The Computational and Neural Substrates of Ambiguity Avoidance in Anxiety

Theoretical accounts have linked anxiety to intolerance of ambiguity. However, this relationship has not been well operationalized empirically. Here, we used computational and neuro-imaging methods to characterize anxiety-related differences in aversive decision-making under ambiguity and associated patterns of cortical activity. Adult human participants chose between two urns on each trial. The ratio of tokens (‘O’s and ‘X’s) in each urn determined probability of electrical stimulation receipt. A number above each urn indicated the magnitude of stimulation that would be received if a shock was delivered. On ambiguous trials, one of the two urns had tokens occluded. By varying the number of tokens occluded, we manipulated the extent of missing information. At higher levels of missing information, there is greater second order uncertainty, i.e., more uncertainty as to the probability of pulling a given type of token from the urn. Adult human participants demonstrated avoidance of ambiguous options which increased with level of missing information. Extent of ‘information-level dependent’ ambiguity aversion was significantly positively correlated with trait anxiety. Activity in both the dorsal anterior cingulate cortex and inferior frontal sulcus during the decision-making period increased as a function of missing information. Greater engagement of these regions, on high missing information trials, was observed when participants went on to select the ambiguous option; this was especially apparent in high trait anxious individuals. These findings are consistent with individuals vulnerable to anxiety requiring greater activation of frontal regions supporting rational decision-making to overcome a predisposition to engage in ambiguity avoidance at high levels of missing information.

Comparing mechanisms by which ambiguity may influence choice behavior: models 6-10.
In the models considered in the main manuscript (models 1-4), we account for the influence of ambiguity upon choice behavior in three ways.First, estimating the probability of pulling an 'O' out of the ambiguous urn (P a ) using a beta-binomial correction (E(p), p~Beta (1+k, 1+n-k), where k =number of 'O's shown and n = the total number of tokens revealed, allows for the rational adjustment of P a to take into account the extent of missing information.As an example, if no information is missing, and there are 40 'O's and 10 'X's, P a is 0.8.If 20 tokens are hidden and the ratio of revealed tokens is the same (i.e.24 'O's and 6 'X's), P a will be adjusted a little towards 0.5 due to the missing information (specifically, Pa = 0.78); if 45 tokens are hidden and the ratio of revealed tokens is the same (i.e. 4 'O's and 1 'X'), P a will be adjusted towards 0.5 to a greater extent (specifically, Pa = 0.71).Over and above this rational adjustment of P a , in models 3 and 4, we also include parameters that allow for an additional irrational influence of ambiguity on choice.Specifically, positive values of β 0 capture a general categorical preference for the unambiguous urn over the ambiguous urn while β 3 the extent to which avoidance of the ambiguous urn increases (or decreases) as a function of the level of missing information.Note, the beta-binomial correction of P a will effectively mean that high P a estimates (as calculated purely on the basis of the ratio of 'O's to 'X's) will be reduced when missing information is high but low estimates of P a (as calculated purely on the basis of the ratio of 'O's to 'X's) will be increased under the same high levels of missing information.In contrast, β 3 captures an increasing tendency to avoid urns as a function of missing information that is irrespective of the ratio of 'O's to 'X's revealed.
In the models below, we examine the impact of removing the beta binomial correction in the calculation of P a or removing the parameters capturing either categorical ambiguity avoidance (β 0 ) or increased avoidance of the ambiguous urn as a function of missing information level (β 3 ) Model 6: Removing the parameter capturing increased avoidance of the ambiguous urn as a function of missing information level (β 3 ) This model includes 3 parameters β 0, β 1, β 2 This model is identical to model 3 (that is, the winning model of models 1-4) except that the parameter allowing for an irrational influence of missing information level on choice (β 3 * A) has been removed.Note, this model still includes the beta-binomial correction of P a (as in model 3) and a parameter allowing for a difference in urn preference according to the categorical presence or absence of ambiguity (β 0 ) All other variables are as defined in model 3.As in model 3, on each ambiguous trial, P(U) is the event that the unambiguous urn is chosen.On unambiguous trials, P(U) is replaced with P(1), the event that Urn 1 is chosen.
Model 7: Removing the parameter capturing preference for the unambiguous urn over the ambiguous urn (effect of the categorical absence versus presence of ambiguity, β 0 ).

