tokens: therefore agree. At 5.5 z 5.9, the GOLD distribution lies between the bounds shown in Fig. 8 . At z > 5.9, the difference is attributable to the small sample size of the sub-samples (see the text). The differences between the SILVER and GOLD samples at 5.7 z 5.9 are due to the small sample size of the GOLD sample. The difference in number of lines of sight in this range is a factor of 2.5, which reflects the fact that very high-quality spectra are harder to obtain for quasars at z > 6.0. The SILVER and GOLD sample are marginally consistent according to a KS test( p 0.2). On the other hand, the sizes of the SILVER and GOLD samples are similar at 5.9 z 6.1, and agree with each other well. However, the additional lines of sight included in the BRONZE sample are of insufficient quality to distinguish opacity beyond τ eff ≳ 3. Since the mean opacity measured in the SILVER sample is roughly τ eff ∼ 4.5, these S/N 5 spectra yield upper limits (equal to twice the error) which are very poor in comparison. The small sample size in this bin (8 measurements in the GOLD sample, and 16 in the BRONZE one) mitigates the significance of this discrepancy, with the KS level indicating only mild discrepancy ( p 0.2). In addition, two of the BRONZE lines of sight do show tentative signs of residual transmission. The z = 6.34 quasar J1148+0702 displays a transmission peak within 6 Å of the formal end of the proximity zone, while the z = 6.23 quasar J2325 displays such a peak outside of its proximity zone but has an S/N of 1.8, making it impossible to definitely rule of reduction issues. Further scrutiny of these objects is required in order to determine whether these peaks may be related to particularly long and sporadic proximity zones. In light of these results, we decide to adopt the SILVER distribution in every instance in this paper where the data are presented or analysed in the form of a CDF. The maximum-likelihood method described above has been explicitly designed to account for observational errors and sensitivity, and we accordingly use the BRONZE sample only in Section 6 . 5 COMPARISON WITH MODELS In this section, we compare the updated CDFs of Lyman-α transmission in 50 cMpc h −1 windows with three simulations. Here, we briefly describe these simulations and outline their most relevant features. When comparing predictions from these numerical simulations to observational results, it is important to keep in mind a few caveats. First, all of the following numerical models explicitly rescale the ionizing background intensities to match the observed mean effective optical depth of the observations presented in this paper, 〈 F 〉 obs , by freely choosing a parameter A suchthat: At low redshift ( z ≲ 5.7), this rescaling is small and is somewhat justified by the difficulty of self-consistently generating the ionizing UVB. In the following analysis, all simulation snapshots have been rescaled in this way to observed 〈 F 〉 obs for each redshift bin. The
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