Detection Of Variance Changes Research Articles

Real-time detection of mean and variance changes in experience sampling data: A comparison of existing and novel statistical process control approaches.

Retrospective analyses of experience sampling (ESM) data have shown that changes in mean and variance levels may serve as early warning signs of an imminent depression. Detecting such early warning signs prospectively would pave the way for timely intervention and prevention. The exponentially weighted moving average (EWMA) procedure seems a promising method to scan ESM data for the presence of mean changes in real-time. Based on simulation and empirical studies, computing and monitoring day averages using EWMA works particularly well. We therefore expand this idea to the detection of variance changes and propose to use EWMA to prospectively scan for mean changes in day variability statistics (i.e., , , ln( )). When both mean and variance changes are of interest, the multivariate extension of EWMA (MEWMA) can be applied to both the day averages and a day statistic of variability. We evaluate these novel approaches to detecting variance changes by comparing them to EWMA-type procedures that have been specifically developed to detect a combination of mean and variance changes in the raw data: EWMA- , EWMA-ln( ), and EWMA- - . We ran a simulation study to examine the performance of the two approaches in detecting mean, variance, or both types of changes. The results indicate that monitoring day statistics using (M)EWMA works well and outperforms EWMA- and EWMA-ln( ); the performance difference with EWMA- - is smaller but notable. Based on the results, we provide recommendations on which statistic of variability to monitor based on the type of change (i.e., variance increase or decrease) one expects.

A new multivariate variability control chart based on a covariance matrix combination

AbstractIn the field of multivariate quality control, there are many control charts related to the process mean but few options addressing process variability. Variability control charts have two main drawbacks: the first relates to the number of parameters to tune and the second relates to how changes in the mean affect the performance of these charts. Thus, in this paper, we propose a new multivariate variability control chart, called the multivariate exponentially weighted covariance matrix combination, which solves these two problems. The results show that this new chart performs well in the detection of changes in variance when the mean does not change and outperforms other charts when the mean does change.

Multi‐Scale Detection of Variance Changes in Renewal Processes in the Presence of Rate Change Points

Non‐stationarity of the rate or variance of events is a well‐known problem in the description and analysis of time series of events, such as neuronal spike trains. A multiple filter test (MFT) for rate homogeneity has been proposed earlier that detects change points on multiple time scales simultaneously. It is based on a filtered derivative approach, and the rejection threshold derives from a Gaussian limit process L which is independent of the point process parameters.Here, we extend the MFT to variance homogeneity of life times. When the rate is constant, the MFT extends directly to the null hypothesis of constant variance. In the presence of rate change points, we propose to incorporate estimates of these in the test for variance homogeneity, using an adaptation of the test statistic. The resulting limit process shows slight deviations from L that depend on unknown process parameters. However, these deviations are small and do not considerably change the properties of the statistical test. This allows practical application, for example, to neuronal spike trains, which indicates various profiles of rate and variance change points.

CnAnalysis450k: an R package for comparative analysis of 450k/EPIC Illumina methylation array derived copy number data.

Detailed copy number (CN) variation data can be obtained from 450k or EPIC Illumina methylation assays. However, the effects of different preprocessing strategies (normalization, transformation and selection of gain/loss cutoff values) on variant calling have not been evaluated systematically. We provide an R package which allows to directly compare any preprocessed CN data. It provides its own CN alteration detection methodology: segments are identified through detection of changes in variance of CN data and are subsequently filtered for significance. Meaningful cutoffs for gain/loss definition can be identified automatically through analysis of the resulting ΔCN distributions of all analyzed samples. Three exemplary datasets (2x450k, 1xEPIC) were selected for comparative analyses of Raw, Illumina, SWAN, Quantile, Noob, Funnorm and Dasen normalizations. Importantly, all CN data distributions were skewed (-0.66 to -1.2) therefore requiring different gain/loss cutoffs. Depending on the normalization method, prominent baseline differences between samples could be observed. We present a workflow, which alleviates both issues: Z-transformation removes baseline differences between samples, and automatic cutoff selection circumvents the problems accompanying the skewed distributions. Additional filtering of candidates by significance yields comparable results for most enumerated normalization methods except for SWAN. In contrast, manual cutoff determination results in highly variable numbers of variant calls, highly dependent on the selected normalization method. Taken together, we present a workflow which allows to robustly identify copy number alterations in methylation array data fairly independent of the applied normalization. The cnAnalysis450k package is available on github ( https://github.com/mknoll/cnAnalysis450k ). m.knoll@dkfz.de. Supplementary data are available at Bioinformatics online.

