MOTIVATION: Haplotype models enjoy a wide range of applications in population inference and disease gene discovery. The hidden Markov models traditionally used for haplotypes are hindered by the dubious assumption that dependencies occur only between consecutive pairs of variants. In this article, we apply the multivariate Bernoulli (MVB) distribution to model haplotype data. The MVB distribution relies on interactions among all sets of variants, thus allowing for the detection and exploitation of long-range and higher-order interactions. We discuss penalized estimation and present an efficient algorithm for fitting sparse versions of the MVB distribution to haplotype data. Finally, we showcase the benefits of the MVB model in predicting DNaseI hypersensitivity (DH) status--an epigenetic mark describing chromatin accessibility--from population-scale haplotype data. RESULTS: We fit the MVB model to real data from 59 individuals on whom both haplotypes and DH status in lymphoblastoid cell lines are publicly available. The model allows prediction of DH status from genetic data (prediction R2=0.12 in cross-validations). Comparisons of prediction under the MVB model with prediction under linear regression (best linear unbiased prediction) and logistic regression demonstrate that the MVB model achieves about 10% higher prediction R2 than the two competing methods in empirical data. AVAILABILITY AND IMPLEMENTATION: Software implementing the method described can be downloaded at http://bogdan.bioinformatics.ucla.edu/software/. CONTACT: [email protected] or [email protected].