Table 3.

Means and variances of the priors on perceptual parameters and starting values of the beliefs of the winning HGF₂ model

Prior	Mean	Variance
κ (all)	1	0
ω2 (Study 1)	−2.17	16
ω2 (Study 2)	−2.16	16
ω2 (Study 3)	−2.22	16
ω3(0) (all)	−7	0
μ2(0) (all)	0	0
σ2(0) (all)	0.1	0
μ3(0) (all)	1	0
σ3(0) (all)	1	0
ζ (all)	48	1

Free parameter ω₂ was estimated in its unbounded (linear) space. The prior values on ω₂ [mean (variance)] were: −2.17 (16), −2.16 (16), and −2.22 (16) for Studies 1, 2, and 3, respectively. These prior values were obtained using an ideal observer model that received the input that each participant had experienced. The response model parameter, ζ, was log-transformed, to allow for its estimation in an unbounded space. The remaining parameters were fixed and not estimated in each participant: σ₂⁽⁰⁾, σ₃⁽⁰⁾, κ, μ₂⁽⁰⁾, μ₃⁽⁰⁾. The coupling strength between levels 2 and 3 is κ, which was fixed to 1 (Hein et al., 2021). Among the fixed parameters, the following ones operate in their log-transformed space: σ₂⁽⁰⁾, σ₃⁽⁰⁾, κ, μ₃⁽⁰⁾. The prior variances are given in the space in which the parameters are typically estimated.