Affective Bias Through the Lens of Signal Detection Theory Abstract

Affective bias through the lens of Signal Detection Theory

Shannon M. Locke1 & Oliver J. Robinson2,3*

1 Laboratoire des Syst`emesPerceptifs, D´epartement d’Etudes´ Cognitives, Ecole´ Normale

Sup´erieure,PSL University, CNRS, 75005 Paris, France

2 Institute of Cognitive Neuroscience, University College London, London, UK

3 Research Department of Clinical, Educational and Health Psychology, University College

London, London, UK

*Corresponding author: [email protected]

Abstract 1

Affective bias - a propensity to focus on negative information at the expense of positive in- 2 formation - is a core feature of many mental health problems. However, it can be caused by 3 wide range of possible underlying cognitive mechanisms. Here we illustrate this by focusing on 4 one particular behavioural signature of affective bias - increased tendency of anxious/depressed 5 individuals to predict lower rewards - in the context of the Signal Detection Theory (SDT) 6 modelling framework. Specifically, we apply this framework to a tone-discrimination task (Ayl- 7 ward et al., 2019a), and argue that the same behavioural signature (differential placement of 8 the ’decision criterion’ between healthy controls and individuals with mood/anxiety disorders) 9 might be driven by multiple SDT processes. Building on this theoretical foundation, we propose 10

five experiments to test five hypothetical sources of this affective bias: beliefs about prior proba- 11 bilities, beliefs about performance, subjective value of reward, learning differences, and need for 12 accuracy differences. We argue that greater precision about the mechanisms driving affective 13 bias may eventually enable us to better understand and treat mood and anxiety disorders. 14

Author Summary 15

We apply the Signal Detection Theory framework to understanding the mechanisms behind 16 affective bias in individuals with mood and anxiety disorders. Based on previous explanations 17 of perceptual bias in healthy human observers, we generate five testable hypotheses about the 18 causes of affective bias in clinical populations. 19

1 Keywords: affective bias, mood disorders, anxiety disorders, signal detection theory, decision- 20 making 21

Affective bias 22

Affective bias is a broad term that encompasses cognitive or behavioural bias towards (or away 23 from) rewards or punishments. Such bias forms an important part of the aetiology of a wide 24 range of mental health problems (Roiser et al., 2011). Mood and anxiety disorders, for instance, 25 are thought to involve substantial ‘negative’ affective biases, whereby an individual’s cognitive 26 processes (e.g. perception, attention or learning) are biased towards punishing stimuli and 27 away from rewarding stimuli (Robinson and Chase, 2017; Pizzagalli et al., 2005; Halahakoon 28 et al., 2020). This bias promotes negative mood (e.g. if you are biased to learn and remember 29 negative things that happen to you, it makes your overall mood more negative), which in turn 30 further promotes the underlying negative bias, and can eventually lead to a pathological state. 31

These biases therefore form a key part of the diagnosis of mood disorders; where bias away from 32 reward, for example, is encompassed within the diagnostic criterion of “diminished interest or 33 pleasure” (American Psychiatric Association, 2013). 34

Whilst the presence and importance of such biases in mental health has been established 35 for many decades (Beck, 1964), their underlying causes and mechanisms are far from clear 36

(Robinson and Chase, 2017). And whilst some interventions, most prominently Cognitive Be- 37 havioural Therapy, are able to successfully target affective biases without a clear understanding 38 of how these biases emerge (Beck, 1991), a large number of individuals fail to respond to any 39 of our current treatments (Aylward et al., 2019a). Development of new treatments has also, 40 unfortunately, stalled in part due a large number of failed clinical trials over the last decades 41

(Choi et al., 2016; Scannell and Bosley, 2016). At least one reason for this is that treatments 42 are largely targeted at endpoints (e.g. depressed mood) and not directly at the neurocognitive 43 mechanisms that drive these symptoms, such as affective bias. A clearer and more mechanis- 44 tic account of how affective bias emerges may therefore faciliate the development of improved 45 treatments that target the causes of mental ill health at their source. 46

One way to achieve this understanding is to comprehensively break-down all possible under- 47 lying causes of a given behavioural bias and then systematically narrow down the root cause. 48

In this paper, we therefore take recent example of a translational perceptual task that is sensi- 49

2 tive to affective bias in individuals with mood and anxiety disorders (as well as animal models, 50

Aylward et al., 2019a) and explore the multiple potential sources of this bias from a Signal De- 51 tection Theory perspective. We highlight how this perspective can force us to be more precise 52 about the nature of affective bias and ultimately enable us to narrow down the underlying cause 53 of this bias. 54

Optimal decision making 55

Optimal decision making involves the the selection of the best possible choice taking into account 56 the choice context (Berger, 1980). Choice contexts typically have two salient features that need 57 to be considered: the prior probability of possible states of the world and the rewards or losses 58 for selecting or not selecting each choice, often referred to as payoffs. For example, when a 59 doctor is deciding on a cancer diagnosis for a patient, they may consider other aspects of the 60 patient’s history to gauge the prior probability of developing cancer (e.g., smoker/non-smoker) 61 in addition to the medical results they have just obtained. They should also consider the payoffs 62 of different choice and outcome pairings. For the doctor, these could be: correctly detecting 63 cancer early is good for survival chances but incorrectly diagnosing cancer is stressful and costly 64 for the patient, whereas correctly identifying there is no cancer relieves stress but incorrectly 65 telling the patient they are cancer-free can be deadly. 66

