. 2020 Aug 11;9:e54051. doi: 10.7554/eLife.54051

Table 1. (a) Results of Bayesian model selection: Model probability ( $p (m | y)$ ) and protected exceedance probabilities ( $ϕ_{p}$ ).

Please refer to the participants’ LME and BMS results in Table 1—source datas 1 and 2, respectively. (b) Average maximum a-posteriori estimates of the learning and arbitration parameters of the winning model (Arbitrated three-level HGF). Please refer to participants’ individual posterior parameter estimates for perceptual and response model parameters in Table 1—source datas 3 and 4.

Table 1—source data 1. Log model evidences for all models.

elife-54051-table1-data1.mat^{(4.5KB, mat)}

Table 1—source data 2. Random effects Bayesian model selection.

elife-54051-table1-data2.mat^{(9.4KB, mat)}

Table 1—source data 3. Maximum a posteriori estimates of the perceptual model parameters and response model parameters influencing choice along with subject IDs.

elife-54051-table1-data3.mat^{(3.9KB, mat)}

Table 1—source data 4. Maximum a posteriori estimates of the response model parameters influencing wagers along with subject IDs.

elife-54051-table1-data4.mat^{(4.2KB, mat)}

	Perceptual Models:
Response models:	Arbitrated	Advice Only	Card Only
	3-level HGF
$p (m \| y)$	0.63	0.04	0.02
$ϕ_{p}$	0.99	4.7e-12	4.7e-12
	Normative HGF
$p (m \| y)$	0.03	0.03	0.02
$ϕ_{p}$	4.7e-12	4.7e-12	4.7e-12
	2-level HGF
$p (m \| y)$	0.15	0.06	0.02
$ϕ_{p}$	6.2e-05	4.7e-12	4.7e-12
Perceptual Model Parameters	Mean	SD	Response Model Parameters	Mean	SD
$κ_{c}$	0.58	0.17	$ζ$	1.03	1.24
$κ_{a}$	0.56	0.28	$β_{1}$	−1.59	0.94
$ϑ_{c}$	0.59	0.07	$β_{2}$	1.42	1.69
$ϑ_{a}$	0.62	0.09	$β_{3}$	0.23	1.37
			$β_{4}$	0.63	1.24
			$β_{5}$	−2.97	2.47
			$β_{6}$	−0.51	1.83
			$β_{c h}$	2.25	0.92

Table 1. (a) Results of Bayesian model selection: Model probability (p(m|y)) and protected exceedance probabilities (ϕp).

Table 1. (a) Results of Bayesian model selection: Model probability ( $p (m | y)$ ) and protected exceedance probabilities ( $ϕ_{p}$ ).