False discovery rate: setting the probability of false claim of detection

When testing multiple hypothesis in a survey --e.g. many different source locations, template waveforms, and so on-- the final result consists in a set of confidence intervals, each one at a desired confidence level. But the probability that at least one of these intervals does not cover the true value increases with the number of trials. With a sufficiently large array of confidence intervals, one can be sure that at least one is missing the true value. In particular, the probability of false claim of detection becomes not negligible. In order to compensate for this, one should increase the confidence level, at the price of a reduced detection power. False discovery rate control is a relatively new statistical procedure that bounds the number of mistakes made when performing multiple hypothesis tests. We shall review this method, discussing exercise applications to the field of gravitational wave surveys.Comment: 7 pages, 3 table, 3 figures. Prepared for the Proceedings of GWDAW 9 (http://lappc-in39.in2p3.fr/GWDAW9) A new section was added with a numerical example, along with two tables and a figure related to the new section. Many smaller revisions to improve readibilit

Detection of Anomalous Reactor Activity Using Antineutrino Count Rate Evolution Over the Course of a Reactor Cycle

This paper analyzes the sensitivity of antineutrino count rate measurements to changes in the fissile content of civil power reactors. Such measurements may be useful in IAEA reactor safeguards applications. We introduce a hypothesis testing procedure to identify statistically significant differences between the antineutrino count rate evolution of a standard 'baseline' fuel cycle and that of an anomalous cycle, in which plutonium is removed and replaced with an equivalent fissile worth of uranium. The test would allow an inspector to detect anomalous reactor activity, or to positively confirm that the reactor is operating in a manner consistent with its declared fuel inventory and power level. We show that with a reasonable choice of detector parameters, the test can detect replacement of 73 kg of plutonium in 90 days with 95% probability, while controlling the false positive rate at 5%. We show that some improvement on this level of sensitivity may be expected by various means, including use of the method in conjunction with existing reactor safeguards methods. We also identify a necessary and sufficient daily antineutrino count rate to achieve the quoted sensitivity, and list examples of detectors in which such rates have been attained.Comment: 9 pages, 7 figures, submitted to J. Appl. Phy

Detecting the Baryons in Matter Power Spectra

We examine power spectra from the Abell/ACO rich cluster survey and the 2dF Galaxy Redshift Survey (2dfGRS) for observational evidence of features produced by the baryons. A non-negligible baryon fraction produces relatively sharp oscillatory features at specific wavenumbers in the matter power spectrum. However, the mere existence of baryons will also produce a global suppression of the power spectrum. We look for both of these features using the false discovery rate (FDR) statistic. We show that the window effects on the Abell/ACO power spectrum are minimal, which has allowed for the discovery of discrete oscillatory features in the power spectrum. On the other hand, there are no statistically significant oscillatory features in the 2dFGRS power spectrum, which is expected from the survey's broad window function. After accounting for window effects, we apply a scale-independent bias to the 2dFGRS power spectrum, P_{Abell}(k) = b^2P_{2dF}(k) and b = 3.2. We find that the overall shapes of the Abell/ACO and the biased 2dFGRS power spectra are entirely consistent over the range 0.02 <= k <= 0.15hMpc^-1. We examine the range of Omega_{matter} and baryon fraction for which these surveys could detect significant suppression in power. The reported baryon fractions for both the Abell/ACO and 2dFGRS surveys are high enough to cause a detectable suppression in power (after accounting for errors, windows and k-space sampling). Using the same technique, we also examine, given the best fit baryon density obtained from BBN, whether it is possible to detect additional suppression due to dark matter-baryon interaction. We find that the limit on dark matter cross section/mass derived from these surveys are the same as those ruled out in a recent study by Chen, Hannestad and Scherrer.Comment: 11 pages of text, 6 figures. Submitted to Ap

ExplainIt! -- A declarative root-cause analysis engine for time series data (extended version)

We present ExplainIt!, a declarative, unsupervised root-cause analysis engine that uses time series monitoring data from large complex systems such as data centres. ExplainIt! empowers operators to succinctly specify a large number of causal hypotheses to search for causes of interesting events. ExplainIt! then ranks these hypotheses, reducing the number of causal dependencies from hundreds of thousands to a handful for human understanding. We show how a declarative language, such as SQL, can be effective in declaratively enumerating hypotheses that probe the structure of an unknown probabilistic graphical causal model of the underlying system. Our thesis is that databases are in a unique position to enable users to rapidly explore the possible causal mechanisms in data collected from diverse sources. We empirically demonstrate how ExplainIt! had helped us resolve over 30 performance issues in a commercial product since late 2014, of which we discuss a few cases in detail.Comment: SIGMOD Industry Track 201

On a random walk with memory and its relation to Markovian processes

We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk. The time evolution of the displacement is given by an equivalent Markovian dynamical process. The probability density for the position of the walker is the same at any time as for a random walk with shrinking steps, although the two-time correlation functions are quite different.Comment: 10 pages, 4 figure

The Inverse Shapley Value Problem

For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice theory as a measure of the "influence" of voters. The \emph{Inverse Shapley Value Problem} is the problem of designing a weighted voting scheme which (approximately) achieves a desired input vector of values for the Shapley-Shubik indices. Despite much interest in this problem no provably correct and efficient algorithm was known prior to our work. We give the first efficient algorithm with provable performance guarantees for the Inverse Shapley Value Problem. For any constant \eps > 0 our algorithm runs in fixed poly$(n)$ time (the degree of the polynomial is independent of \eps) and has the following performance guarantee: given as input a vector of desired Shapley values, if any "reasonable" weighted voting scheme (roughly, one in which the threshold is not too skewed) approximately matches the desired vector of values to within some small error, then our algorithm explicitly outputs a weighted voting scheme that achieves this vector of Shapley values to within error \eps. If there is a "reasonable" voting scheme in which all voting weights are integers at most \poly(n) that approximately achieves the desired Shapley values, then our algorithm runs in time \poly(n) and outputs a weighted voting scheme that achieves the target vector of Shapley values to within error $\eps=n^{-1/8}.