Calculation of signal detection theory measures

Signal detection theory (SDT) may be applied to any area of psychology in which two different types of stimuli must be discriminated. We describe several of these areas and the advantages that can be realized through the application of SDT. Three of the most popular tasks used to study discriminability are then discussed, together with the measures that SDT prescribes for quantifying performance in these tasks. Mathematical formulae for the measures are presented, as are methods for calculating the measures with lookup tables, computer software specifically developed for SDT applications, and general purpose computer software (including spreadsheets and statistical analysis software).

Uncertainty, neuromodulation, and attention

Uncertainty in various forms plagues our interactions with the environment. In a Bayesian statistical framework, optimal inference and prediction, based on unreliable observations in changing contexts, require the representation and manipulation of different forms of uncertainty. We propose that the neuromodulators acetylcholine and norepinephrine play a major role in the brain's implementation of these uncertainty computations. Acetylcholine signals expected uncertainty, coming from known unreliability of predictive cues within a context. Norepinephrine signals unexpected uncertainty, as when unsignaled context switches produce strongly unexpected observations. These uncertainty signals interact to enable optimal inference and learning in noisy and changeable environments. This formulation is consistent with a wealth of physiological, pharmacological, and behavioral data implicating acetylcholine and norepinephrine in specific aspects of a range of cognitive processes. Moreover, the model suggests a class of attentional cueing tasks that involve both neuromodulators and shows how their interactions may be part-antagonistic, part-synergistic.

The human amygdala: an evolved system for relevance detection

Evidence from pioneering animal research has suggested that the amygdala is involved in the processing of aversive stimuli, particularly fear-related information. Fear is central in the evolution of the mammalian brain: it is automatically and rapidly elicited by potentially dangerous and deadly events. The view that the amygdala shares the main characteristics of modular systems, e.g. domain specificity, automaticity, and cognitive impenetrability, has become popular in neuroscience. Because of its computational properties, it has been proposed to implement a rapid-response 'fear module'. In this article, we review recent patient and neuroimaging data of the human brain and argue that the fundamental criteria for the amygdala to be a modular system are not met. We propose a different computational view and suggest the notion of a specific involvement of the human amygdala in the appraisal of relevant events that include, but are not restricted to, fear-related stimuli. Considering the amygdala as a 'relevance detector' would integrate the 'fear module' hypothesis with the concept of an evolved neural system devoted to the processing of a broader category of biologically relevant stimuli. In primates, socially relevant events appear to have become, through evolution, the dominant elements of the amygdala's domain of specificity.

Reduced hedonic capacity in major depressive disorder: evidence from a probabilistic reward task

OBJECTIVE

Anhedonia, the lack of reactivity to pleasurable stimuli, is a cardinal feature of depression that has received renewed interest as a potential endophenotype of this debilitating disease. The goal of the present study was to test the hypothesis that individuals with major depression are characterized by blunted reward responsiveness, particularly when anhedonic symptoms are prominent.

METHODS

A probabilistic reward task rooted within signal-detection theory was utilized to objectively assess hedonic capacity in 23 unmedicated subjects meeting DSM-IV criteria for major depressive disorder (MDD) and 25 matched control subjects recruited from the community. Hedonic capacity was defined as reward responsiveness - i.e., the participants' propensity to modulate behavior as a function of reward.

RESULTS

Compared to controls, MDD subjects showed significantly reduced reward responsiveness. Trial-by-trial probability analyses revealed that MDD subjects, while responsive to delivery of single rewards, were impaired at integrating reinforcement history over time and expressing a response bias toward a more frequently rewarded cue in the absence of immediate reward. This selective impairment correlated with self-reported anhedonic symptoms, even after considering anxiety symptoms and general distress.

CONCLUSIONS

These findings indicate that MDD is characterized by an impaired tendency to modulate behavior as a function of prior reinforcements, and provides initial clues about which aspects of hedonic processing might be dysfunctional in depression.

