Figure 1.
Experimental design of a single trial. In 50% of the trials, fish were coming from the mainly black lake, and in 50%, they were coming from the mainly gold lake. The order was pseudo-randomized so that the same sequences were used for all participants. Feedback, depending on the block, was either of the words “Correct” and “Incorrect” in Block 1 or the number of points won (or lost) during the trial in all subsequent blocks.
Figure 2.
State space schematic. A) Markovian transitions in this task. Top: belief (probabilistic) component of states; middle: observable part of the state (data/feedback). Down arrows: actions (sample, declare). Bottom: true state. For example, let the cost of sampling be very high. Then b 0 may be “equiprobable lakes,” Action 1 “sample,” s 1 “B,” b 1 “60% B,” Action 2 “declare B,” and s 1 “Wrong.” B) In this example, sampling cost is very low. A person has drawn 15 fishes, 7 of them g, hence the position of 15 on the x-axis and +1 on the y-axis as there is a +1 excess of black fish so far. The visible states corresponding to all possible future draws are shown. Looking ahead (example: gray arrow), the agent finds the “sampling” action more valuable in that the current preference for the B lake is likely to be strengthened at very low cost.
Table 1.
Sample characteristics for healthy controls and patients with early psychosis
| Variable | Controls (n = 31) | Early psychosis (n = 31) | Statistics | ||
|---|---|---|---|---|---|
| Mean | SD | Mean | SD | ||
| Age (years) | 21.58 | 2.41 | 22.52 | 4.66 | t(60) = 0.993, p = 0.325 |
| Gender (male/female) | 18/13 | 18/13 | χ(1) = 0.0, p = 1 | ||
| IQ | 110.52 | 15.79 | 102.26 | 17.91 | t(60) = −1.926, p = 0.059 |
| Level of education | 2.35 | 0.79 | 2.00 | 1.17 | U(2) = 373.5, p = 0.117 |
| Mother’s level of education | 2.19 | 0.91 | 2.11 | 1.37 | U(2) = 440.0, p = 0.884 |
| Smoking (yes/no) a , * | 6/25 | 18/13 | χ(1) = 9.79, p = 0.004 | ||
| Alcohol | 2.42 | 0.85 | 1.78 | 1.37 | U(2) = 419.5, p = 0.368 |
| Cannabis | 0.90 | 0.79 | 1.26 | 1.23 | U(2) = 430.0, p = 0.459 |
| Other drugs b , * | 0.49 | 1.02 | 1.11 | 1.36 | U(2) = 355.5, p = 0.039 |
| PDI-21* | 4.45 | 2.34 | 7.83 | 4.58 | t(45) = 3.359, p = 0.002 |
| Distress* | 9.52 | 6.94 | 24.00 | 15.32 | t(45) = 4.430, p < 0.001 |
| Preoccupation* | 10.28 | 6.48 | 24.78 | 16.11 | t(45) = 4.341, p < 0.001 |
| Conviction* | 13.31 | 8.13 | 26.56 | 17.11 | t(45) = 3.58, p = 0.001 |
| BDI* | 3.40 | 3.90 | 25.34 | 14.12 | t(57) = 8.197, p < 0.001 |
| CAARMS summary score c , * | 0.52 | 1.15 | 18.00 | 7.53 | t(60) = 12.776, p < 0.001 |
Note. Intelligence was measured with a Culture Fair Intelligence Test. BDI = Beck Depression Inventory; CAARMS = Comprehensive Assessment of At Risk Mental States; PDI = Peter’s Delusion Inventory.
b Substance use was measured on a 5-point scale ranging from 0 (never used) to 5 (daily user). Other drugs included hallucinogens, stimulants, or sedatives.
c A summary score of Unusual Thought Content, Non-bizarre Ideas, and Perceptual Abnormalities intensity and frequency subscales (for individual subscales of CAARMS and other clinical assessment measures, see Table 2).
Table 2.
Clinical assessment measures for 31 patients with psychosis
| Mean | SD | |
|---|---|---|
| UTC | 2.44 | 2.19 |
| UTC frequency | 2.33 | 2.01 |
| NBI | 3.41 | 1.67 |
| NBI frequency | 3.52 | 1.48 |
| PA | 3.33 | 2.06 |
| PA frequency | 2.52 | 1.89 |
| DS | 0.59 | 1.28 |
| DS frequency | 0.96 | 1.99 |
| ADB | 1.81 | 1.82 |
| ADB frequency | 2.15 | 1.92 |
| SS | 1.59 | 1.48 |
| SS frequency | 1.30 | 1.44 |
| GAF score | 55.00 | 18.54 |
| SANS score | 0.35 | 0.75 |
| PANSS positive | 13.68 | 3.99 |
| PANSS negative | 9.87 | 4.88 |
[i] Note. BDI = Beck Depression Inventory; GAF = Global Assessment of Functioning; SANS = Scale for Assessment of Negative Symptoms. Comprehensive Assessment of At Risk Mental States (CAARMS) subscales included Unusual Thought Content (UTC), Non-bizarre Ideas (NBI), Perceptual Abnormalities (PA), Disorganized Speech (DA), Aggression/Dangerous Behavior (ADB), Suicidality and Self-Harm (SS).
