Real time change-point detection in a nonlinear quantile model

Hypothesis tests

This paper presents an automatic extraction approach of worm signatures based on behavioral footprint analysis. Firstly, the suspicious worm traffic is detected based on worm behavior and is an instance of the Sequential Change Point Detection. To make the detection mechanism insensitive to site and access pattern, a non-parametric Cumulative Sum (CUSUM) method is applied, thus making the detection mechanism much more generally applicable and its deployment much easier. Secondly, worm behavioral footprint is defined and classified. The chronicle formalism is applied to correlate the footprint in suspicious worm traffic. Finally, worm signatures are extracted and ascertained by the evaluation function. The experiment shows that the approach can extract worm signatures effectively and accurately. There is a conclusion that worm behavioral footprint can't identify the worm accurately, but it helps to locate worm signatures, so signatures can be extracted effectively.

Cumulative Sum Curves and Their Prediction Limits

The problem of sequential detection of spontaneous changes in equations for unobserved state variables and observations of linear and nonlinear multivariate state-space models is considered. We consider the case of new additive terms and the case of changing coefficients of these equations. The proposed nonparametric method uses the idea of the “moving window” of observations. In Theorem 4.1 the exponential rate of convergence to zero for type 1 error probability (a wrong decision about a change) is proved. In Theorem 4.2 we consider type 2 error probability and the normalized (by the volume N of the moving window) delay time in change-point detection. Asymptotic optimality of the proposed method is proved in Theorem 5.1. Experimental study includes Monte Carlo examples of sequentially detected changes in coefficients of linear and nonlinear state-space models.

Use of the cumulative sum method (CUSUM) to assess the learning curves of ultrasound-guided continuous femoral nerve block

BACKGROUNDBile leakage is a common complication following laparoscopic common bile duct exploration (LCBDE) with primary duct closure (PDC). Identifying and analyzing the risk factors associated with bile leakage is crucial for improving surgical outcomes.AIMTo explore the value analysis of common risk factors for bile leakage after LCBDE and PDC, with a focus on strict adherence to indications.METHODSClinical data of 106 cases undergoing LCBDE + PDC in the Hepatobiliary and Pancreatic Surgery Department (Division 1) of Chuzhou First People’s Hospital from April 2019 to March 2024 were collected. Retrospective and multiple factor regression analysis were conducted on common risk factors for bile leakage. The change in surgical time was analyzed using the cumulative summation (CUSUM) method, and the minimum number of cases required to complete the learning curve for PDC was obtained based on the proposed fitting curve by identifying the CUSUM maximum value.RESULTSMultifactor logistic regression analysis showed that fibrinous inflammation and direct bilirubin/indirect bilirubin were significant independent high-risk factors for postoperative bile leakage (P < 0.05). The time to drain removal and length of hospital stay in cases without bile leakage were significantly shorter than in cases with bile leakage (P < 0.05), with statistical significance. The CUSUM method indicated that a minimum of 51 cases were required for the surgeon to complete the learning curve (P = 0.023).CONCLUSIONWith a good assessment of duodenal papilla sphincter function, unobstructed bile-pancreatic duct convergence, exact stone clearance, and sufficient surgical experience to complete the learning curve, PDC remains the preferred method for bile duct closure and is worthy of clinical promotion.

In this paper, a new method of sensing primary user's signal for cognitive radios in Grassmann manifold is proposed. The Grassmann covariance matrix (GCM) is formed with the help of covariance matrix of the transmitted and the received symbols. By using GCM, a new test statistic is defined, which is the modification of Binet-Cauchy metric. On the basis of this new test statistic, primary user's signal is detected. We also show that the new test statistic is a valid detector since it follows the concentration phenomena. We derive the distribution of new test statistic under null hypothesis and alternative hypothesis. Lower bound for the probability of detection of signal is also derived using separating function and distribution of new test statistic. Simulations using the real-world measurements of digital television (DTV) signal show performance gain of the proposed method in terms of signal detection over existing methods and their agreement with the derived distribution. Additionally, we extend the proposed method for the cooperative spectrum sensing and derive the distribution under both hypotheses. Experimental verification on the software defined radio is also performed and it is found that the proposed method fulfills the requirement of maximum protection of the DTV signal.

