Fast and accurate variance-segmentation of white Gaussian data

Two new algorithms are presented for the segmentation of a white Gaussian-distributed time series having unknown but piecewise-constant variances, a problem for which only dynamic-programming (DP) approaches have. generally been suitable. The first “Sequential/MDL” includes a rough parsing via the GLR, a penalization of busy segmentations via MDL, and a refinement. The second “Gibbs Sampling” approach uses Monte Carlo ideas. From simulation it appears that both schemes are very accurate in terms of their segmentation; but that the Sequential/MDL approach is orders of magnitude lower in its computational needs both than DP or Gibbs, with Gibbs preferable to DP in this regard. The Gibbs approach can, however, be useful and efficient as a final post-processing step.