Once the priors and payoffs are known, the best possible choice can be made by selecting the 67 choice alternative that maximises the expected reward. Many real-world cases have complex 68 rewards and losses that are difficult to quantify expected gain, like in our medical example, 69 but in economic or laboratory settings, choice outcomes can expressed in terms monetary or 70 points-based payoffs. For example, consider a lottery game with two choices, A and B, where 71 selecting A gives a 25% chance of winning a reward of 4 pts versus selecting B which gives a 72

75% probability of winning 2 pts. The expected gain of selecting lottery A is 1 pt (0.25 × 4) 73 and for B is 1.5 pts (0.75 × 2). Thus, the optimal decision would be to select lottery B because 74

1.5 pts is greater than 1 pt. In our medical scenario, we cannot usually make such a precise 75 calculation, but weighing up the relative risk of death (extremely high cost) versus causing some 76 mental and financial stress (lower cost), the doctor might err towards a positive diagnosis in an 77 ambiguous case. 78

3 The Signal Detection Theory framework 79

Signal Detection Theory (SDT) is a well established computational framework for modelling 80 perceptual decision making (Green and Swets, 1966). Perceptual decision-making is based on 81 noisy information reaching our senses that is then stochastically represented in the brain. Both 82 of these factors add an additional layer of uncertainty in the decision process. Returning to 83 our medical example of a doctor deciding on a cancer diagnosis, the information the doctor 84 receives can be corrupted by noise in various ways, such as the visual blur in an x-ray image 85 or neuronal noise involved in the sense of touch when inspecting a lump. The SDT framework 86 is flexible in that can be applied to most scenarios of repeated perceptual discrimination or 87 categorisation, such as reporting whether stimuli have rightward motion or leftward motion in 88 the laboratory, or a series of cancer/not-cancer diagnoses in the hospital. SDT can be both 89 descriptive, when applied in the context of empirical observations (e.g., quantifying how two 90 doctors differ in how readily they diagnose cancer), or prescriptive, in the sense that it can 91 describe what the ideal observer would do according to statistical decision theory. A feature 92 of this approach, and perhaps its greatest strength, is SDT’s ability to dissociate the separate 93 effects of perceptual sensitivity and perceptual bias on the decision making process. That is, 94 the degree of noise in the sensory evidence vs. the observer’s propensity to choose one choice 95 alternative over the others. Furthermore, the measurements of sensitivity and bias provided by 96 this modelling framework can be directly compared between observers and tasks. 97

From the perspective of affective bias, SDT enables us to quantify biases in the decision- 98 making process towards or away from differently rewarded stimuli, that takes into account 99 individual variation in the perception of the stimuli (i.e., sensitivity). In other words, breaking 100 down whether an individual is biased towards negative stimuli because they actually perceive 101 the stimuli differently, or whether they accurately perceive the stimuli but subsequently decide 102 to use the information differently (for example, this approach has been used to examine the 103 response biases and anhedonia by Pizzagalli et al., 2005). In addition to simply improving the 104 measure of bias, there are also many theories of bias, developed in the SDT framework, poten- 105 tially relevant for understanding the source of affective bias that can be tested experimentally. 106

Together, increasing measurement quality and better understanding the cause for the bias have 107 the potential to improve the understanding of and treatments for affective bias. 108

The standard SDT model describes the decision-making process for when one of two potential 109 sensory stimuli, A and B, can be presented to an observer and asking them to report which 110

4 A B k kopt say “A” say “B” P (A) = 0.75 P (B) = 0.25

P (x A) P (x B) | | Probability Probability

Decision Variable, x Decision Variable, x

C affective bias D conservative k

8 6 4 2 kopt kAff.Bias . . . . = 0 = 0 = 0 = 0 kopt α α α α kneu VA,A = 2 VB,B = 4 Probability Probability

Decision Variable, x Decision Variable, x

Figure 1: Illustration of the Signal Detection Theory (SDT) framework. A) The observer makes a measurement, x, of the stimulus, either stimulus A or stimulus B. The prob- ability of a measurement, conditioned on the stimulus, is assumed to be Gaussian distributed due to the effect of sensory noise. The observer selects a decision criterion, k, that provides a mapping from x to a response (e.g., say “A”). B) When priors are not equal for the two choice alternatives, the optimal criterion, kopt is no longer at the neutral location centred between the two measurement distributions. As shown, stimulus A is more probable than stimulus B, caus- ing a rightward shift in kopt. Consequently, stronger evidence of B is needed to report “B”. C) Similarly for unequal payoffs. Correctly guessing A receives 2 units of reward, whereas correctly guessing B receives 4 units. This shifts the optimal criterion leftward so that stronger evidence of A is needed to report poorly rewarded “A”. In an unequal reward context, affective bias is an increased preference to report the low-reward option (here “A”). This can be modelled as a shift in the criterion towards the high-reward distribution. An example of a criterion influenced by affective bias is shown by the dashed line. D) Conservatism is an insufficient shift of the criterion from neutral, kneu, to kopt. Where k falls between these two locations can be described by the proportional constant, α. Here the observer is conservative with α = 0.6 as denoted by the shading behind the plot.

