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Table. 1 Comparison between uGCA methods and conventional GCA under different noise level

From: Robust unified Granger causality analysis: a normalized maximum likelihood form

  uGCA-TP (%) uGCA-MIX (%) uGCA-NML (%) GCA (\(\alpha =0.05\)) (%) GCA (\(\alpha =0.01\)) (%)
Low      
 TPR 100 98.678 100 100 100
 TNR 99.062 99.662 99.662 94.162 98.010
 Ground-truth rate 81.9 86.3 93.1 25.6 64.0
Moderate      
 TPR 100 98.478 100 100 100
 TNR 98.714 99.662 99.624 93.576 97.729
 Ground-truth rate 74.5 84.6 91.2 18.9 58.4
High       
 TPR 100 98.678 100 100 100
 TNR 98.410 99.433 99.371 93.048 97.148
 Ground-truth rate 69.7 81.7 87.5 16.0 52.1
  1. The variance of the low noise level data ranges from 1.5 to 2, and the moderate (high) level data ranges from 3.5 to 3 (5.5–6). The ground-truth rate denoted the total numbers of the obtained individual connection network which was same as the ground-truth network, divided by the sample number (1000)
  2. Bold values indicate more indicative of the method's performance