In this paper, we analyze the polio incidence data based on the Poisson autoregressive models, focusing particularly on change-point detection. Since the data include some strongly deviating observations, we employ the robust cumulative sum (CUSUM) test proposed by Kang and Song (2015) to perform the test for parameter change. Contrary to the result of Kang and Lee (2014), our data analysis indicates that there is no significant change in the case of the CUSUM test with strong robustness and the same result is obtained after ridding the polio data of outliers. We additionally consider the comparison of the forecasting performance. All the results demonstrate that the robust CUSUM test performs adequately in the presence of seemingly outliers.

For monitoring a sequence of random variables, the cumulative sum (CUSUM) sequential change-point detection scheme has optimality properties if the mean experiences a single, one-time jump increase from one known level to another. However, many monitoring situations are not realistically described by this stylized change-point model. For example, in modeling tool wear, gradual monotonic changes in the mean should be allowed. In this paper, we introduce a model that assumes only that the mean is nondecreasing over time and investigate how to let the process continue as long as its mean is under some specified threshold value, stopping it as soon as possible after the mean exceeds the threshold. We show how to apply the CUSUM and the exponentially weighted moving average (EWMA) to this problem as well as compare these procedures to a repeated generalized likelihood ratio test (GLR) designed specifically for the monotone setting. A simulation study demonstrates that the CUSUM and EWMA, properly applied, perform surprisingly well compared to the GLR test, usually outperforming it. We argue that the CUSUM is the best overall choice.

ABSTRACTWe consider multiple comparison test procedures among treatment effects in a randomized block design. We propose closed testing procedures based on maximum values of some two-sample t test statistics and based on F test statistics. It is shown that the proposed procedures are more powerful than single-step procedures and the REGW (Ryan/Einot–Gabriel/Welsch)-type tests. Next, we consider the randomized block design under simple ordered restrictions of treatment effects. We propose closed testing procedures based on maximum values of two-sample one-sided t test statistics and based on Batholomew’s statistics for all pairwise comparisons of treatment effects. Although single-step multiple comparison procedures are utilized in general, the power of these procedures is low for a large number of groups. The closed testing procedures stated in the present article are more powerful than the single-step procedures. Simulation studies are performed under the null hypothesis and some alternative hypotheses. In this studies, the proposed procedures show a good performance.

Sequential change-point detection when the distribution parameters are unknown is a fundamental problem in statistics and machine learning. When the post-change parameters are unknown, we consider a set of detection procedures based on sequential likelihood ratios with non-anticipating estimators constructed using online convex optimization algorithms such as online mirror descent, which provides a more versatile approach to tackling complex situations where recursive maximum likelihood estimators cannot be found. When the underlying distributions belong to a exponential family and the estimators satisfy the logarithm regret property, we show that this approach is nearly second-order asymptotically optimal. This means that the upper bound for the false alarm rate of the algorithm (measured by the average-run-length) meets the lower bound asymptotically up to a log-log factor when the threshold tends to infinity. Our proof is achieved by making a connection between sequential change-point and online convex optimization and leveraging the logarithmic regret bound property of online mirror descent algorithm. Numerical and real data examples validate our theory.

We study sequential change-point detection when obser- vations form a sequence of independent Gaussian random fields, and the change-point is the time at which a sig- nal of known functional form involving a finite number of unknown parameters appears. Building on Siegmund and Yakir (2008), which identifies in a simpler problem a detec- tion procedure of Shiryayev-Roberts type that is asymptot- ically minimax up to terms that vanish as the false detec- tion rate converges to zero, we compare easily computed ap- proximations to the Shiryayev-Roberts detection procedure with similar approximations to CUSUM type procedures. Although the CUSUM type procedures are suboptimal, our studies indicate that they compare favorably to the asymp- totically optimal procedures. gradually. Generally speaking, the problem is to detect the signal as soon as possible after it appears, under the con- straint that (false) detection occurs very rarely if no signal appears. To illustrate the principles involved we will assume that the observations consist of a sequence of uncorrelated Gaussian random fields and that the signal is a parameter- ized function of a known form superimposed on the noisy observations at an unknown change-point. The discussion will be formulated in the context of image analysis. Yet the results and the principles that we introduce are meaningful in other settings as well. Following the developments in the companion to this paper (12), we measure detection delay by the expected Kullback-Leibler information accumulated between the change-point and its detection. We begin in the next sub- section with a precise description of the model. In Subsec- tion 1.2 the criterion for asymptotic minimax optimality, which is stated and proved in the companion paper, is re- formulated to fit the current context. The asymptotic minimax policy uses a randomized form of the Shiryayev-Roberts monitoring scheme. The alterna- tive Cumulative Sum (CUSUM) monitoring scheme is a bet- ter known approach. In Section 2 expressions describing the asymptotic performance of optimal CUSUM and optimal Shiryayev-Roberts rules are obtained. Suboptimal formula- tions of these procedures are also assessed. It turns out that the natural candidate for optimal Shiryayev-Roberts and CUSUM rules may require substan- tial computation. In Section 3 we propose alternative rules which are asymptotically equivalent but require less com- putational effort. A simulation study is conducted in order to investigate the finite-sample properties of these simplified rules. The paper concludes with a discussion of related open problems. The analysis of the different detection methods draws on a substantial literature for its justification. The calculations are only sketched here and emphasize new features of the present formulation. See (12) and the references cited there, and (3).

