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Since software fault detection process is well-modeled by a non-homogeneous Poisson process, it is of great interest to estimate accurately the intensity function from observed software-fault data. In the existing work the same authors introduced the wavelet-based techniques for this problem and found that the Haar wavelet transform provided a very powerful performance in estimating software intensity function. In this paper, we also study the Haar-wavelet-transform-based approach to be investigated from the point of view of multiscale analysis. More specifically, a Bayesian multiscale intensity estimation algorithm is employed. In numerical study with real software-fault count data, we compare the Bayesian multiscale intensity estimation with the existing non-Bayesian wavelet-based estimation as well as the conventional maximum likelihood estimation method and least squares estimation method.