Do wavelets really detect non-Gaussianity in the 4-year COBE data?
Version of Record online: 4 APR 2002
Monthly Notices of the Royal Astronomical Society
Volume 318, Issue 4, pages 1157–1163, November 2000
How to Cite
Mukherjee, P., Hobson, M. P. and Lasenby, A. N. (2000), Do wavelets really detect non-Gaussianity in the 4-year COBE data?. Monthly Notices of the Royal Astronomical Society, 318: 1157–1163. doi: 10.1046/j.1365-8711.2000.03800.x
- Issue online: 4 APR 2002
- Version of Record online: 4 APR 2002
- Accepted 2000 June 23. Received 2000 June 12; in original form 1999 September 20
- methods: data analysis;
- cosmic microwave background
We investigate the detection of non-Gaussianity in the 4-year COBE data reported by Pando, Valls-Gabaud & Fang, using a technique based on the discrete wavelet transform. Their analysis was performed on the two DMR faces centred on the North and South Galactic poles, respectively, using the Daubechies 4 wavelet basis. We show that these results depend critically on the orientation of the data, and so should be treated with caution. For two distinct orientations of the data, we calculate estimates of the skewness, kurtosis and scale–scale correlation of the corresponding wavelet coefficients in all of the available scale domains of the transform. We obtain several detections of non-Gaussianity in the DMR-DSMB map at greater than the 99 per cent confidence level, but most of these occur on pixel–pixel scales and are therefore not cosmological in origin. Indeed, after removing all multipoles beyond ℓ=40 from the COBE maps, only one robust detection remains. Moreover, using Monte Carlo simulations, we find that the probability of obtaining such a detection by chance is 0.59. We repeat the analysis for the 53+90 GHz coadded COBE map. In this case, after removing ℓ>40 multipoles, two non-Gaussian detections at the 99 per cent level remain. Nevertheless, again using Monte Carlo simulations, we find that the probability of obtaining two such detections by chance is 0.28. Thus, we conclude the wavelet technique does not yield strong evidence for non-Gaussianity of cosmological origin in the 4-year COBE data.