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Table 5 Summary of log-predictive scores and Kullback–Leibler divergences for boys and girls in the flexible priors setting

From: Bayesian probabilistic forecasting with large-scale educational trend data: a case study using NAEP

  LPS KLD
EBL HG-3 HG-4 HG-UIP HG-RIC HG-BRIC EBL HG-3 HG-4 HG-UIP HG-RIC HG-BRIC
Boys
 Uniform 0.395* 0.402 0.410 0.398 0.397 0.398 0.098* 0.098 0.098 0.097 0.097 0.097
 Binomial (m = 2) 0.397 0.404 0.411 0.403 0.401 0.403 0.097 0.098 0.098 0.098 0.097 0.098
 Binomial (m = 4) 0.395* 0.403* 0.412* 0.397 0.395 0.397 0.098* 0.099* 0.099* 0.097 0.097 0.097
 Beta-binomial 0.397 0.405 0.412 0.407 0.405 0.412 0.097 0.098 0.099 0.098 0.097 0.098
Girls
 Uniform 0.397* 0.406 0.412 0.401 0.400 0.401 0.095 0.096 0.097 0.096 0.096 0.096
 Binomial (m = 2) 0.406 0.416 0.423 0.413 0.413 0.413 0.096 0.097 0.098 0.097 0.097 0.097
 Binomial (m = 4) 0.392* 0.400* 0.407* 0.394 0.394 0.394 0.095* 0.096* 0.096* 0.095 0.095 0.095
 Beta-binomial 0.394 0.403 0.410 0.401 0.394 0.401 0.096 0.096 0.097 0.096 0.096 0.096
  1. Values with * indicate that these analyses was based on fewer than the full 64 total possible models due to computational tolerances being reached in the calculation of likelihoods. In no case were fewer than 30 models used in the LPS and KLD calculations for these cases
  2. EBL: Local empirical Bayes; HG-3: Hyper-g prior with \(\alpha = 3\); HG-4: Hyper-g prior with \(\alpha = 4\); HG-UIP: Hyper-g prior with UIP setting; HG-RIC: Hyper-g prior with RIC setting; HG-BRIC: Hyper-g prior with BRIC setting. Uniform: uniform model prior; Binomial (m = 2): Binomial model prior with model size = 2; Binomial (m = 4): Binomial model prior with model size = 4; Beta-binomial: Beta-binomial model prior