Reaaliaikainen käännepisteiden havainta hylkäysvirheaste- ja kommunikaatiorajoitteilla

In a quickest detection problem, the objective is to detect abrupt changes in a stochastic sequence as quickly as possible, while limiting rate of false alarms. The development of algorithms that after each observation decide to either stop and declare a change as having happened, or to continue the monitoring process has been an active line of research in mathematical statistics. The algorithms seek to optimally balance the inherent trade-off between the average detection delay in declaring a change and the likelihood of declaring a change prematurely. Change-point detection methods have applications in numerous domains, including monitoring the environment or the radio spectrum, target detection, financial markets, and others. Classical quickest detection theory focuses settings where only a single data stream is observed. In modern day applications facilitated by development of sensing technology, one may be tasked with monitoring multiple streams of data for changes simultaneously. Wireless sensor networks or mobile phones are examples of technology where devices can sense their local environment and transmit data in a sequential manner to some common fusion center (FC) or cloud for inference. When performing quickest detection tasks on multiple data streams in parallel, classical tools of quickest detection theory focusing on false alarm probability control may become insufficient. Instead, controlling the false discovery rate (FDR) has recently been proposed as a more useful and scalable error criterion. The FDR is the expected proportion of false discoveries (false alarms) among all discoveries. In this thesis, novel methods and theory related to quickest detection in multiple parallel data streams are presented. The methods aim to minimize detection delay while controlling the FDR. In addition, scenarios where not all of the devices communicating with the FC can remain operational and transmitting to the FC at all times are considered. The FC must choose which subset of data streams it wants to receive observations from at a given time instant. Intelligently choosing which devices to turn on and off may extend the devices’ battery life, which can be important in real-life applications, while affecting the detection performance only slightly. The performance of the proposed methods is demonstrated in numerical simulations to be superior to existing approaches. Additionally, the topic of multiple hypothesis testing in spatial domains is briefly addressed. In a multiple hypothesis testing problem, one tests multiple null hypotheses at once while trying to control a suitable error criterion, such as the FDR. In a spatial multiple hypothesis problem each tested hypothesis corresponds to e.g. a geographical location, and the non-null hypotheses may appear in spatially localized clusters. It is demonstrated that implementing a Bayesian approach that accounts for the spatial dependency between the hypotheses can greatly improve testing accuracy

Controlling the False Discovery Rate in Astrophysical Data Analysis

The False Discovery Rate (FDR) is a new statistical procedure to control the number of mistakes made when performing multiple hypothesis tests, i.e. when comparing many data against a given model hypothesis. The key advantage of FDR is that it allows one to a priori control the average fraction of false rejections made (when comparing to the null hypothesis) over the total number of rejections performed. We compare FDR to the standard procedure of rejecting all tests that do not match the null hypothesis above some arbitrarily chosen confidence limit, e.g. 2 sigma, or at the 95% confidence level. When using FDR, we find a similar rate of correct detections, but with significantly fewer false detections. Moreover, the FDR procedure is quick and easy to compute and can be trivially adapted to work with correlated data. The purpose of this paper is to introduce the FDR procedure to the astrophysics community. We illustrate the power of FDR through several astronomical examples, including the detection of features against a smooth one-dimensional function, e.g. seeing the ``baryon wiggles'' in a power spectrum of matter fluctuations, and source pixel detection in imaging data. In this era of large datasets and high precision measurements, FDR provides the means to adaptively control a scientifically meaningful quantity -- the number of false discoveries made when conducting multiple hypothesis tests.Comment: 15 pages, 9 figures. Submitted to A

False discovery rate regression: an application to neural synchrony detection in primary visual cortex

Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis. But this may be inappropriate for many of today's large-scale screening problems, where auxiliary information about each test is often available, and where a combined analysis can lead to poorly calibrated error rates within different subsets of the experiment. To address this issue, we introduce an approach called false-discovery-rate regression that directly uses this auxiliary information to inform the outcome of each test. The method can be motivated by a two-groups model in which covariates are allowed to influence the local false discovery rate, or equivalently, the posterior probability that a given observation is a signal. This poses many subtle issues at the interface between inference and computation, and we investigate several variations of the overall approach. Simulation evidence suggests that: (1) when covariate effects are present, FDR regression improves power for a fixed false-discovery rate; and (2) when covariate effects are absent, the method is robust, in the sense that it does not lead to inflated error rates. We apply the method to neural recordings from primary visual cortex. The goal is to detect pairs of neurons that exhibit fine-time-scale interactions, in the sense that they fire together more often than expected due to chance. Our method detects roughly 50% more synchronous pairs versus a standard FDR-controlling analysis. The companion R package FDRreg implements all methods described in the paper

A comparison of the Benjamini-Hochberg procedure with some Bayesian rules for multiple testing

In the spirit of modeling inference for microarrays as multiple testing for sparse mixtures, we present a similar approach to a simplified version of quantitative trait loci (QTL) mapping. Unlike in case of microarrays, where the number of tests usually reaches tens of thousands, the number of tests performed in scans for QTL usually does not exceed several hundreds. However, in typical cases, the sparsity $p$ of significant alternatives for QTL mapping is in the same range as for microarrays. For methodological interest, as well as some related applications, we also consider non-sparse mixtures. Using simulations as well as theoretical observations we study false discovery rate (FDR), power and misclassification probability for the Benjamini-Hochberg (BH) procedure and its modifications, as well as for various parametric and nonparametric Bayes and Parametric Empirical Bayes procedures. Our results confirm the observation of Genovese and Wasserman (2002) that for small p the misclassification error of BH is close to optimal in the sense of attaining the Bayes oracle. This property is shared by some of the considered Bayes testing rules, which in general perform better than BH for large or moderate $p$'s.Comment: Published in at http://dx.doi.org/10.1214/193940307000000158 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Local False Discovery Rate Based Methods for Multiple Testing of One-Way Classified Hypotheses

This paper continues the line of research initiated in \cite{Liu:Sarkar:Zhao:2016} on developing a novel framework for multiple testing of hypotheses grouped in a one-way classified form using hypothesis-specific local false discovery rates (Lfdr's). It is built on an extension of the standard two-class mixture model from single to multiple groups, defining hypothesis-specific Lfdr as a function of the conditional Lfdr for the hypothesis given that it is within a significant group and the Lfdr for the group itself and involving a new parameter that measures grouping effect. This definition captures the underlying group structure for the hypotheses belonging to a group more effectively than the standard two-class mixture model. Two new Lfdr based methods, possessing meaningful optimalities, are produced in their oracle forms. One, designed to control false discoveries across the entire collection of hypotheses, is proposed as a powerful alternative to simply pooling all the hypotheses into a single group and using commonly used Lfdr based method under the standard single-group two-class mixture model. The other is proposed as an Lfdr analog of the method of \cite{Benjamini:Bogomolov:2014} for selective inference. It controls Lfdr based measure of false discoveries associated with selecting groups concurrently with controlling the average of within-group false discovery proportions across the selected groups. Simulation studies and real-data application show that our proposed methods are often more powerful than their relevant competitors.Comment: 26 pages, 17 figure