5 they perceived. The presentation of stimulus A does not produce the same sensory response 111 in the observer each time it is shown, due to the various sources of noise (e.g. in neural 112 processing) corrupting the signal, nor does B. Instead, we refer to the noisy measurement of the 113 stimulus in the observer’s brain as x, the value of which is unobserveable to the experimenter. 114

An assumption of the standard SDT model is that the sensory noise affecting A and B is 115

Gaussian, with the conditional-measurement distributions p(x|A) and p(x|B) modelled as two 116 equal-variance Gaussian distributions (see Figure 1A). These distributions represent the values 117 of x one can expect to observe for repeated presentations of identical A and identical B. 118

The perceptual sensitivity of the observer is reflected in the separation of these distributions 119 in units of SD of noise, 120 µ − µ d0 = B A , (1) σ

0 and is referred to as d (“dee-prime”). A common modelling choice, which we adopted for this 121 paper, is to rescale the decision axis by a factor of 1/σ so the variance of p(x|A) and p(x|B) 122

0 is 1. This allows d to be read directly as the distance between the distributions because the 123 re-scaling takes care of the denominator in Eq. 1. Consequently, when sensory noise is higher, 124

0 the measurement distributions are closer together, and perceptual sensitivity (d ) is lower. This 125 is intuitive: from the observer’s perspective, they must infer if their measurement x came from 126 the p(x|A) or the p(x|B) distribution, which are more easy to confuse if the distributions are 127 closer together. If the decision axis is unscaled the confusion resulting from increasing noise can 128 be thought of in terms of simply a greater overlap in the two conditional distributions. 129

To convert the noisy measurement x into a categorical response “A” or “B”, the observer 130 must place a decision criterion, k. This criterion divides the decision space into two regions: 131 values of x that lead to “A” responses and those that lead to “B” responses. The criterion 132 can also be converted to the more general β representation, which is independent of perceptual 133 sensitivity, through the following relationship: 134

ln β k = (2) d0

The criterion can be placed at any point along the decision axis, but there is only one location 135 that is optimal according to statistical decision theory. This theoretical benchmark is often 136 referred to as the ideal observer, who makes the best decision possible given the noisy sensory 137 input (Tanner and Birdsall, 1958; Green and Swets, 1966). The optimal criterion, kopt, depends 138

6 on both the prior probability of A and B as well as payoff structure of the environment (see 139

Figure 1B-D): 140 ln β k = opt (3) opt d0 where 141 P (A) VA,A − VA,B βopt = . (4) P (B) VB,B − VB,A

P (A) and P (B) are the prior probabilities of each stimulus. The outcomes for four possible 142 stimulus-response pairs have the associated payoff Vr,s for responding r to stimulus s (rewards 143 are positive; losses negative). If one alternative is more probable or is rewarded more highly, the 144 ideal observer will shift their criterion from the neutral position (kneu = 0) so more responses 145 will be of that category (see Figure 1). This is equivalent to requiring less sensory information 146 consistent with that category to select it. When both priors and payoffs are asymmetric, then 147 their effects on the optimal criterion are additive (Stevenson et al., 1990). Biases in perceptual 148 decision making can be quantified by comparing where the observer chose to place their criterion 149 relative to the optimal criterion, in a manner that takes into account the perceptual sensitivity 150 of the observer. For example, one way a ‘negative’ affective bias might emerge is by moving the 151 criterion towards the highly rewarded option relative to the optimal (e.g. a criterion rightward 152 of kopt in Figure 1C), leading the individual to choose the low-reward option more frequently 153 than they should. 154

In sum, the SDT framework quantifies both the perceptual sensitivity and perceptual bias 155 of an observer, with independent measures, that is directly comparable to optimal decision- 156 making. As affective bias can manifest as a suboptimal propensity to choose the low reward 157 outcome, as shown in the following example, we propose that the SDT framework is ideal for 158 quantifying affective bias in perceptual tasks and comparing amongst observers with potentially 159 different perceptual capabilities. 160

Using SDT to understand affective bias in tone discrimination 161

To illustrate how affective bias can distort optimal decision-making, we consider the response 162 of human participants in the tone-discrimination task of Aylward et al. (2019a). This paper 163 recruited participants were either experiencing clinically significant low-mood and/or anxiety 164 symptoms or were asymptomatic controls. They discriminated between a high tone (1kHz), 165 which was highly rewarded when correctly identified, and a low tone (0.5kHz), that yielded four 166

7 A B nraigsensitivity Increasing d’= 3.5 1 d’= 0

d’= 1 500 Hz 1 kHz 0.75 high reward d’= 2 low reward d’= 3 d’= 4

750 Hz 0.5 ambiguous

0.25 4 2 0 2 4 − − Decision Variable

Proportion of “high tone” Responses 0 Control Anxiety

Figure 2: The tone-discrimination task of Aylward et al. (2019a). A) Participants reported if they heard the low-frequency tone (red) or the high-frequency tone (blue). The reward for correctly guessing the high-frequency tone was four times larger than for the low- frequency tone. On some trials, an ambiguous tone (purple) was played and was rewarded randomly. The graph illustrates the SDT model with the expected probability distributions of the decision variable for each of the tones. Example shown for an observer with a perceptual sensitivity of d0 = 3.5 (i.e., the sensitivity of the average anxiety-group participant). The optimal decision boundary (dashed grey) provides the decision rule that maximises expected reward: choose “low tone” if the decision variable is lower than this value, and “high tone” if it is above. Critically, this boundary does not align with the mid-point between the red and blue distributions (peak of the purple distribution) because it is optimal to have a bias for responding with the more highly rewarded “high tone”. B) Boxplots of the empirical distributions of the proportion of “high tone” judgements for the ambiguous stimulus, split by test population. The lower proportion of high-tone responses of the anxiety group is the affective bias effect. Horizontal dashed lines indicate the expected proportion of responses for the ideal observer who uses the optimal decision boundary. The expected proportions are shown for several perceptual sensitivities ranging from no sensitivity (d0 = 0) to near-perfect sensitivity (d0 = 4).

