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Table 1 Number of significant pairs in synthetic data

From: Determining significance of pairwise co-occurrences of events in bursty sequences

Dataset Number of significant pairs
  W C D  
  UL FL FL(r) UL FL FL(r) UL FL FL(r)  
1. Uncorrelated 39 0 0 54 1 0 54 1 0  
2. Correlated 33 1 2 54 2 2 53 2 2  
3. Directed 38 1 1 54 1 1 54 2 1.5 (1)
4. Distinct correlated 38 1 1 54 1 1 54 1 1  
5. Distinct directed 39 1 1 54 1 1 54 1 1  
  Number of randomizations where (a, b) found significant
1. Uncorrelated 85 1 0 97 0 0 90:92 1:1 0:1  
2. Correlated 100 100 100 100 100 100 100:100 100:100 100:100  
3. Directed 100 93 99 100 88 99 100:98 100:1 100:2 (2)
4. Distinct correlated 94 34 35 97 33 34 95:94 35:33 36:33  
5. Distinct directed 93 29 31 99 5 17 96:97 31:5 33:0  
  1. (1) Median number of pairs of event types, over 100 randomly generated sequences, whose co-occurrence score is significant. Results are shown for five types of synthetic datasets. (2) The number of randomizations in which the planted pair (a, b) is found significant. UL, FL, and FL(r) correspond to the null models, and W, C, and D to the window, undirected, and directed co-occurrence scores. For the D score, the two values s1: s2 denote the number of randomizations in which (ab) and (ba) are found significant. The empirical p-values are based on 1000 randomizations. Results are shown for p-value threshold 0.01, with 10 event types, w = 50, burst lengths in [100, 200], sequence length 100000, and parameter values p1 = 0.01, p2 = 0.1, with 50 bursts per sequence. For the datasets 4 and 5, the number of bursts containing correlations was randomly chosen from [5, 25].