Dual-process theory and signal-detection theory of recognition memory

Two influential models of recognition memory, the unequal-variance signal-detection model and a dual-process threshold/detection model, accurately describe the receiver operating characteristic, but only the latter model can provide estimates of recollection and familiarity. Such estimates often accord with those provided by the remember-know procedure, and both methods are now widely used in the neuroscience literature to identify the brain correlates of recollection and familiarity. However, in recent years, a substantial literature has accumulated directly contrasting the signal-detection model against the threshold/detection model, and that literature is almost unanimous in its endorsement of signal-detection theory. A dual-process version of signal-detection theory implies that individual recognition decisions are not process pure, and it suggests new ways to investigate the brain correlates of recognition memory.

Change detection

Five aspects of visual change detection are reviewed. The first concerns the concept of change itself, in particular the ways it differs from the related notions of motion and difference. The second involves the various methodological approaches that have been developed to study change detection; it is shown that under a variety of conditions observers are often unable to see large changes directly in their field of view. Next, it is argued that this "change blindness" indicates that focused attention is needed to detect change, and that this can help map out the nature of visual attention. The fourth aspect concerns how these results affect our understanding of visual perception-for example, the implication that a sparse, dynamic representation underlies much of our visual experience. Finally, a brief discussion is presented concerning the limits to our current understanding of change detection.

A direct brainstem–amygdala–cortical ‘alarm’ system for subliminal signals of fear

We examined whether consciously undetected fear signals engage a collateral brainstem pathway to the amygdala and prefrontal cortex in the intact human brain, using functional neuroimaging. 'Blindsight' lesion patients can respond to visual fear signals independently from conscious experience, suggesting that these signals reach the amygdala via a direct pathway that bypasses the primary visual cortex. Electrophysiological evidence points to concomitant involvement of prefrontal regions in automatic orienting to subliminal signals of fear, which may reflect innervation arising from brainstem arousal systems. To approximate blindsight in 22 healthy subjects, facial signals of fear were presented briefly (16.7 ms) and masked such that conscious detection was prevented. Results revealed that subliminal fear signals elicited activity in the brainstem region encompassing the superior colliculus and locus coeruleus, pulvinar and amygdala, and in fronto-temporal regions associated with orienting. These findings suggest that crude sensory input from the superior colliculo-pulvinar visual pathway to the amygdala may allow for sufficient appraisal of fear signals to innervate the locus coeruleus. The engagement of the locus coeruleus could explain the observation of diffuse fronto-temporal cortical activity, given its role in evoking collateral ascending noradrenergic efferents to the subcortical amygdala and prefrontal cortex. This network may represent an evolutionary adaptive neural 'alarm' system for rapid alerting to sources of threat, without the need for conscious appraisal.

A model of saccade generation based on parallel processing and competitive inhibition

During active vision, the eyes continually scan the visual environment using saccadic scanning movements. This target article presents an information processing model for the control of these movements, with some close parallels to established physiological processes in the oculomotor system. Two separate pathways are concerned with the spatial and the temporal programming of the movement. In the temporal pathway there is spatially distributed coding and the saccade target is selected from a "salience map." Both pathways descend through a hierarchy of levels, the lower ones operating automatically. Visual onsets have automatic access to the eye control system via the lower levels. Various centres in each pathway are interconnected via reciprocal inhibition. The model accounts for a number of well-established phenomena in target-elicited saccades: the gap effect, express saccades, the remote distractor effect, and the global effect. High-level control of the pathways in tasks such as visual search and reading is discussed; it operates through spatial selection and search selection, which generally combine in an automated way. The model is examined in relation to data from patients with unilateral neglect.

