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We discuss methods currently in use for determining the significance of peaks in the periodograms of time series. We discuss some general methods for constructing significance tests, false alarm probability functions, and the role played in these by independent random variables and by empirical and theoretical cumulative distribution functions. We also discuss the concept of independent frequencies in periodogram analysis. We propose a practical method for estimating the significance of periodogram peaks, applicable to all time series irrespective of the spacing of the data. This method, based on Monte Carlo simulations, produces significance tests that are tailor-made for any given astronomical time series.
I present the Phase Distance Correlation (PDC) periodogram -- a new periodicity metric, based on the Distance Correlation concept of Gabor Szekely. For each trial period PDC calculates the distance correlation between the data samples and their phase
We give qualitative and quantitative improvements to theorems which enable significance testing in Markov Chains, with a particular eye toward the goal of enabling strong, interpretable, and statistically rigorous claims of political gerrymandering.
We compare our analysis of the Baryon Acoustic Oscillations (BAO) feature in the correlation functions of SDSS BOSS DR12 LOWZ and CMASS galaxy samples with the findings of arXiv:1509.06371v2. Using subsets of the data we obtain an empirical estimate
Three peaks and two dips have been detected in the power spectrum of the cosmic microwave background from the BOOMERANG experiment, at $ell sim 210, 540, 840$ and $ell sim 420, 750$, respectively. Using model-independent analyses, we find that all fi
In this paper we discuss several methods of significance calculation and point out the limits of their applicability. We then introduce a self consistent scheme for source detection and discuss some of its properties. The method allows incorporating