Table 2. Prior mean and variance of the perceptual and response model parameters.

Model		Prior mean	Prior variance
Perceptual models:
Three-level HGF	${\kappa }_a$, ${\kappa }_c$	0.5	1
	${\vartheta }_a$, ${\vartheta }_c$	0.55	1
Normative HGF	${\kappa }_a$, ${\kappa }_c$	0.5	0
	${\vartheta }_a$, ${\vartheta }_c$	0.55	0
Two-level HGF	${\vartheta }_a$, ${\vartheta }_c$	0.00062	0
Response models:
	${\beta }_{1-6}$	0	4
	${\beta }_{ch}$	48	1
	${\beta }_0$	6.21	4
	${\beta }_{wager}$	1.50	100
1. Arbitrated	$\zeta$	0	25
2. Advice Only	$\zeta$	Inf	0
3. Card Only	$\zeta$	0	0

Note: The prior variances are given in the numeric space in which parameters are estimated. $\kappa$, $\vartheta$, and ${\displaystyle {\mu }_3^{\left(k=0\right)}}$ are estimated in logit-space, while the other parameters are estimated in log-space. Although the prior variances for all parameters are set to be rather broad, we selected a shrinkage prior mean and variance for the decision noise parameter ${\beta }_{ch}$ such that behavior is explained more by variations in the remaining parameters rather than decision noise.