Weighted Kolmogorov-Smirnov test: Accounting for the tails

Chicheportiche, Rémy; Bouchaud, Jean‐Philippe

doi:10.1103/physreve.86.041115

Cited by 41 publications

(39 citation statements)

References 25 publications

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“…In this domain the K-S test generates hugely overestimated confidence ranges, making us essentially blind to small but in principle detectable deviations. This problem was considered by Chicheportiche & Bouchaud (2012), who suggest a weighted modification of the K-S statistic (A1):…”

Section: Discussionmentioning

confidence: 99%

Enhanced models for stellar Doppler noise reveal hints of a 13-year activity cycle of 55 Cancri

Baluev

2014

Monthly Notices of the Royal Astronomical Society

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We consider the impact of Doppler noise models on the statistical robustness of the exoplanetary radial-velocity fits. We show that the traditional model of the Doppler noise with an additive jitter can generate large non-linearity effects, decreasing the reliability of the fit, especially in the cases when a correleated Doppler noise is involved. We introduce a regularization of the additive noise model that can gracefully eliminate its singularities together with the associated non-linearity effects.We apply this approach to Doppler time-series data of several exoplanetary systems. It demonstrates that our new regularized noise model yields orbital fits that have either increased or at least the same statistical robustness, in comparison with the simple additive jitter. Various statistical uncertainties in the parametric estimations are often reduced, while planet detection significance is often increased.Concerning the 55 Cnc five-planet system, we show that its Doppler data contain significant correlated ("red") noise. Its correlation timescale is in the range from days to months, and its magnitude is much larger than the effect of the planetary N -body perturbations in the radial velocity (these perturbations thus appear undetectable). Characteristics of the red noise depend on the spectrograph/observatory, and also show a cyclic time variation in phase with the public Ca II H&K and photometry measurements. We interpret this modulation as a hint of the long-term activity cycle of 55 Cnc, similar to the Solar 11-year cycle. We estimate the 55 Cnc activity period by 12.6± 2.5 1.0 yrs, with the nearest minimum presumably expected in 2014 or 2015.

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Section: Discussionmentioning

confidence: 99%

Enhanced models for stellar Doppler noise reveal hints of a 13-year activity cycle of 55 Cancri

Baluev

2014

Monthly Notices of the Royal Astronomical Society

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“…This problem was revisited in detail in Ref. [71] in connection with a generalization of the KolmogorovSmirnov ("goodness-of-fit") test. In particular, the prefactor of the power law decay of Q(t) was computed.…”

Section: Brownian Walker In An Expanding Cagementioning

confidence: 99%

Persistence and first-passage properties in nonequilibrium systems

Bray

Majumdar

Schehr

2013

Advances in Physics

519

669

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In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

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“…of neuronal data. A weighted Kolmogorov-Smirnov test with a refined goodness of fit estimate valid up to extreme tails [76].…”

Section: Discussionmentioning

confidence: 99%

Power-law statistics and universal scaling in the absence of criticality

2017

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Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates, and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.

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Weighted Kolmogorov-Smirnov test: Accounting for the tails

Cited by 41 publications

References 25 publications

Enhanced models for stellar Doppler noise reveal hints of a 13-year activity cycle of 55 Cancri

Enhanced models for stellar Doppler noise reveal hints of a 13-year activity cycle of 55 Cancri

Persistence and first-passage properties in nonequilibrium systems

Power-law statistics and universal scaling in the absence of criticality

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