times less reward. Occasionally, an ambiguous intermediate (0.75kHz) tone was played and was 167 randomly treated as a low or high tone for scoring purposes including the magnitude of reward 168

(i.e., half the trials a low-tone response was required and furnished the small reward value, and 169 the other trials a high-tone response was required and was rewarded well). Figure 2A shows 170 the SDT diagram for this experiment, with three distributions for each of the three possible 171 tones. Participants had overall high discrimination performance between low and high tones, 172

0 reflecting high perceptual sensitivity. The mean d for the control and anxiety groups were 3.6 173 and 3.5 respectively. 174

To maximise reward, the participant should be biased towards responding “high tone” be- 175 cause it is more highly rewarded. This can be seen in the criterion (dashed grey line) depicted 176 in Figure 2A, which is shifted leftward from the neutral position at 0. The bias should be most 177 the evident for the ambiguous trials, where the proportion of “high-tone” to “low-tone” trials 178 is a good indicator of criterion placement. The dashed lines in Figure 2B show the expected 179

8 proportion of “high-tone” judgements in the ambiguous condition for ideal observers with sev- 180 eral different levels of perceptual sensitivity. The optimal criterion is affected by sensitivity 181

(see Eq.1): the higher the sensitivity, the more the observer should trust the sensory measure- 182 ment and consequently lowering the bias from reward. Yet, even for extremely high perceptual 183 sensitivity, it is still optimal to have a bias for the more rewarded stimulus. 184

Participants in this task, however, showed a wide range of biases when presented with the 185 ambiguous stimulus. On average, the control group responded “high tone” more often than the 186 anxiety group. But many of them, as well as, critically, more than half of the anxiety group, 187 showed a preference for selecting the low-rewarded “low-tone” option, interpreted as an affective 188 bias. Thus, in this choice task, the affective bias is in direct opposition with optimal decision- 189 making. We also note that using a log-space representation, typical for auditory experiments 190 of tone frequency discrimination (to match the encoding characteristics of the cochlea), does 191 not change the interpretation of the results and in fact predicts overall higher proportions of 192

“high-tone” responses. There are a number of possible causes of this affective bias away from 193 optimal decision-making, which we discuss in turn below. 194

Biased Criterion Placement 195

It is not uncommon to find that ‘healthy’ control observers fail to place their criterion at the 196 optimal location (Ulehla, 1966; Ackermann and Landy, 2015). In the Aylward et al. (2019a) 197 example, the average control-group participant had a rate of “high tone” responses outside the 198 range that could be considered optimal for even the most sensitive observer, instead responding 199 with “high tone” and “low tone” more or less equally (Figure 2B). In the terms of SDT, we 200 can say the average observer placed their criterion between the neutral criterion at 0 (i.e., the 201 mid-point between the two conditional response distributions) and the optimal criterion that 202 maximises expected gain. This phenomenon is referred to as conservatism in criterion placement 203

(Green and Swets, 1966) and can be quantified as the fractional shift from the neutral to the 204 optimal criterion, α = k/kopt, with 0 < α < 1 consistent with conservatism (see Figure 1D). 205

Criterion conservatism, as well as other criterion biases more generally, can be a behavioural 206 signature of one or more processes influencing the decision making process, which we discuss in 207 turn below with reference to the tone task of Aylward et al. (2019a). 208

9 1: Incorrect beliefs: Correctly calculating the optimal criterion requires three pieces of 209 knowledge: the prior probabilities of each stimulus, the payoff structure of the environment, 210 and perceptual sensitivity of the observer. If the observer is incorrect in their beliefs for one or 211 more of these components, then they may set their criterion suboptimally. Humans can learn 212 the properties of the choice environment through experience, however this takes time and and 213 can be conservatively distorted (Norton et al., 2019). Alternatively, information about priors 214 and payoffs can be explicitly conveyed to the observer, but they still may choose to rely on 215 the recent stimulus history for judging the context (Yu and Cohen, 2009). How observers come 216 to form an estimate of their own perceptual sensitivity is less understood and rarely discussed 217

(Rouault et al., 2019; Rouault and Fleming, 2020), but it has been proposed observers may make 218 incorrect inferences about the underlying noise distributions when placing a criterion (Kubovy, 219

0 1977; Locke et al., 2020). For example, if the observer judges their d to be greater than it 220 actually is (i.e., overconfidence) then this will lead to conservative criterion placement. 221

From an affective bias perspective, the anxious/depressed individuals of Aylward et al. 222

(2019a) may have misjudged the experimental context or their perceptual abilities. The most 223 likely explanation is that they incorrectly believe that the highly rewarded high-tone stimulus is 224 presented less frequently than the low-tone stimulus, leading to conservative criterion placement 225 due to an incorrect assessment of prior probabilities. This may be due to a general belief that 226 things good things do not happen often, or a focus towards remembering low-reward events and 227 forgetting high-reward events. 228

2: Subjective probability and value: Another way the optimal criterion may be miscal- 229 culated is if cognitive biases distort the prior probabilities and payoff values. According to 230

Prospect Theory, both the probability of events and the value of rewards are susceptible to 231 biases (Kahneman and Tversky, 1979; Fox and Poldrack, 2009). That is, humans tend to over- 232 estimate the probability of unlikely events and under-estimate quite certain events. There is 233 also a consideration of the utility of the possible rewards against what is already obtained or 234 possessed. Gaining rewards is more useful to someone that has very little, compared someone 235 who has a lot, and so the value of the reward is higher to a poorer individual. In general, 236 individuals can differ significantly in how they perceive the value of a reward. Ackermann and 237

