| . | Main dataset (n = 15) . | Replication dataset (n = 16) . | ||
|---|---|---|---|---|
| Model . | PP . | XP . | PP . | XP . |
| Model family comparison—perceptual models | ||||
| Full hierarchical Bayesian family | 0.873 | 0.999 | 0.777 | 0.997 |
| Reduced model family (|$\vartheta = 0$|) | 0.064 | <0.001 | 0.105 | 0.001 |
| Reduced model family (|$x_3^{(t)} = 0$|) | 0.063 | <0.001 | 0.118 | 0.002 |
| Model family comparison—response models | ||||
| “Precision” family | 0.756 | 0.991 | 0.642 | 0.930 |
| “Belief” family | 0.076 | 0.001 | 0.251 | 0.066 |
| “Surprise” family | 0.168 | 0.008 | 0.107 | 0.004 |
| Model comparison of all 11 models | ||||
| Full hierarchical Bayesian model “Precision” | 0.499 | 0.995 | 0.381 | 0.914 |
| Reduced model (|$\vartheta = 0$|) “Precision” | 0.006 | <0.001 | 0.182 | 0.074 |
| Reduced model (|$x_3^{(t)} = 0$|) “Precision” | 0.119 | 0.004 | 0.047 | <0.001 |
| Full hierarchical Bayesian model “Belief” | 0.040 | <0.001 | 0.041 | <0.001 |
| Reduced model (|$\vartheta = 0$|) “Belief” | 0.040 | <0.001 | 0.042 | <0.001 |
| Reduced model (|$x_3^{(t)} = 0$|) “Belief” | 0.040 | <0.001 | 0.074 | 0.004 |
| Full hierarchical Bayesian model “Surprise” | 0.040 | <0.001 | 0.079 | 0.004 |
| Reduced model (|$\vartheta = 0$|) “Surprise” | 0.040 | <0.001 | 0.039 | <0.001 |
| Reduced model (|$x_3^{(t)} = 0$|) “Surprise” | 0.040 | <0.001 | 0.039 | <0.001 |
| Rescorla–Wagner model | 0.040 | <0.001 | 0.038 | <0.001 |
| True categorical probability model | 0.040 | <0.001 | 0.038 | <0.001 |
| . | Main dataset (n = 15) . | Replication dataset (n = 16) . | ||
|---|---|---|---|---|
| Model . | PP . | XP . | PP . | XP . |
| Model family comparison—perceptual models | ||||
| Full hierarchical Bayesian family | 0.873 | 0.999 | 0.777 | 0.997 |
| Reduced model family (|$\vartheta = 0$|) | 0.064 | <0.001 | 0.105 | 0.001 |
| Reduced model family (|$x_3^{(t)} = 0$|) | 0.063 | <0.001 | 0.118 | 0.002 |
| Model family comparison—response models | ||||
| “Precision” family | 0.756 | 0.991 | 0.642 | 0.930 |
| “Belief” family | 0.076 | 0.001 | 0.251 | 0.066 |
| “Surprise” family | 0.168 | 0.008 | 0.107 | 0.004 |
| Model comparison of all 11 models | ||||
| Full hierarchical Bayesian model “Precision” | 0.499 | 0.995 | 0.381 | 0.914 |
| Reduced model (|$\vartheta = 0$|) “Precision” | 0.006 | <0.001 | 0.182 | 0.074 |
| Reduced model (|$x_3^{(t)} = 0$|) “Precision” | 0.119 | 0.004 | 0.047 | <0.001 |
| Full hierarchical Bayesian model “Belief” | 0.040 | <0.001 | 0.041 | <0.001 |
| Reduced model (|$\vartheta = 0$|) “Belief” | 0.040 | <0.001 | 0.042 | <0.001 |
| Reduced model (|$x_3^{(t)} = 0$|) “Belief” | 0.040 | <0.001 | 0.074 | 0.004 |
| Full hierarchical Bayesian model “Surprise” | 0.040 | <0.001 | 0.079 | 0.004 |
| Reduced model (|$\vartheta = 0$|) “Surprise” | 0.040 | <0.001 | 0.039 | <0.001 |
| Reduced model (|$x_3^{(t)} = 0$|) “Surprise” | 0.040 | <0.001 | 0.039 | <0.001 |
| Rescorla–Wagner model | 0.040 | <0.001 | 0.038 | <0.001 |
| True categorical probability model | 0.040 | <0.001 | 0.038 | <0.001 |
Note: PP, posterior probability; XP, exceedance probability.