The spatial resolution of visual attention

Two tasks were used to evaluate the grain of visual attention, the minimum spacing at which attention can select individual items. First, observers performed a tracking task at many viewing distances. When the display subtended less than 1 degrees in size, tracking was no longer possible even though observers could resolve the items and their motions: The items were visible but could not be individuated one from the other. The limiting size for selection was roughly the same whether tracking one or three targets, suggesting that the resolution limit acts independently of the capacity limit of attention. Second, the closest spacing that still allowed individuation of single items in dense, static displays was examined. This critical spacing was about 50% coarser in the radial direction compared to the tangential direction and was coarser in the upper as opposed to the lower visual field. The results suggest that no more than about 60 items can be arrayed in the central 30 degrees of the visual field while still allowing attentional access to each individually. Our data show that selection has a coarse grain, much coarser than visual resolution. These measures of the resolution of attention are based solely on the selection of location and are not confounded with preattentive feature interactions that may contribute to measures from flanker and crowding tasks. The results suggest that the parietal area is the most likely locus of this selection mechanism and that it acts by pointing to the spatial coordinates (or cortical coordinates) of items of interest rather than by holding a representation of the items themselves.

Noise characteristics and prior expectations in human visual speed perception

Human visual speed perception is qualitatively consistent with a Bayesian observer that optimally combines noisy measurements with a prior preference for lower speeds. Quantitative validation of this model, however, is difficult because the precise noise characteristics and prior expectations are unknown. Here, we present an augmented observer model that accounts for the variability of subjective responses in a speed discrimination task. This allowed us to infer the shape of the prior probability as well as the internal noise characteristics directly from psychophysical data. For all subjects, we found that the fitted model provides an accurate description of the data across a wide range of stimulus parameters. The inferred prior distribution shows significantly heavier tails than a Gaussian, and the amplitude of the internal noise is approximately proportional to stimulus speed and depends inversely on stimulus contrast. The framework is general and should prove applicable to other experiments and perceptual modalities.

Two-stage dynamic signal detection: a theory of choice, decision time, and confidence

The 3 most often-used performance measures in the cognitive and decision sciences are choice, response or decision time, and confidence. We develop a random walk/diffusion theory-2-stage dynamic signal detection (2DSD) theory-that accounts for all 3 measures using a common underlying process. The model uses a drift diffusion process to account for choice and decision time. To estimate confidence, we assume that evidence continues to accumulate after the choice. Judges then interrupt the process to categorize the accumulated evidence into a confidence rating. The model explains all known interrelationships between the 3 indices of performance. Furthermore, the model also accounts for the distributions of each variable in both a perceptual and general knowledge task. The dynamic nature of the model also reveals the moderating effects of time pressure on the accuracy of choice and confidence. Finally, the model specifies the optimal solution for giving the fastest choice and confidence rating for a given level of choice and confidence accuracy. Judges are found to act in a manner consistent with the optimal solution when making confidence judgments.

Modeling auditory processing of amplitude modulation. I. Detection and masking with narrow-band carriers

This paper presents a quantitative model for describing data from modulation-detection and modulation-masking experiments, which extends the model of the "effective" signal processing of the auditory system described in Dau et al. [J. Acoust. Soc. Am. 99, 3615-3622 (1996)]. The new element in the present model is a modulation filterbank, which exhibits two domains with different scaling. In the range 0-10 Hz, the modulation filters have a constant bandwidth of 5 Hz. Between 10 Hz and 1000 Hz a logarithmic scaling with a constant Q value of 2 was assumed. To preclude spectral effects in temporal processing, measurements and corresponding simulations were performed with stochastic narrow-band noise carriers at a high center frequency (5 kHz). For conditions in which the modulation rate (fmod) was smaller than half the bandwidth of the carrier (delta f), the model accounts for the low-pass characteristic in the threshold functions [e.g., Viemeister, J. Acoust. Soc. Am. 66, 1364-1380 (1979)]. In conditions with fmod > delta f/2, the model can account for the high-pass characteristic in the threshold function. In a further experiment, a classical masking paradigm for investigating frequency selectivity was adopted and translated to the modulation-frequency domain. Masked thresholds for sinusoidal test modulation in the presence of a competing modulation masker were measured and simulated as a function of the test modulation rate. In all cases, the model describes the experimental data to within a few dB. It is proposed that the typical low-pass characteristic of the temporal modulation transfer function observed with wide-band noise carriers is not due to "sluggishness" in the auditory system, but can instead be understood in terms of the interaction between modulation filters and the inherent fluctuations in the carrier.

Vision as Bayesian inference: analysis by synthesis?