Landy (2015) showed that both these factors were predictive of criterion placement, suggest- 238 ing distorted subjective prior probabilities and the expected utility of rewards contribute to 239

10 conservatism in perceptual decision-making. 240

In the tone-discrimination task, both groups may have been aware the high tone leads to 241 higher reward, but the anxious/depressed individuals may be more indifferent to the relative 242 reward value (i.e., the utility of the low and high rewards are more similar). This is most likely 243 from under-valuing the large reward (Ackermann and Landy, 2015), but over-valuing the small 244 reward would also produce a similar result. 245

3: Maximisation strategy: The optimal strategy for maximising expected gain will some- 246 times lead to scenarios where the ideal observer selects the choice alternative that is less likely 247 to be correct because it is rewarded more in terms of points/money/etc. This is because there is 248 the tension between maximising gain versus maximising accuracy when payoffs are unequal. It 249 has been suggested that human observers attempt to find a trade-off between these two goals, 250 which leads to conservative criterion placement but higher overall choice accuracy (Maddox 251 and Bohil, 1998, 2003). It is as if there is a cognitive cost to being incorrect and/or cognitive 252 reward for being correct that is at play in perceptual decision-making. Another explanation for 253 this phenomenon is that sacrificing some gains for better accuracy may foster more accurate 254 judgements of perceptual confidence (Locke et al., 2020). 255

Applied to the tone-discrimination experiment, the depressed/anxious individual under- 256 stands the reward structure of the experiment, but is less inclined to choose the high-tone 257 response they think might be incorrect even if they will earn more money overall for doing so; 258 they value more giving the correct answer in the task than their final earnings. Alternatively, 259 if they are unable to prevent rewards from influencing their confidence, they will also have a 260 sense of confidence more closely calibrated to reality if they do not let the payoff structure 261 influence their decision. By selecting the low- and high-reward options more equally, they will 262 avoid falsely optimistic confidence for high-reward responses. 263

4: Criterion adjustment: Criterion placement may also be the result of a learning process 264 by which the observer incrementally adjusts their criterion in response to the rate of change in 265 reward (Busemeyer and Myung, 1992; Maddox and Bohil, 2003). Adjustment stops when the 266 rate of reward appears to be no longer increasing (i.e., the maximum is found). Conservatism 267 occurs when there is insufficient adjustment of the decision criterion, from the neutral criterion, 268 to reach the optimal criterion. According to this theory, the priors-payoff structure of the 269 environment play a large role in determining the degree of conservatism. When small changes 270

11 in the location of the decision boundary dramatically affect the rate of reward, learning should 271 lead to a placement close to optimal. Conversely, inconsequential changes in reward rate are 272 thought to lead to greater conservatism, as there is little to gain from further adjustment. 273

From the perspective of the Aylward et al. (2019a) example, the anxious/depressed indi- 274 viduals may simply learn and/or adjust their criterion more slowly. If they were given more 275 stimulus presentations they may eventually match the performance of the controls, although 276 this is perhaps unlikely in this case as there is little change in performance in either group over 277 time (and a version of this task has been shown to have very high split half reliability in a large 278 sample; Daniel-Watanabe et al., 2020). 279

5: Other sources of bias: There are also general response biases that arise for various 280 reasons: the observer has a task-unrelated preference for one stimulus (e.g., they have place 281 a sentimental value on an outcome), the experimenter’s instructions, perhaps inadvertently, 282 encourage bias (Morgan et al., 2012) (e.g., the experimenter says that they should select one 283 option if unsure), or there different amounts of effort required to make each of the responses 284

(Hagura et al., 2017) (e.g., an individual chooses the lower value option that is easier to ob- 285 tain). It should also be noted that if the Gaussian-noise assumption of the basic SDT model 286 is incorrect, then the predicted ideal criterion placement may also appear biased due to model 287 misspecification rather than any actual bias in the individual (Maloney and Thomas, 1991). 288

Directions for future research 289

Affective biases have been long known to play a critical role in promoting and maintaining core 290 symptoms of mental ill health. We have highlighted, however, how even a relatively clear-cut 291 example of affective bias (e.g. reduced bias towards high vs low rewarding options in a simple 292 perceptual task) can have multiple underlying causes. While biases in general are not unusual 293 in perceptual tasks (Rahnev and Denison, 2018), investigating the source of the bias responsible 294 for divergent behaviour between clinical and healthy populations could lead to a more precise 295 understanding of the underlying symptoms. Furthermore, narrowing down which of these causes 296 drives the overall bias can provide us with more precise targets for treatment intervention. In 297 this next section we suggest a number of future directions to clarify the underlying cause of 298 biased decision-making behind affective bias from a signal detection perspective. 299

12 1. Beliefs about prior probabilities 300

Perhaps the most compelling hypothesis for affective bias in perceptual tasks is the incorrect 301 beliefs about prior probabilities. One of the key clinical features of depression and anxiety is 302 a belief that bad things are more likely to happen than good things. This is the basis, for 303 example, of negative cognitive schemata that are targeted by cognitive behavioural therapy 304

(Beck, 1964). If the individual believes that low-reward stimuli are presented more often than 305 the high reward stimuli (due to their negative schemata), then it is rational to shift the decision 306 criterion so as to select the low-reward stimulus more often. As illustrated in Figure 3A-B, 307 this bias can offset the optimal shift due to the payoff structure (i.e., move the criterion back 308 towards the neutral location), or, in the case of extreme over-estimation of the low-reward 309 stimulus probability, reverse the bias entirely. Previous work has indicated that those with 310 higher trait anxiety make stronger use of prior probabilities (Kraus et al., 2021), so an incorrect 311 belief is likely to have a large behavioural effect such as the reversal of preference from high- to 312 low-reward stimuli. Thus, incorrect beliefs about priors can account for both the affective bias 313 signature of showing a degree of conservatism in their responses, as well as showing stronger 314 attraction to the low-reward stimulus than the high-reward stimulus (e.g., as in Aylward et al., 315

