A computer-implemented method for calling variations in mapped mated reads obtained from a sample polynucleotide sequence compared to a reference polynucleotide sequence, the method comprising: receiving the reference polynucleotide sequence and mapped mated reads, wherein the mapped mated reads are obtained from the sample polynucleotide sequence and are mapped to locations in the reference polynucleotide sequence; for each of a plurality of positions on the reference polynucleotide sequence: calculating one or more reference scores, each reference score for a hypothesis different from the reference polynucleotide sequence at the position and calculated based on the mapped mated reads using a Bayesian formulation for the hypothesis; identifying local areas corresponding to positions having a reference score above a threshold; using de Bruijn graph-based algorithms for determining graphs to identify local de novo intervals, each local de novo interval comprising one or more positions at which the graph diverges from the reference polynucleotide sequence; combining the local areas and the local de novo intervals to form optimization intervals; for each optimization interval: using the reference scores or one or more graphs of the optimization interval to generate an initial sequence hypothesis; and modifying the initial sequence hypothesis to obtain an optimized sequence hypothesis having an increased probability of being correct based on the mapped mated reads that map to the optimization interval; using the optimized sequence hypotheses to identify and call variations detected in the mapped mated reads in relation to the reference polynucleotide sequence; and outputting a list of the variations, each describing a manner in which the mapped mated reads are observed to differ from the reference polynucleotide sequence at or near a specific location. receiving the reference polynucleotide sequence and mapped mated reads, wherein the mapped mated reads are obtained from the sample polynucleotide sequence and are mapped to locations in the reference polynucleotide sequence; for each of a plurality of positions on the reference polynucleotide sequence: calculating one or more reference scores, each reference score for a hypothesis different from the reference polynucleotide sequence at the position and calculated based on the mapped mated reads using a Bayesian formulation for the hypothesis; calculating one or more reference scores, each reference score for a hypothesis different from the reference polynucleotide sequence at the position and calculated based on the mapped mated reads using a Bayesian formulation for the hypothesis; identifying local areas corresponding to positions having a reference score above a threshold; using de Bruijn graph-based algorithms for determining graphs to identify local de novo intervals, each local de novo interval comprising one or more positions at which the graph diverges from the reference polynucleotide sequence; combining the local areas and the local de novo intervals to form optimization intervals; for each optimization interval: using the reference scores or one or more graphs of the optimization interval to generate an initial sequence hypothesis; and modifying the initial sequence hypothesis to obtain an optimized sequence hypothesis having an increased probability of being correct based on the mapped mated reads that map to the optimization interval; using the reference scores or one or more graphs of the optimization interval to generate an initial sequence hypothesis; and modifying the initial sequence hypothesis to obtain an optimized sequence hypothesis having an increased probability of being correct based on the mapped mated reads that map to the optimization interval; using the optimized sequence hypotheses to identify and call variations detected in the mapped mated reads in relation to the reference polynucleotide sequence; and outputting a list of the variations, each describing a manner in which the mapped mated reads are observed to differ from the reference polynucleotide sequence at or near a specific location.