We argue that the study of human vision should be aimed at determining how humans perform natural tasks with natural images. Attempts to understand the phenomenology of vision from artificial stimuli, although worthwhile as a starting point, can lead to faulty generalizations about visual systems, because of the enormous complexity of natural images. Dealing with this complexity is daunting, but Bayesian inference on structured probability distributions offers the ability to design theories of vision that can deal with the complexity of natural images, and that use 'analysis by synthesis' strategies with intriguing similarities to the brain. We examine these strategies using recent examples from computer vision, and outline some important implications for cognitive science.

Recollection and familiarity: examining controversial assumptions and new directions

It is well accepted that recognition memory reflects the contribution of two separable memory retrieval processes, namely recollection and familiarity. However, fundamental questions remain regarding the functional nature and neural substrates of these processes. In this article, we describe a simple quantitative model of recognition memory (i.e., the dual-process signal detection model) that has been useful in integrating findings from a broad range of cognitive studies, and that is now being applied in a growing number of neuroscientific investigations of memory. The model makes several strong assumptions about the behavioral nature and neural substrates of recollection and familiarity. A review of the literature indicates that these assumptions are generally well supported, but that there are clear boundary conditions in which these assumptions break down. We argue that these findings provide important insights into the operation of the processes underlying recognition. Finally, we consider how the dual-process approach relates to recent neuroanatomical and computational models and how it might be integrated with recent findings concerning the role of medial temporal lobe regions in other cognitive functions such as novelty detection, perception, implicit memory and short-term memory.

Inhibitory control in mind and brain: An interactive race model of countermanding saccades

The stop-signal task has been used to study normal cognitive control and clinical dysfunction. Its utility is derived from a race model that accounts for performance and provides an estimate of the time it takes to stop a movement. This model posits a race between go and stop processes with stochastically independent finish times. However, neurophysiological studies demonstrate that the neural correlates of the go and stop processes produce movements through a network of interacting neurons. The juxtaposition of the computational model with the neural data exposes a paradox-how can a network of interacting units produce behavior that appears to be the outcome of an independent race? The authors report how a simple, competitive network can solve this paradox and provide an account of what is measured by stop-signal reaction time.

Is vision continuous with cognition? The case for cognitive impenetrability of visual perception

Although the study of visual perception has made more progress in the past 40 years than any other area of cognitive science, there remain major disagreements as to how closely vision is tied to cognition. This target article sets out some of the arguments for both sides (arguments from computer vision, neuroscience, psychophysics, perceptual learning, and other areas of vision science) and defends the position that an important part of visual perception, corresponding to what some people have called early vision, is prohibited from accessing relevant expectations, knowledge, and utilities in determining the function it computes--in other words, it is cognitively impenetrable. That part of vision is complex and involves top-down interactions that are internal to the early vision system. Its function is to provide a structured representation of the 3-D surfaces of objects sufficient to serve as an index into memory, with somewhat different outputs being made available to other systems such as those dealing with motor control. The paper also addresses certain conceptual and methodological issues raised by this claim, such as whether signal detection theory and event-related potentials can be used to assess cognitive penetration of vision. A distinction is made among several stages in visual processing, including, in addition to the inflexible early-vision stage, a pre-perceptual attention-allocation stage and a post-perceptual evaluation, selection, and inference stage, which accesses long-term memory. These two stages provide the primary ways in which cognition can affect the outcome of visual perception. The paper discusses arguments from computer vision and psychology showing that vision is "intelligent" and involves elements of "problem solving." The cases of apparently intelligent interpretation sometimes cited in support of this claim do not show cognitive penetration; rather, they show that certain natural constraints on interpretation, concerned primarily with optical and geometrical properties of the world, have been compiled into the visual system. The paper also examines a number of examples where instructions and "hints" are alleged to affect what is seen. In each case it is concluded that the evidence is more readily assimilated to the view that when cognitive effects are found, they have a locus outside early vision, in such processes as the allocation of focal attention and the identification of the stimulus.