2019a). 316

Proposed prior-beliefs test: To test this hypothesis, patients and controls could be given 317 a task where the prior probability of the stimuli are directly manipulated. For example, in one 318 block of trials the split between low- and high-reward stimuli could be 30%-70% and the next 319

60%-40%, and so on. Participants would be told at the beginning of each block the probabilities 320 of the stimuli have changed but would be left to work out the ratio themselves. Then, at the 321 end of a block, they would be asked to report their belief about the prior probabilities. A 322 survey before beginning the experiment could also be conducted to gauge to their beliefs about 323 prior probabilities in laboratory settings, and ensure task comprehension. These reported priors 324 could be used in several analyses. The first, to assess if the clinical group overestimates the 325 probability of the low-reward event as compared to the non-clinical group. The second, would 326 be to see how these reported prior beliefs predict criterion placement. That is, after accounting 327 for any incorrect prior beliefs, are the individuals otherwise rational in the placement of the 328 decision criterion? 329

13 A prior belief B 1

.5 .6 .7 .8 .9

) = 0 ) = 0 ) = 0 ) = 0 ) = 0 A A A A A 0.8 ( ( ( ( ( ˆ ˆ ˆ ˆ ˆ P P P P P

0.6

0.4

0.2 Probability Proportion “A” Responses P (x A) P (x B) 0 | | 0.5 0.6 0.7 0.8 0.9 Decision Variable, x Belief About Prior for A: Pˆ(A)

C performance belief D 1

.5 .75 = 0 = 0 = 1 = 2 = 3 0.8 ˆ0 ˆ0 ˆ0 ˆ0 ˆ0 d d d d d

0.6

0.4

0.2 Probability Proportion “A” Responses P (x A) P (x B) 0 | | 0.5 1 1.5 2 2.5 3

Decision Variable, x Belief About Performance: dˆ0

Figure 3: Predictions for criterion placement and proportion of low-reward responses for different incorrect beliefs. Predicted results shown for low-reward stimulus A (red) and high-reward stimulus B (blue), with equal priors (P (A) = P (B) = 0.5), correct B responses being rewarded twice as much as correct A responses (VA,A = 2 and VB,B = 4), and perceptual sensitivity of d0 = 1. A) Criterion placement for different beliefs about the prior probability of stimulus A. The greater the estimated probability of A (Pˆ(A)), the greater the rightward shift in the criterion. B) The proportion of low-reward responses, for different beliefs about the prior probability of A. Prediction for the use of the optimal criterion with correct beliefs shown by the red marker, and incorrect prior beliefs by the black markers. The more the observer believes A is probable, the more low-reward responses. C) Criterion placement for different beliefs about perceptual performance. Under-estimations of performance (dˆ0 < 1) lead to leftward criterion shifts, and over-estimations of performance (dˆ0 > 1) lead to rightward criterion shifts. D) The proportion of low-reward responses, for different beliefs about performance. Predicted proportion with correct beliefs shown by the red marker, and incorrect beliefs by the black markers. Over-estimations of performance lead to more A responses and under-estimations to less.

2. Beliefs about performance 330

Another incorrect belief that could lead to an affective bias is the observer’s belief about their 331 own performance. Specifically, if an observer believes their performance to be much better 332

0 than it actually is (i.e., higher perceived d ), then we would expect to see conservatism in 333 their criterion placement consistent with the affective bias identified by Aylward et al. (2019a). 334

This is because the influence of contextual factors, such as payoffs and prior probabilities, is 335

14 diminished when the perceptual sensitivity is high. Thus, over-estimation of ability will lead the 336 observer to trust their senses more than they should. Conversely, observers who under-estimate 337 their ability should show the opposite pattern, responding more strongly in accordance with 338 the relative value of rewards. These predictions are illustrated in Figure 3C-D. 339

Consistent with low self-confidence that forms a key part of the clinical presentation of 340 deperession (Beck, 1964), previous research shows that individuals with anxiety/depression 341 symptoms tend to report low confidence when performing perceptual tasks (Rouault et al., 342

2018). These trial-to-trial reports, if they inform a global sense of belief in performance, would 343 predict a bias in criterion placement that is a reverse of affective bias. That is, the observer would 344 be strongly influenced by the reward structure of the task, reporting the high-reward option 345 against their own sensory evidence. It is for this reason that we believe investigating beliefs 346 about overall task performance is important to understanding the interplay between affective 347 bias and metacognitive differences in observers with anxiety or mood disorders. Recent research 348 has demonstrated that beliefs about task performance are influenced by external feedback and 349 trial-to-trial judgements of confidence (Rouault et al., 2019). Thus the role of feedback and 350 confidence should be examined for their role in affect biases. 351

Proposed performance-beliefs test: An experiment to investigate beliefs about perfor- 352 mance could vary the task difficulty in blocks. After each perceptual decision, the observer 353 would report their sense of confidence in the correctness of their decision. At the end of each 354 block, the observer would report their belief about their performance (e.g., on a scale of 0 to 355