| . | Main dataset (n = 15) . | Replication dataset (n = 16) . | ||
|---|---|---|---|---|
| Model . | PP . | XP . | PP . | XP . |
| Model family comparison—perceptual models | ||||
| Full hierarchical Bayesian family | 0.873 | 0.999 | 0.777 | 0.997 |
| Reduced model family (|$\vartheta = 0$|) | 0.064 | <0.001 | 0.105 | 0.001 |
| Reduced model family (|$x_3^{(t)} = 0$|) | 0.063 | <0.001 | 0.118 | 0.002 |
| Model family comparison—response models | ||||
| “Precision” family | 0.756 | 0.991 | 0.642 | 0.930 |
| “Belief” family | 0.076 | 0.001 | 0.251 | 0.066 |
| “Surprise” family | 0.168 | 0.008 | 0.107 | 0.004 |
| Model comparison of all 11 models | ||||
| Full hierarchical Bayesian model “Precision” | 0.499 | 0.995 | 0.381 | 0.914 |
| Reduced model (|$\vartheta = 0$|) “Precision” | 0.006 | <0.001 | 0.182 | 0.074 |
| Reduced model (|$x_3^{(t)} = 0$|) “Precision” | 0.119 | 0.004 | 0.047 | <0.001 |
| Full hierarchical Bayesian model “Belief” | 0.040 | <0.001 | 0.041 | <0.001 |
| Reduced model (|$\vartheta = 0$|) “Belief” | 0.040 | <0.001 | 0.042 | <0.001 |
| Reduced model (|$x_3^{(t)} = 0$|) “Belief” | 0.040 | <0.001 | 0.074 | 0.004 |
| Full hierarchical Bayesian model “Surprise” | 0.040 | <0.001 | 0.079 | 0.004 |
| Reduced model (|$\vartheta = 0$|) “Surprise” | 0.040 | <0.001 | 0.039 | <0.001 |
| Reduced model (|$x_3^{(t)} = 0$|) “Surprise” | 0.040 | <0.001 | 0.039 | <0.001 |
| Rescorla–Wagner model | 0.040 | <0.001 | 0.038 | <0.001 |
| True categorical probability model | 0.040 | <0.001 | 0.038 | <0.001 |
| . | Main dataset (n = 15) . | Replication dataset (n = 16) . | ||
|---|---|---|---|---|
| Model . | PP . | XP . | PP . | XP . |
| Model family comparison—perceptual models | ||||
| Full hierarchical Bayesian family | 0.873 | 0.999 | 0.777 | 0.997 |
| Reduced model family (|$\vartheta = 0$|) | 0.064 | <0.001 | 0.105 | 0.001 |
| Reduced model family (|$x_3^{(t)} = 0$|) | 0.063 | <0.001 | 0.118 | 0.002 |
| Model family comparison—response models | ||||
| “Precision” family | 0.756 | 0.991 | 0.642 | 0.930 |
| “Belief” family | 0.076 | 0.001 | 0.251 | 0.066 |
| “Surprise” family | 0.168 | 0.008 | 0.107 | 0.004 |
| Model comparison of all 11 models | ||||
| Full hierarchical Bayesian model “Precision” | 0.499 | 0.995 | 0.381 | 0.914 |
| Reduced model (|$\vartheta = 0$|) “Precision” | 0.006 | <0.001 | 0.182 | 0.074 |
| Reduced model (|$x_3^{(t)} = 0$|) “Precision” | 0.119 | 0.004 | 0.047 | <0.001 |
| Full hierarchical Bayesian model “Belief” | 0.040 | <0.001 | 0.041 | <0.001 |
| Reduced model (|$\vartheta = 0$|) “Belief” | 0.040 | <0.001 | 0.042 | <0.001 |
| Reduced model (|$x_3^{(t)} = 0$|) “Belief” | 0.040 | <0.001 | 0.074 | 0.004 |
| Full hierarchical Bayesian model “Surprise” | 0.040 | <0.001 | 0.079 | 0.004 |
| Reduced model (|$\vartheta = 0$|) “Surprise” | 0.040 | <0.001 | 0.039 | <0.001 |
| Reduced model (|$x_3^{(t)} = 0$|) “Surprise” | 0.040 | <0.001 | 0.039 | <0.001 |
| Rescorla–Wagner model | 0.040 | <0.001 | 0.038 | <0.001 |
| True categorical probability model | 0.040 | <0.001 | 0.038 | <0.001 |
Note: PP, posterior probability; XP, exceedance probability.
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