Inferring climate variability from nonlinear proxies: application to palaeo-ENSO studies

Abstract. Inferring climate from palaeodata frequently assumes a direct, linear relationship between the two, which is seldom met in practice. Here we simulate an idealized proxy characterized by a nonlinear, thresholded relationship with surface temperature, and we demonstrate the pitfalls of ignoring nonlinearities in the proxy–climate relationship. We explore three approaches to using this idealized proxy to infer past climate: (i) methods commonly used in the palaeoclimate literature, without consideration of nonlinearities; (ii) the same methods, after empirically transforming the data to normality to account for nonlinearities; and (iii) using a Bayesian model to invert the mechanistic relationship between the climate and the proxy. We find that neglecting nonlinearity often exaggerates changes in climate variability between different time intervals and leads to reconstructions with poorly quantified uncertainties. In contrast, explicit recognition of the nonlinear relationship, using either a mechanistic model or an empirical transform, yields significantly better estimates of past climate variations, with more accurate uncertainty quantification. We apply these insights to two palaeoclimate settings. Accounting for nonlinearities in the classical sedimentary record from Laguna Pallcacocha leads to quantitative departures from the results of the original study, and it markedly affects the detection of variance changes over time. A comparison with the Lake Challa record, also a nonlinear proxy for El Niño–Southern Oscillation, illustrates how inter-proxy comparisons may be altered when accounting for nonlinearity. The results hold implications for how univariate, nonlinear recorders of normally distributed climate variables are interpreted, compared to other proxy records, and incorporated into multiproxy reconstructions.

Detection of changes in variance of oceanographic time-series using changepoint analysis

Changepoint analysis is used to detect changes in variability within GOMOS hindcast time-series for significant wave heights of storm peak events across the Gulf of Mexico for the period 1900–2005. To detect a change in variance, the two-step procedure consists of (1) validating model assumptions per geographic location, followed by (2) application of a penalized likelihood changepoint algorithm. Results suggest that the most important changes in time-series variance occur in 1916 and 1933 at small clusters of boundary locations at which, in general, the variance reduces. No post-war changepoints are detected. The changepoint procedure can be readily applied to other environmental time-series.

Detection of Variance Changes and Mean Value Jumps in Measurement Noise for Multipath Mitigation in Urban Navigation

This paper investigates an urban navigation filter for land vehicles. Typical urban canyon phenomena due to multipath and GPS outages seriously degrade positioning performance. To deal with these scenarios, a hybrid navigation system using GPS and dead-reckoning sensors is presented. This navigation system is complemented by a two-step detection procedure that aims at classifying outliers according to their associated source of error. Two different situations will be considered in the presence of multipath. These situations correspond to the presence or absence of line of sight signal for the different GPS satellites. Therefore, two kinds of errors are potentially “corrupting” the pseudoranges, modeled as variance changes or mean value jumps in noise measurements. An original multiple model approach is proposed to detect, identify and correct these errors and provide a final consistent solution.

Indexing variability: A case study with climate change impacts on ecosystems

We developed a methodology to index statistical changes in the variance of ecological measures over time. While ecological indicators are used to assess ecosystem health, vulnerability, risk and damage to ecosystems, their primary focus has been on changes to the mean of the ecological state or process. Little work has been done on incorporating variability into ecological indices. The methodology developed here is based on the Modified Levene's test of variance and a moving block where an initial time period (block) of ecosystem behavior is compared to the moving block. This allows for the detection of not only shifts in variance but also the magnitude of the shift on a continuous basis. Our results compared well with the benchmarked results from the Centered Cumulative Sum of Squares Algorithm (CUSUM) for detection of variance changes in fixed time series. The output from this methodology is a continuous stream of parameters (significant variance shift, magnitude of the shift, and the direction of the variance shift) suitable for indexing variance or integrating into an index measuring ecosystem change. Results suggest that the block interval widths should be at least 50 and that a smoothing factor of five be used to avoid false positives. We used modeled vegetation carbon output to analyze the utility of the methodology, illustrating that different model assumptions and CO2 regimes affect the variability of the ecological response. The degree of risk resource managers may want to explore can be altered by choices in the block length, the length of the string used to smooth variance shifts, the assumption that the initial period has constant variance and the alpha levels used to determine statistical significance.