100% correct). The prediction is that the anxiety/mood individuals would report lower confi- 356 dence in their performance. They may have both the conservative criterion placement indicative 357 of affective bias and low beliefs about performance (in conflict with the predictions of SDT), 358 or the signature of affective bias with high beliefs about performance. Additionally, given that 359 beliefs about performance are typically lower when no trial feedback is given (Rouault et al., 360

2019), half of the blocks could contain feedback and the other half with no feedback. This 361 would permit a within-subject analysis on the relationship between criterion placement and 362 belief about performance as a function of feedback. 363

15 3. Subjective value of reward 364

Another plausible explanation is that the individuals with affective bias actually value rewards 365 differently. In particular, if there is is a devaluing of the high reward, then the subjective value 366 of the low and high reward are more similar, and thus there is less motivation to prefer one 367 outcome over the other. This would be consistent with anhedonia in depression, framed as ‘loss 368 of interest or pleasure’ in diagnostic criteria (American Psychiatric Association, 2013), in which 369 previously enjoyable things lose their value to depressed individuals. This is indeed observed on 370 a wide range of reward-based cognitive tasks (Pizzagalli et al., 2005; Halahakoon et al., 2020). 371

To understand how an individual subjectively experiences reward, scientists can measure the 372 subjective utility function, which maps the objective value of a reward, V , to its subjective 373 value, u(V ), and is typically expressed as in terms of a power function 374

u(V ) = V α (5)

(see Figure 4A) with 0 < α < 1 typical (Kahneman and Tversky, 1979; Fox and Poldrack, 2009). 375

In the SDT context, changing the subjective utility function has implications for the reward 376 landscape (Figure 4B) and consequently the placement of the decision criterion (Figure 4C). 377

The closer the subjective reward values are to equal, the closer the rational observer will place 378 their criterion to the neutral location, because biasing the responses in favour of the high-reward 379 stimulus makes little sense if the difference in reward is small, resulting in fewer high-reward 380 responses (Figure 4D). Given this context, we would hypothesise individuals expressing affective 381 bias have smaller α values than a healthy control population if subjective utility is the source 382 of affective bias in perceptual tasks. Clinical support for this hypothesis on subjective value in 383 mood and anxiety disorders is limited and of mixed results (Chung et al., 2017; Baek et al., 384

2017; Charpentier et al., 2017), suggesting further research is required to understand the role of 385 reward value distortions in choice behaviour. Additionally, to our knowledge, subjective reward 386 values and bias in a perceptual task have not been compared within individuals with anxiety 387 or mood disorders. 388

Proposed subjective-value test: To measure the subjective utility functions of partici- 389 pants, it is necessary to include Prospect Theory measures in addition to the perceptual task 390

(Ackermann and Landy, 2015). Presenting a series of lottery choices like we described earlier 391

16 (e.g., 25% chance of winning 10 dollars, or 100% chance of 2 dollars), it is possible to mea- 392 sure each participant’s subjective utility function. Then one could assess group-level differences 393 in the subjective evaluation of reward (i.e., differences in α), as well as the degree to which 394 subjective value predicts criterion placement in the perceptual task (see Figure 4C-D). 395

A B 5 α = 1 0

α = 0.25 0.5 4 −

α = 0.75 1 − α = 0.5 3 1.5 α = 0.5 − α = 0.75 2 2 α = 0.25 Relative to Maximum − α = 1 Subjective Reward Value Subjective Expected Gain 1 2.5 − 1 2 3 4 5 2 1 0 1 2 − − Objective Reward Value Criterion Placement, k

C Subjective Reward D 0.5

.75 .5 .25 = 1 = 0 = 0 = 0 0.4 α α α α

0.3

0.2

0.1 Probability Proportion “A” Responses P (x A) P (x B) 0 | | 0.2 0.4 0.6 0.8 1 Decision Variable, x Utility Function α

Figure 4: The effect of subjective value on decision-making. Predicted results shown for low-reward stimulus A (red) and high-reward stimulus B (blue), with equal priors (P (A) = P (B) = 0.5), correct B responses being rewarded twice as much as correct A responses (VA,A = 2 0 and VB,B = 4), and perceptual sensitivity of d = 1. A) Example subjective utility functions. When α < 1, the subjective value of the two reward outcomes (A/B) is more similar. B) Reward landscape is affected by subjective utility function. Dashed lines show the criterion placement expected to maximise expected gain with the subjective reward values. When α < 1, there is a dampening affect, with the perceived consequence of criterion misplacement being small (i.e., loss incurred is minimal for other values of k). C) Optimal criterion placement according to the subjective reward ratios. As α → 0, the criterion placement that maximises expected reward with these distorted reward values shifts towards the neutral position between the distributions. D) The proportion of low-reward responses when criterion is adjusted according to the subjective value of reward. When the subjective value matches objective value (red), the proportion of A responses is lower than if the subjective value is used with α < 1 (black).

