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Register a new userOn the The Kolmogorov-Smirnov test for the CMB by M.Frommert, R.Durrer and J.Michaud
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In arxiv:1108.5354 the Kolmogorov-Smirnov (K-S) test and Kolmogorov stochasticity parameter (KSP) is applied to CMB data. Their interpretation of the KSP method, however, lacks essential elements. In addition, their main result on the Gaussianity of CMB was not a matter of debate in previous KSP-CMB studies which also included predictions on cold spots, point sources.
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We investigate the statistics of the cosmic microwave background using the Kolmogorov-Smirnov test. We show that, when we correctly de-correlate the data, the partition function of the Kolmogorov stochasticity parameter is compatible with the Kolmogorov distribution and, contrary to previous claims, the CMB data are compatible with Gaussian fluctuations with the correlation function given by standard Lambda-CDM. We then use the Kolmogorov-Smirnov test to derive upper bounds on residual point source power in the CMB, and indicate the promise of this statistics for further datasets, especially Planck, to search for deviations from Gaussianity and for detecting point sources and Galactic foregrounds.
This short note is concerned with a recent paper by N{ae}ss [arXiv:1105.5051]. We explain why the statements in the paper are absolutely irrelevant.
A new method for the determination of electric signal time-shifts is introduced. As the Kolmogorov-Smirnov test, it is based on the comparison of the cumulative distribution functions of the reference signal with the test signal. This method is very fast and thus well suited for on-line applications. It is robust to noise and its performances in terms of precision are excellent for time-shifts ranging from a fraction to several sample durations. PACS. 29.40.Gx (Tracking and position-sensitive detectors), 29.30.Kv (X- and -ray spectroscopy), 07.50.Qx (Signal processing electronics)
We consider stochastic resonance for a diffusion with drift given by a potential, which has two metastable states and two pathways between them. Depending on the direction of the forcing, the height of the two barriers, one for each path, will either oscillate alternating or in synchronisation. We consider a simplified model given by a continuous time Markov Chains with two states. This was done for alternating and synchronised wells. The invariant measures are derived for both cases and shown to be constant for the synchronised case. A PDF for the escape time from an oscillatory potential is studied. Methods of detecting stochastic resonance are presented, which are linear response, signal-noise ratio, energy, out-of-phase measures, relative entropy and entropy. A new statistical test called the conditional Kolmogorov-Smirnov test is developed, which can be used to analyse stochastic resonance. An explicit two dimensional potential is introduced, the critical point structure derived and the dynamics, the invariant state and escape time studied numerically. The six measures are unable to detect the stochastic resonance in the case of synchronised saddles. The distribution of escape times however not only shows a clear sign of stochastic resonance, but changing the direction of the forcing from alternating to synchronised saddles an additional resonance at double the forcing frequency starts to appear. The conditional KS test reliably detects the stochastic resonance. This paper is mainly based on the thesis Stochastic Resonance for a Model with Two Pathways
We present a two-dimensional version of the classical one-dimensional Kolmogorov-Smirnov (K-S) test, extending an earlier idea due to Peacock (1983) and an implementation proposed by Fasano & Franceschini (1987). The two-dimensional K-S test is used to optimise the goodness of fit in an iterative source-detection scheme for astronomical images. The method is applied to a ROSAT/HRI x-ray image of the post core-collapse globular cluster NGC 6397 to determine the most probable source distribution in the cluster core. Comparisons to other widely-used source detection methods, and to a Chandra image of the same field, show that our iteration scheme is superior in measuring statistics-limited sources in severely crowded fields.
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