( ) ( ( ))
This model includes 3 parameters: β 1, β 2, β 3 Model 7 is based on model 3.The parameter (β 0 ) allowing for a difference in preference for urns according to the categorical presence or absence of ambiguity (C= 1 or 0) has been removed.Note, this model still includes the beta-binomial correction of P a (as in model 3).There is also still a parameter allowing for an additional influence of missing information level on choice (β 3 * A); this captures avoidance of the ambiguous urn that increases as missing information increases.In this model, A is not z-scored; with β 0 omitted, this is necessary to distinguish unambiguous trials from ambiguous trials with an average level of ambiguity.Other variables are as defined in model 3.As in model 3, on each ambiguous trial, P(U) is the event that the unambiguous urn is chosen.On unambiguous trials, P(U) is replaced with P(1), the event that Urn 1 is chosen.
Model 8: No rational use of missing information to adjust Pa (probability of drawing an 'O' from the ambiguous urn).

( ) ( ( ))
This model includes 4 parameters: β 0, β 1, β 2, β 3 .Pdiff on ambiguous trials = P a -P u where P a = k/n On each ambiguous trial, P(U) is the event that the unambiguous urn is chosen.On unambiguous trials, P(U) is replaced with P(1), the event that Urn 1 is chosen.In model 3, estimating the probability of drawing an 'O' out of the ambiguous urn (P a ) using a beta-binomial correction (E(p), p~Beta (1+k, 1+n-k) where k =number of 'O's shown and n = the total number of tokens revealed) allows for the rational adjustment of P a to take into account the extent of missing information.In model 8, we replace this by simply using the observed proportion of 'O's (k/n) to estimate P a (as is the case for P u , P 1 and P 2 ).In this model, ambiguity can still influence choice through avoidance (or seeking) of ambiguous urns in general (β 0 ), or increasing avoidance (or seeking) of ambiguous urns as a function of missing information level (β 3 ) These biases are irrational as they do not take into account outcome probability or magnitude (as specified in the Methods, difference in outcome magnitude and outcome probability were varied orthogonally with respect to both categorical ambiguity and level of missing information).
Model 9: No accounting (rational or irrational) for influence of missing information on choice behavior This model includes 2 parameters: β 1, β 2 .
Pdiff on ambiguous trials = P a -P u where P a = k/n; Mdiff = M a -M u .
On each ambiguous trial, P(U) is the event that the unambiguous urn is chosen.On unambiguous trials, P(U) is replaced with P(1), the event that Urn 1 is chosen; here, Pdiff = P 2 - In this model, we remove all influences of ambiguity on choice from model 3. P a is calculated using k/n as for P u , P 1 and P 2 , where k is the number of 'O's revealed and n is the total number of tokens revealed.The parameters allowing for an influence of categorical ambiguity (β 0 ) and level of missing information upon choice (β 3 ) are also both removed.Note, this model differs from model 1 in that model 1 allows missing information to rationally influence choice through use of the beta-binomial correction to estimate P a .All variables not otherwise specified are as defined in model 3 (and model 1).
Model 10: Expected Utility model with additive ambiguity parameter (accounting for categorical ambiguity aversion). ( ) This model includes 3 parameters: β 0, β 1 The expected utility models perform more poorly as a class (as previously discussed in relation to models 2 and 4).However, we include model 10 for comparability with other work in the literature that has explored decision-making under ambiguity in healthy adults 10 .This model is based on Model 2 but includes a parameter (β 0 ) to allow for the influence of the categorical presence or absence of ambiguity (C=1 or 0) upon urn choice.On each ambiguous trial, P(U) is the event that the unambiguous urn is chosen.On unambiguous trials, P(U) is replaced with P(1), the event that Urn 1 is chosen.On these trials, EU a is replaced by EU 2 , and EU u is replaced by EU 1. Variables not specified here are as defined in Model 2. Missing information informs the estimate of P a via the beta-binomial correction (as detailed in model 1).Unlike model 4, no additional influence of missing information on choice is included (i.e.β 3 ).
Section 3. Exploring the influence of ambiguity on use of probabilities and magnitudes: models 11-16.
In the models considered so far, we have modeled the influence of missing information upon participants' choice through applying a beta-binomial correction in the estimation of P a and through parameters (β 0 , β 3 ) that allow the presence and level of missing information (C, A respectively) to have an additive effect on participants' choice (in addition to outcome probability and magnitude).In the models below, we explore whether the presence or level of missing information influences the weighting given to probability or magnitude information, such that these variables differentially influence behavior on unambiguous and ambiguous trials.
Model 11: Model 3 is extended to allow the influence upon choice of the difference in outcome probability between urns and that of the difference in outcome magnitude between urns to vary between ambiguous and unambiguous trials.
This model includes 6 parameters: .
Note C and A are 0 on unambiguous trials so fall out of the equation for P(1).
On each ambiguous trial, P(U) is the event that the unambiguous urn is chosen.On unambiguous trials, P(U) is replaced with P(1), the event that Urn 1 is chosen.Model 11 is identical to model 3 except that the influence of magnitude difference and probability differences on choice is allowed to vary between ambiguous and unambiguous trials.See Model 3 for definition of variables.