Schizophrenic deficits in the processing of context. A test of a theoretical model

BACKGROUND

Schizophrenic patients show various deficits in cognitive functions that have been difficult to understand in terms of a common unifying hypothesis. Previously described neural network models of cognitive tasks suggest that several schizophrenic performance deficits may be related to a single function-an impairment in maintaining contextual information over time and in using that information to inhibit inappropriate responses.

METHODS

We tested first-episode schizophrenic patients and patients later in the course of their illness on a new variant of the Continuous Performance Test designed specifically to elicit deficits in the processing of contextual information.

RESULTS

Unmedicated schizophrenic patients showed a deterioration of their signal detection performance that followed the pattern predicted by the context hypothesis, ie, they responded inappropriately when correct responding required the maintenance of context information over time to inhibit the expression of a habitual response. This deficit correlated with positive symptoms. The results also suggested that the deficit may be worse in unmedicated patients who have had a longer course of illness. Medicated patients showed a more diffuse performance deficit.

CONCLUSIONS

These results support the view that a single deficit in the processing of context information may underlie various cognitive impairments observed in schizophrenia. They also suggest that such an impairment is associated with positive rather than negative symptoms, and that it may worsen with the course of the illness as in the kraepelinian view of schizophrenia.

Is there a geometric module for spatial orientation? Squaring theory and evidence

There is evidence, beginning with Cheng (1986), that mobile animals may use the geometry of surrounding areas to reorient following disorientation. Gallistel (1990) proposed that geometry is used to compute the major or minor axes of space and suggested that such information might form an encapsulated cognitive module. Research reviewed here, conducted on a wide variety of species since the initial discovery of the use of geometry and the formulation of the modularity claim, has supported some aspects of the approach, while casting doubt on others. Three possible processing models are presented that vary in the way in which (and the extent to which) they instantiate the modularity claim. The extant data do not permit us to discriminate among them. We propose a modified concept of modularity for which an empirical program of research is more tractable.

An EZ-diffusion model for response time and accuracy

The EZ-diffusion model for two-choice response time tasks takes mean response time, the variance of response time, and response accuracy as inputs. The model transforms these data via three simple equations to produce unique values for the quality of information, response conservativeness, and nondecision time. This transformation of observed data in terms of unobserved variables addresses the speed-accuracy trade-off and allows an unambiguous quantification of performance differences in two-choice response time tasks. The EZ-diffusion model can be applied to data-sparse situations to facilitate individual subject analysis. We studied the performance of the EZ-diffusion model in terms of parameter recovery and robustness against misspecification by using Monte Carlo simulations. The EZ model was also applied to a real-world data set.

How the neurocircuitry and genetics of fear inhibition may inform our understanding of PTSD

Exposure to traumatic events that produce extreme fear and horror is all too common in both military and civilian populations, but not all individuals develop posttraumatic stress disorder (PTSD) as a result of the exposure. What mediates risk and resilience in the development of PTSD and other stress-related psychopathology is of paramount importance to our further understanding of trauma-related psychopathology as well as the development of new treatment approaches. Biological factors, such as genotype and neurobiology, interact with environmental factors, such as childhood background and trauma load, to affect vulnerability and resilience in the aftermath of trauma exposure. One of the core symptoms of PTSD is the inability to control fear, which has led some investigators and clinicians to conceptualize PTSD as a disorder of fear or, more importantly, its inhibition. This review focuses on translational methods that have been used to examine fear conditioning and inhibition of fear in PTSD and summarizes genetic and neurobiological factors related to fear inhibition. The authors also discuss different pharmacological approaches that enhance fear inhibition and may improve treatment outcomes for patients with PTSD.

Remember-Know: A Matter of Confidence

This article critically examines the view that the signal detection theory (SDT) interpretation of the remember-know (RK) paradigm has been ruled out by the evidence. The author evaluates 5 empirical arguments against a database of 72 studies reporting RK data under 400 different conditions. These arguments concern (a). the functional independence of remember and know rates, (b). the invariance of estimates of sensitivity, (c). the relationship between remember rates and overall hit and false alarm rates, (d). the relationship between RK responses and confidence judgments, and (e). dissociations between remember and overall hit rates. Each of these arguments is shown to be flawed, and despite being open to refutation, the SDT interpretation is consistent with existing data from both the RK and remember-know-guess paradigms and offers a basis for further theoretical development.

