Beyond Cumulative Sum Charting in Non-Stationarity Detection and Estimation
| Autor: | Nilab Rai, Moinak Bhaduri, Anthony Martinez, Matthew Swan, Felix Zhan, Richard Mcconnell, Justin Zhan, Laxmi Gewali, Paul Oh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
010504 meteorology & atmospheric sciences
General Computer Science Computer science CUSUM Context (language use) weak corruption 01 natural sciences 010104 statistics & probability Econometrics General Materials Science 0101 mathematics Electrical and Electronic Engineering Statistic 0105 earth and related environmental sciences Parametric statistics strong corruption Stochastic process Non-stationarity General Engineering Probabilistic logic CUSUM chart Term (time) classification 13. Climate action change points Probability distribution lcsh:Electrical engineering. Electronics. Nuclear engineering lcsh:TK1-9971 |
| Zdroj: | IEEE Access, Vol 7, Pp 140860-140874 (2019) |
| ISSN: | 2169-3536 |
| Popis: | In computer science, stochastic processes, and industrial engineering, stationarity is often taken to imply a stable, predictable flow of events and non-stationarity, consequently, a departure from such a flow. Efficient detection and accurate estimation of non-stationarity are crucial in understanding the evolution of the governing dynamics. Pragmatic considerations include protecting human lives and property in the context of devastating processes such as earthquakes or hurricanes. Cumulative Sum (CUSUM) charting, the prevalent technique to weed out such non-stationarities, suffers from assumptions on a priori knowledge of the pre and post-change process parameters and constructs such as time discretization. In this paper, we have proposed two new ways in which non-stationarity may enter an evolving system - an easily detectable way, which we term strong corruption, where the post-change probability distribution is deterministically governed, and an imperceptible way which we term hard detection, where the post-change distribution is a probabilistic mixture of several densities. In addition, by combining the ordinary and switched trend of incoming observations, we develop a new trend ratio statistic in order to detect whether a stationary environment has changed. Surveying a variety of distance metrics, we examine several parametric and non-parametric options in addition to the established CUSUM and find that the trend ratio statistic performs better under the especially difficult scenarios of hard detection. Simulations (both from deterministic and mixed inter-event time densities), sensitivity-specificity type analyses, and estimated time of change distributions enable us to track the ideal detection candidate under various non-stationarities. Applications on two real data sets sampled from volcanology and weather science demonstrate how the estimated change points are in agreement with those obtained in some of our previous works, using different methods. Incidentally, this study sheds light on the inverse nature of dependence between the Hawaiian volcanoes Kilauea and Mauna Loa and demonstrates how inhabitants of the now-restless Kilauea may be relocated to Mauna Loa to minimize the loss of lives and moving costs. |
| Databáze: | OpenAIRE |
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