4. Learning the context 396

In several aspects, observers must succeed in learning about the context and their own per- 397 formance to respond optimally. There is extensive clinical evidence for learning differences in 398

17 depression and anxiety, from general cognitive impairment (Rock et al., 2014) through to more 399 specific changes to learning captured by, for example, reinforcement learning models (Aylward 400 et al., 2019b; Halahakoon et al., 2020). In perceptual tasks, participants must learn to correctly 401 estimate the prior probabilities of the stimuli and the reward contingencies, as well as moni- 402 toring feedback and confidence to estimate perceptual sensitivity. Some models consider this 403 learning process as a gradual adjustment of the criterion to its optimal position (Busemeyer 404 and Myung, 1992) whereas others investigate the learning process at the component level (e.g., 405 priors) (Norton et al., 2019). An additional consideration is that the reward landscapes experi- 406 enced by the participant can be affected by their subjective value of the reward (see Figure 4B). 407

Additionally, if learning rates differ between those with and without anxiety/mood symptoms 408

(Vrieze et al., 2013; Aylward et al., 2019b), this could increase criterion conservatism. Sup- 409 porting this hypothesis is work by Pizzagalli et al. (2008) showing that clinically depressed 410 individuals have difficulties integrating the reinforcement history over time to correctly bias 411 their responses towards highly rewarded options. 412

Proposed learning test: To investigate the role of learning in affective bias, one could use the 413 overt-criterion task of Norton et al. (2019) where observers complete a perceptual task with high 414 external noise (i.e., experimenter controlled noise) that requires them to continually monitor 415 the stimulus priors and adjust their criterion accordingly. Instead of reporting stimulus A or B, 416 observers are asked to explicitly place a criterion and their response would be scored as correct 417 if this criterion correctly categorises the stimulus. This modification allows for rapid shift in 418 criterion to be detected and modelled. We predict that observers who display affective bias could 419 either 1) have a slower learning rate, 2) a stronger bias towards equal probabilities, or 3) a bias 420 inflating the probability of the low-reward stimulus. This task would be well complemented by 421 including additional learning tasks, such as the multiarmed bandit task (Aylward et al., 2019b), 422 to directly compare learning parameters with SDT parameters, as well as the Prospect Theory 423 measures mentioned in the previous future direction. 424

5. Need for accuracy 425

There are two ways in which a need for accuracy could affect criterion placement. The first 426 is by selecting a decision strategy that emphasises getting the perceptual judgements correct 427 over earning the most reward in the task. In the extreme, ignoring the reward values entirely 428

18 would lead to the highest perceptual decision accuracy, but in practice observers are more 429 likely to select a mixture strategy that is a trade-off between accuracy and gains (Maddox and 430

Bohil, 1998, 2003). This trade-off behaviour in strategy selection can also be interpreted as a 431 different need for accuracy: the need for our sense of confidence to best reflect true probability 432 of being correct (Locke et al., 2020). The payoffs of a task can influence confidence ratings 433

(Lebreton et al., 2018; Locke et al., 2020) despite not changing that probability that the decision 434 was correct. For example, this can be an overconfidence when reporting the highly rewarded 435 stimulus and underconfidence when reporting the low reward option. As such, the less influence 436 such observers give to the payoffs of a task, the more accurate their confidence judgements will 437 be. This hypothesis is supported in the affective bias literature by a phenomenon known as 438 a ‘catastrophic response to perceived failure’ (Elliott et al., 1996; Roiser et al., 2011), where 439 one instance of failure can have a snowball effect for a future series of failures. Thus the 440 consequence of making a judgement against what the observer believes to be correct has a strong 441 psychological cost that has not been factored into the optimal criterion calculation (Eq. 4) by 442 the experimenter. In terms of confidence ratings, individuals with anxious-depression symptoms 443 are also more accurate in their confidence judgements than those with other psychopathologies 444

(Rouault et al., 2018), as would be predicted by this hypothesis. 445

Proposed need-for-accuracy test: To test this hypothesis, individuals with and without 446 anxiety and/or mood disorder symptoms could perform a perceptual task with the reward values 447 changing from block to block. Strategy could be assessed by asking participants to self-report 448 the importance they placed on getting the answers correct versus earning the most reward at 449 the end of each block. Additionally, confidence judgements, on the correctness of their decision, 450 could be included after every trial. Standard extensions of the SDT framework for confidence 451 would then reveal if that observer let the rewards influence their confidence (Locke et al., 2020). 452

If affective bias is driven by a need for high accuracy, we would see the anxiety/mood disorder 453 individuals giving greater preference for being correct over earning more reward and being more 454 susceptible to letting reward influence their sense of confidence. 455

Summary 456

In this paper, we have highlighted the advantage of considering the SDT framework for quan- 457 tifying suboptimal decision-making and the various underling mechanisms which may drive 458

19 affective bias in psychiatric disorders. We have also suggested a series of studies that could 459 tease apart which of these mechanisms lead to affective bias, reframed as criterion conservatism 460 within the SDT framework (Ackermann and Landy, 2015; Rahnev and Denison, 2018). The 461 appeal of studying affective bias with low-level perceptual tasks is that such tasks are partic- 462 ularly amenable for testing both humans and animal models (Choi et al., 2016; Scannell and 463

Bosley, 2016). Thus, being more precise about the causes of affective bias in humans will al- 464 low us to more precisely test how representative the animal models are, and hence bolster the 465 theoretical underpinnings of drug development pipelines for treatments of anxiety and mood 466 disorders. The approach we outline also allows us to recast seemingly “irrational” behaviour as 467 rational decision-making operating on incorrect or subjectively-distorted information. A better 468 understanding of these distortions may eventually allow us to more precisely target treatments, 469 and hence close the treatment gap in mood and anxiety disorders. 470

Acknowledgements 471

We would like to thank Lucie Charles and Lucie Berkovitch for organising the Metacognition 472 and freedom of choice in mental illness workshop in Paris that led to this collaboration. This 473 work was supported by a postdoctoral fellowship from the Fyssen Foundation (SML), the French 474

Agence Nationale de la Recherche grant ANR-17-EURE-0017 “FrontCog” (SML), and Medical 475

Research Council Senior Non Clinical Fellow MR/R020817/1 (OJR). 476

Author Contributions 477

Project was formulated by SML and OJR. Both authors wrote and edited the manuscript. 478

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