Table 2 Accuracy of different methods for choosing summary statistics on a global scale
MethodεParameterRARMISEaRAEb modeRAE meanRAE medianEmbedded ImagecCov. Pd
all0.001Embedded Image0.143(0.147)0.062(0.074)0.065(0.075)0.062(0.075)0.0720.011*
Embedded Image0.452(0.231)0.269(0.213)0.269(0.222)0.265(0.218)0.0340.610
ω0.446(0.272)0.221(0.225)0.215(0.218)0.219(0.22)0.0270.859
0.01Embedded Image0.141(0.145)0.061(0.072)0.064(0.074)0.065(0.075)0.0820.003*
Embedded Image0.466(0.257)0.299(0.21)0.286(0.225)0.282(0.226)0.0190.992
ω0.432(0.259)0.233(0.232)0.226(0.23)0.232(0.232)0.0260.880
0.1Embedded Image0.140(0.134)0.065(0.075)0.067(0.078)0.067(0.075)0.0810.003*
Embedded Image0.463(0.272)0.324(0.238)0.306(0.248)0.296(0.243)0.0320.677
ω0.431(0.263)0.234(0.229)0.228(0.22)0.226(0.223)0.0380.482
pls.glob0.001Embedded Image0.171(0.16)0.077(0.087)0.083(0.089)0.081(0.088)0.0380.466
Embedded Image0.488(0.276)0.291(0.223)0.289(0.252)0.276(0.228)0.0240.936
ω0.451(0.275)0.238(0.221)0.234(0.224)0.237(0.227)0.0220.969
0.01Embedded Image0.166(0.152)0.080(0.09)0.079(0.09)0.079(0.089)0.0350.562
Embedded Image0.480(0.291)0.307(0.223)0.295(0.268)0.293(0.242)0.0380.473
ω0.441(0.262)0.241(0.234)0.230(0.225)0.229(0.226)0.0350.562
0.1Embedded Image0.171(0.146)0.083(0.091)0.086(0.097)0.087(0.094)0.0370.497
Embedded Image0.469(0.283)0.319(0.237)0.307(0.286)0.310(0.276)0.0560.089
ω0.433(0.265)0.240(0.226)0.234(0.224)0.234(0.23)0.0490.178
lgb.glob0.001Embedded Image0.149(0.152)0.064(0.074)0.065(0.076)0.064(0.074)0.0820.002*
Embedded Image0.435(0.204)0.270(0.231)0.261(0.214)0.247(0.205)0.0380.466
ω0.456(0.275)0.235(0.23)0.230(0.237)0.232(0.224)0.0250.913
0.01Embedded Image0.145(0.15)0.066(0.076)0.066(0.078)0.066(0.076)0.103<0.001*
Embedded Image0.450(0.223)0.281(0.215)0.269(0.217)0.258(0.209)0.0460.238
ω0.436(0.27)0.235(0.234)0.222(0.223)0.225(0.228)0.0250.916
0.1Embedded Image0.147(0.142)0.068(0.079)0.067(0.078)0.069(0.079)0.135<0.001*
Embedded Image0.471(0.284)0.288(0.209)0.301(0.249)0.271(0.233)0.0540.103
ω0.427(0.259)0.232(0.222)0.225(0.216)0.228(0.22)0.0420.329
l1b.glob0.001Embedded Image0.188(0.178)0.075(0.087)0.074(0.087)0.076(0.088)0.0350.573
Embedded Image0.445(0.202)0.271(0.236)0.261(0.232)0.256(0.216)0.0230.954
ω0.487(0.297)0.251(0.259)0.226(0.227)0.232(0.226)0.0310.723
0.01Embedded Image0.178(0.17)0.075(0.087)0.075(0.088)0.075(0.085)0.0310.711
Embedded Image0.463(0.217)0.288(0.24)0.271(0.238)0.259(0.221)0.0290.805
ω0.468(0.288)0.255(0.262)0.228(0.222)0.235(0.233)0.0340.595
0.1Embedded Image0.177(0.173)0.078(0.092)0.078(0.094)0.079(0.094)0.0430.311
Embedded Image0.508(0.299)0.307(0.21)0.304(0.269)0.290(0.248)0.0510.144
ω0.449(0.272)0.238(0.241)0.237(0.222)0.239(0.227)0.0310.716
l2b.glob0.001Embedded Image0.183(0.173)0.075(0.087)0.074(0.085)0.074(0.086)0.0290.794
Embedded Image0.441(0.202)0.273(0.229)0.257(0.228)0.254(0.212)0.0280.828
ω0.487(0.296)0.251(0.257)0.231(0.226)0.234(0.229)0.0330.648
0.01Embedded Image0.180(0.173)0.077(0.087)0.077(0.088)0.076(0.087)0.0300.766
Embedded Image0.459(0.213)0.278(0.242)0.262(0.235)0.259(0.214)0.0280.815
ω0.470(0.288)0.253(0.26)0.231(0.221)0.237(0.229)0.0370.497
0.1Embedded Image0.176(0.171)0.080(0.092)0.080(0.096)0.080(0.093)0.0410.365
Embedded Image0.503(0.281)0.300(0.213)0.297(0.249)0.283(0.253)0.0520.139
ω0.445(0.267)0.240(0.24)0.239(0.227)0.236(0.225)0.0300.755
  • RARMISE and RAE are given as the median across 500 independent estimations with true values drawn from the prior (median absolute deviation in parentheses). Embedded Image and ω were estimated on the log10-scale. *P < 0.05 without correction for multiple testing; cf. Figure S8.

  • a Relative absolute root mean integrated squared error (see text) with respect to the true value.

  • b Relative absolute error with respect to the true value.

  • c Kolmogorov–Smirnov distance between empirical distribution of posterior probabilities of the true parameter and U(0, 1).

  • d P-value from a Kolmogorov–Smirnov test.