on the expected mutation frequency and the desired false positive rate (Online Methods). The choice of decision threshold can be used to control the tradeoff between specificity and sensitivity, as described by a Receiver Operating Characteristic (ROC) curve (Fig. 2a, dashed line). We use a fixed threshold of 6.3 for all results presented unless indicated otherwise. This threshold corresponds to a 106.3:1 odds ratio in favor of the reference model, which is reasonable because the frequency of mutations in many tumors is only 1–10 per Mb and thus the a priori odds of a site harboring a mutation may be as low as 1:105 or 1:106.