Figure 3.
Performance: Draws to decision and accuracy according to block and group. A) Mean number of draws to decision in the four blocks of the task. On mixed-model ANOVA, there were significant main effects of block, F(3) = 94.49, p < 0.001, and of group, F(1) = 5.99, p = 0.017, and an interaction between group and block, F(3) = 4.32, p = 0.006, with group differences in Block 1, p = 0.007, and Block 2, p = 0.03. B) Probability of being correct (accuracy) at the time of making the decision in four task blocks. Here there was an effect for block, F(2) = 93.73, p < 0.001, a marginally significant interaction between Block ⋅ Group, F(2) = 2.52, p = 0.086 and a significant groups effect, F(1) = 4.14, p = 0.047.
Table 3.
Information sampling in controls, patients, and an ideal Bayesian agent
| Group | Control (n = 31), Mean (SD) | Psychosis (n = 31), Mean (SD) | Ideal Bayesian agent |
|---|---|---|---|
| DTD 1 | 12.01 (5.42) | 8.14 (6.16) | 20 |
| DTD 2 | 12.69 (5.67) | 9.15 (6.31) | 20 |
| DTD 3 | 5.80 (4.23) | 4.14 (2.64) | Nb − Ng = ±2 |
| DTD 4 | 3.71 (3.12) | 3.03 (2.09) | 1 |
| P corr 1 | 0.72 (0.10) | 0.66 (0.10) | 0.835 |
| P corr 2 | 0.75 (0.09) | 0.69 (0.11) | 0.835 |
| P corr 3 | 0.65 (0.07) | 0.62 (0.08) | 0.692 |
| P corr 4 | 0.62 (0.09) | 0.59 (0.08) | 0.6 |
Figure 4.
Mean number of points won or lost in Blocks 2–3 across all 10 trials. Patients won significantly fewer points in Block 2, F(2) = 4.65, p = 0.035, but did not differ from controls in Block 3 and 4, both p > 0.3.
Table 4.
Percentage and count of people who displayed JTC reasoning style
| Control (n = 31), n (%) | Psychosis (n = 31), n (%) | |
|---|---|---|
| No JTC | 18 (58.1) | 15 (48.4) |
| JTC Blocks 1/2 | 0 (0.0) | 1 (3.2) |
| JTC Blocks 3/4 | 11 (35.5) | 7 (22.6) |
| JTC all Blocks | 2 (6.5) | 8 (25.8) |
Table 5.
Best-fit distribution parameters for all groups in all experiments
| Group | CS M | CS V | T M | T V | LL |
|---|---|---|---|---|---|
| Block 1: No cost | |||||
| Control | 1.9 ⋅ 10−3 | 2.0 ⋅ 10−6 | 3.4 | 13 | −943.747 |
| Psychosis | 1.7 | 13 | 4.2 | 13 | −762.993 |
| Combined | 0.7 | 2.2 | 3.6 | 13 | −1,735.65 |
| Block 2: No cost, but win or loss (±100) | |||||
| Control | 5.0 ⋅ 10−3 | 1.3 ⋅ 10−5 | 3.6 | 21 | −841.202 |
| Psychosis | 3.0 | 44 | 2.9 | 7.5 | −690.567 |
| Combined | 1.5 | 13 | 2.5 | 7.0 | −1,549.28 |
| Block 3: Fixed cost, plus win or loss (±100) | |||||
| Control | 1.6 | 9.9 | 4.1 | 2.2 | −707.604 |
| Psychosis | 5.2 | 100 | 4.4 | 2.2 | −545.704 |
| Combined | 3.1 | 38 | 4.2 | 1.0 | −1,260.45 |
[i] Note. Best-fit parameters were calculated for each participant group separately and for the group formed by combining both participant groups. CS M = mean cost per sample for a particular group; CS V = variance of cost per sample within a particular group; T M is the mean noise parameter for a particular group; T V = variance of the noise parameter within a particular group; LL = log-likelihood of the data given the parameters.
Table 6.
Integrated Bayesian information criterion values for the model where all participants are drawn from the same distribution, compared to the model where the healthy and unhealthy groups differ in their distributions
| Block | iBIC combined | iBIC separate | iBIC difference | iBIC difference after medication exclusions | iBIC difference after closer IQ matching |
|---|---|---|---|---|---|
| 1 (no cost) | 3,489.7 | 3,450.2 | 39.5 (very strong) | 43.9 | 36.1 |
| 2 (no cost, win or loss ±100) | 3,116.9 | 3,100.3 | 16.7 (very strong) | 16.6 | −12.9 |
| 3 (fixed cost, plus win or loss ±100) | 2,539.3 | 2,543.4 | −4.1 (preference for combined model) | −6.2 | −4.1 |
[i] Note. iBIC values and differences are presented for analyses with all participants. iBIC differences are also shown for repeat analyses after exclusions for antipsychotic medication or closer IQ matching. Positive iBIC differences indicate the preference for separate groups, negative for a single combined group. iBIC = integrated Bayesian information criterion.