We describe a model-based method, PING, for predicting nucleosome positions in MNase-Seq and MNase- or sonicated-ChIP-Seq data. PING compares favorably to NPS and TemplateFilter in scalability, accuracy and robustness to low read density. To demonstrate that PING predictions from widely available sonicated data can have sufficient spatial resolution to be to be useful for biological inference, we use Illumina H3K4me1 ChIP-seq data to detect changes in nucleosome positioning around transcription factor binding sites due to tamoxifen stimulation, to discriminate functional and non-functional transcription factor binding sites more effectively than with enrichment profiles, and to confirm that the pioneer transcription factor Foxa2 associates with the accessible major groove of nucleosomal DNA.