Functional anatomy of intrinsic alertness: evidence for a fronto-parietal-thalamic-brainstem network in the right hemisphere

Alertness, the most basic intensity aspect of attention, probably is a prerequisite for the more complex and capacity demanding domains of attention selectivity. Behaviorally, intrinsic alertness represents the internal (cognitive) control of wakefulness and arousal; typical tasks to assess optimal levels of intrinsic alertness are simple reaction time measurements without preceding warning stimuli. Up until now only parts of the cerebral network subserving alertness have been revealed in animal, lesion, and functional imaging studies. Here, in a 15O-butanol PET activation study in 15 right-handed young healthy male volunteers for this basic attention function we found an extended right hemisphere network including frontal (anterior cingulate-dorsolateral cortical)-inferior parietal-thalamic (pulvinar and possibly the reticular nucleus) and brainstem (ponto-mesencephalic tegmentum, possibly involving the locus coeruleus) structures, when subjects waited for and rapidly responded to a centrally presented white dot by pressing a response key with the right-hand thumb.

The benefit of binaural hearing in a cocktail party: effect of location and type of interferer

The "cocktail party problem" was studied using virtual stimuli whose spatial locations were generated using anechoic head-related impulse responses from the AUDIS database [Blauert et al., J. Acoust. Soc. Am. 103, 3082 (1998)]. Speech reception thresholds (SRTs) were measured for Harvard IEEE sentences presented from the front in the presence of one, two, or three interfering sources. Four types of interferer were used: (1) other sentences spoken by the same talker, (2) time-reversed sentences of the same talker, (3) speech-spectrum shaped noise, and (4) speech-spectrum shaped noise, modulated by the temporal envelope of the sentences. Each interferer was matched to the spectrum of the target talker. Interferers were placed in several spatial configurations, either coincident with or separated from the target. Binaural advantage was derived by subtracting SRTs from listening with the "better monaural ear" from those for binaural listening. For a single interferer, there was a binaural advantage of 2-4 dB for all interferer types. For two or three interferers, the advantage was 2-4 dB for noise and speech-modulated noise, and 6-7 dB for speech and time-reversed speech. These data suggest that the benefit of binaural hearing for speech intelligibility is especially pronounced when there are multiple voiced interferers at different locations from the target, regardless of spatial configuration; measurements with fewer or with other types of interferers can underestimate this benefit.

Top-down search strategies cannot override attentional capture

Bacon and Egeth (1994) have claimed that color singletons do not interfere with search for a shape singleton when, instead of using a singleton detection mode, participants are forced to use a feature search mode. Bacon and Egeth induced a feature search mode by adding different shape singletons to the display so that observers could not simply respond to uniqueness to find the target. We did exactly the same but used larger display sizes to ensure that the target and distractor singletons remained salient. The results show that under these conditions, an irrelevant color singleton interferes with search for a shape singleton. It is argued that the notion of differential search modes may be incorrect and that the results can be explained in terms of bottom-up salience signals.

Norms for word lists that create false memories

Roediger and McDermott (1995) induced false recall and false recognition for words that were not presented in lists. They had subjects study 24 lists of 15 words that were associates of a common word (called the critical target or critical lure) that was not presented in the list. False recall and false recognition of the critical target occurred frequently in response to these lists. The purpose of the current work was to provide a set of normative data for the lists Roediger and McDermott used and for 12 others developed more recently. We tested false recall and false recognition for critical targets from 36 lists. Despite the fact that all lists were constructed to produce false remembering, the diversity in their effectiveness was large--60% or more of subjects falsely recalled window and sleep following the appropriate lists, and false recognition for these items was greater than 80%. However, the list generated from king led to 10% false recall and 27% false recognition. Possible reasons for these wide differences in effectiveness of the lists are discussed. These norms serve as a useful benchmark for designing experiments about false recall and false recognition in this paradigm.