners had similar sensitivity to changes in spectral shape. On average, across-frequency correlation functions also were similar for both groups of listeners, suggesting that as long as all components are audible and well separated in frequency, hearing-impaired listeners can use information across frequency as well as normal-hearing listeners. Analysis of the individual data revealed, however, that normal-hearing listeners may be better able to adopt optimal weighting schemes. This conclusion is only tentative, as differences in internal noise may need to be considered to interpret the results obtained from weighting studies between normal-hearing and hearing-impaired listeners.

Effects of a limited class of nonlinearities on estimates of relative weights

Perturbation analyses have been applied in recent years to determine the relative contribution of individual stimulus components in detection and discrimination tasks. Responses to stimulus samples are compared to stimulus parameters to determine the details of the decision rule. Often, a linear model is assumed and it is of interest to determine the relative contribution of different stimulus elements to the decision. Here, biases in estimated relative weights are considered for the case where the decision variable is given by D = (sigma(alphaiXn(i))k)m and the stimulus components, the Xi, are normally distributed, of equal variance, and mutually independent. The alphai are the "true" combination weights, and n, k, and m are positive reals. The method used to estimate relative weights is the correlation coefficient between the Xi and the observer's responses. Estimates of relative alphai do not depend on m but may depend on the mean values of the Xi and the values of n and k (a dependence on the variance, sigmai2, holds even for linear transformations).

Revisiting spatial vision: toward a unifying model

We report contrast detection, contrast increment, contrast masking, orientation discrimination, and spatial frequency discrimination thresholds for spatially localized stimuli at 4 degrees of eccentricity. Our stimulus geometry emphasizes interactions among overlapping visual filters and differs from that used in previous threshold measurements, which also admits interactions among distant filters. We quantitatively account for all measurements by simulating a small population of overlapping visual filters interacting through divisive inhibition. We depart from previous models of this kind in the parameters of divisive inhibition and in using a statistically efficient decision stage based on Fisher information. The success of this unified account suggests that, contrary to Bowne [Vision Res. 30, 449 (1990)], spatial vision thresholds reflect a single level of processing, perhaps as early as primary visual cortex.