To identify a learning curve and monitor operator performance for fetoscopic laser surgery for twin-to-twin transfusion syndrome using cumulative sum analysis. Retrospective cohort study. National tertiary referral center for invasive fetal therapy. A total of 340 consecutive monochorionic pregnancies with twin-to-twin transfusion syndrome treated with fetoscopic laser coagulation between August 2000 and December 2010. A learning curve was generated using learning curve cumulative sum analysis and cumulative sum methodology to assess changes in double survival across the case sequence. Laser surgery was initially performed by two operators, joined by a third and fourth operator after 1 and 2years, respectively. Individual operator performance, double perinatal survival at 4weeks. Overall survival of both twins occurred in 59% (201/340), median gestational age at birth was 32.0weeks. Cumulative sum graphs showed that level of competence for double survival for the operators was reached after 26, 25, 26, and 35 procedures, respectively. Two operators kept their competence level and continued to improve after completing the initial learning process; two others went out of control at one point in time, according to the cumulative sum boundaries. A difference in learning effect was associated with number of procedures performed annually and previous experience with other ultrasound-guided invasive procedures. This study shows that all operators reached a level of competence after at least 25 fetoscopic laser procedures and confirms the value of using the cumulative sum method both for learning curve assessment and for ongoing quality control.

To detect a change in the probability of a sequence of independent binomial random variables, a variety of asymptotic and exact testing procedures have been proposed. Whenever the sample size or the event rate is small, asymptotic approximations of maximally selected test statistics have been shown to be inaccurate. Although exact methods control the type I error rate, they can be overly conservative due to the discreteness of the test statistics in these situations. We extend approaches by Worsley and Halpern to develop a test that is less discrete to increase the power. Building on ideas from binary segmentation, the proposed test utilizes unused information in the binomial sequences to add a new ordering to test statistics that are of equal value. The exact distributions are derived under side conditions that arise in hypothetical segmentation steps and do not depend on the type of test statistic used (e.g., log likelihood ratio, cumulative sum, or Fisher's exact test). Using the proposed exact segmentation procedure, we construct a change point test and prove that it controls the type-I-error rate at any given nominal level. Furthermore, we prove that the new test is uniformly at least as powerful as Worsley's exact test. In a Monte Carlo simulation study, the gain in power can be remarkable, especially in scenarios with small sample size. Giving a clinical database example about pin site infections and an example assessing publication bias in neuropsychiatric drug research, we demonstrate the wide-ranging applicability of thetest.

In the analysis of spatial point patterns, complete spatial randomness (CSR) hypothesis,which is a restriction of a homogenous Poisson process to study region A, operates as a dividinghypothesis between “regular” and “aggregated” patterns. Meanwhile, many alternatives to CSR inaggregated patterns are extensions of homogenous Poisson processes themselves. Therefore, when theCSR hypothesis is rejected, results related to Poisson processes may be used to formulate plausiblealternatives to CSR. In this paper, we propose a new statistic for testing CSR and then by applying it inconjunction with a notion of kernels of a point pattern, we determine the “parents” of a Poisson clusterprocess when the CSR hypothesis is rejected and a Neyman-Scott process is assumed for the pointpattern under alternative hypothesis. We have made power studies for our test statistic by simulation, andhave also surveyed the performance of our method on a certain point pattern. Finally, the whole methodis carried on certain real life data.