Author: Pei, Sen; Morone, Flaviano; Liljeros, Fredrik; Makse, Hernán; Shaman, Jeffrey L
Title: Inference and control of the nosocomial transmission of methicillin-resistant Staphylococcus aureus Document date: 2018_12_18
ID: 0dut9fjn_80
Snippet: We used a maximum likelihood estimator to fit and validate the power-law data in Figure 4B . For computational convenience, we fit the count of infections of each individual among 10 4 simulations (that is, we multiply the frequency in Figure 4B by 10 4 ). Denote the count data by X ¼ ðx 1 ; x 2 ; à à à ; x n Þ, and suppose the data satisfy a power-law distribution Pðx i Þ / x Àg i . Usually, empirical data follow a power-law behavior ab.....
Document: We used a maximum likelihood estimator to fit and validate the power-law data in Figure 4B . For computational convenience, we fit the count of infections of each individual among 10 4 simulations (that is, we multiply the frequency in Figure 4B by 10 4 ). Denote the count data by X ¼ ðx 1 ; x 2 ; à à à ; x n Þ, and suppose the data satisfy a power-law distribution Pðx i Þ / x Àg i . Usually, empirical data follow a power-law behavior above a lower bound: Pðx i Þ / x Àg i for x i ! x min (Clauset et al., 2009) . For a given x min , the maximum likelihood estimator of the power-law exponent g for discrete data isÄ Â¼ 1 þ n½ P n i¼1 lnðx i =x min À 1=2Þ À1 (Clauset et al., 2009) . The standard error onÄ is estimated by s ¼ Ã°Ä Ã€ 1Þ= ffiffi ð p nÞ þ Oð1=nÞ. To find the best lower bound, x min ranging from 0 to 100 was tested. The best x min was selected by choosing the value that minimizes the Kolmogorov-Smirnov (KS) statistic between the data and the fitted model. KS statistic is the maximum distance between two cumulative distribution functions (CDFs): D ¼ max x!xmin jSðxÞ À PðxÞj, where SðxÞ is the CDF of the data larger than x min , and PðxÞ is the CDF of the power-law model obtained from MLE. In Figure 4 -figure supplement 1A, the change of KS statistic for different x min values is reported. We choose the best x min value as 24. The fitted power-law exponent isÄ Â¼ 2:13 with a standard deviation of 0.12.
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