Change Point Detection

Road transport is the main anthropogenic source of NOx in Europe, affecting human health and ecosystems. Thus, mitigation policies have been implemented to reduce on-road vehicle emissions, particularly through the Euro standard limits. To evaluate the effectiveness of these policies, we calculated NO 2 and NOx concentration trends using air quality and meteorological measurements conducted in three European cities over 26 years. These data were also employed to estimate the trends in NOx emission factors (EF NOx , based on inverse dispersion modeling) and NO 2 :NOx emission ratios for the vehicle fleets under real-world driving conditions. In the period 1998-2017, Copenhagen and Stockholm showed large reductions in both the urban background NOx concentrations (-2.1 and -2.6% yr -1 , respectively) and EF NOx at curbside sites (68 and 43%, respectively), proving the success of the Euro standards in diminishing NOx emissions. London presented a modest decrease in urban background NOx concentrations (-1.3% yr -1 ), while EF NOx remained rather constant at the curbside site (Marylebone Road) due to the increase in public bus traffic. NO 2 primary emissions -that are not regulatedincreased until 2008-2010, which also reflected in the ambient concentrations. This increase was associated with a strong dieselization process and the introduction of new after-treatment technologies that targeted the emission reduction of other species (e.g., greenhouse gases or particulate matter). Thus, while regulations on ambient concentrations of specific species have positive effects on human health, the overall outcomes should be considered before widely adopting them. Emission inventories for the on-road transportation sector should include EF NOx derived from real-world measurements, particularly in urban settings. ☆ This paper has been recommended for acceptance by Pavlos Kassomenos.

Long‐term changes in the persistence of atmospheric circulation (measured by the mean residence time of circulation types) over Europe since 1881 are studied using the Hess–Brezowsky classification of Grosswetterlagen. A comprehensive statistical analysis is performed utilizing tests for change points, trends and outliers. The most remarkable feature of the long‐term variations in the persistence of circulation patterns is a general sharp increase from the 1970s to the late 1980s. The shift towards higher persistence is statistically significant in most groups of the types and most seasons and is confirmed by all the statistical tools. The 1986–2000 period is an outlier, and the most pronounced change point in the time series appears in the mid‐1980s. The observed increase in the mean lifetime of the circulation types over European mid‐latitudes seems to be consistent with the idea of global warming, which is likely to shift the areas with the highest baroclinic activity (storm trac...

We study sequential change-point detection when observations form a sequence of independent Gaussian random fields, and the change-point is the time at which a signal of known functional form involving a finite number of unknown parameters appears. Building on , which identifies in a simpler problem a detection procedure of Shiryayev-Roberts type that is asymptotically minimax up to terms that vanish as the false detection rate converges to zero, we compare easily computed approximations 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 asymptotically optimal procedures.

Observations are generated according to a regression with normal error as a function of time, when the process is in control. The process potentially changes at some unknown point of time and then the ensuing observations are normal with the same mean function plus an arbitrary function under suitable regularity conditions. The problem is to obtain a stopping rule that is optimal in the sense that the rule minimizes the expected delay in detecting a change subject to a constraint on the average run length to a false alarm. A bound on the expected delay is first obtained. It is then shown that the cusum and Shiryayev-Roberts procedures achieve this bound to first order.

We consider a linear regression model with errors modeled by martingale difference sequences, which include heteroskedastic augmented GARCH processes. We develop asymptotic theory for two monitoring schemes aimed at detecting a change in the regression parameters. The first method is based on the CUSUM of the residuals and was studied earlier in the context of independent identically distributed errors. The second method is new and is based on the squares of predictions errors. Both methods use a training sample of size m. We show that, as m → ∞, both methods have correct asymptotic size and detect a change with probability approaching unity. The methods are illustrated and compared in a small simulation study.

Introduction
Hydrological regimes play a major role in changing the structure and function of ecological processes and river ecosystems. Significant changes in the hydrological regimes of river flow cause the spatial and temporal heterogeneity of river systems and the degradation of natural ecosystem services and threaten biodiversity. Trend analysis and change point detection are important topics in the analysis of hydrological time series. The study area in this research includes the upstream part of the Hablehroud river basin draining to the Bonekoh hydrometry station, located within the jurisdiction of the Tehran province. The Habaleroud river as the main drain of this watershed has recently encountered the pressures induced by human interventions and climate change, resulting in significant changes in its hydrological status.

Materials and Methods
In this research, using the sequential Mann-Kendall, Pettitt, Buishand Range, Buishand U, Standard Normal Homogeneity, and double mass curve tests, the significant change point in the annual discharge time series (1980–2017) of the Bonekoh hydrometry station at the outlet of the Hableroud watershed was detected. Then, using the Indicators of Hydrologic Alteration (IHA), the alterations in the hydrological condition in the period after the change point (Altered flow regime) compared to the period before the change point (the natural flow regime) were analyzed using the daily observed discharge data of the Hableroud watershed.

Results and Discussion
According to the research results, in the mid-1990s, a statistically significant change point in the annual discharge time series of the Bonekoh hydrometry station occurred, and most of the hydrological indicators show a deterioration in the condition of the Habaleroud watershed flow regime. Whereas for most of the hydrological indicators, after the change point, the frequency of the low values category has increased and the frequencies of the middle and high values categories, have decreased. These reductions have not only occurred for high extreme values, but also for low extreme values. In addition, the mean monthly discharge for all months of the year and the base flow of the basin have decreased. Both the frequency and duration of low-flow pulses have increased. On the contrary, both the frequency and duration of the high-flow pulses have decreased. For this reason, the frequency and magnitude of high extreme events such as medium and large floods have decreased. The long-term trend analysis indicated that 25 out of the 33 IHA have experienced a statistically significant decreasing trend. Therefore, the mean annual discharge of the watershed at the Bonekoh station has declined from 8.43 m3/s during the pre-impact period to 5.43 m3/s during the post-impact period, which is equivalent to about 35 % decline in the watershed outflow. While the watershed’s mean annual precipitation shows a negligible long-term increasing trend. Therefore, it seems that human interventions across the watershed play a major role in the hydrologic regime alteration of the watershed.

Conclusion
In the Benkoh hydrometric station in the mid-1990s, the hydrological regime of the basin has changed significantly. Then, using special software, the hydrological change indicators and key environmental flow indicators were analyzed in the periods before and after the change point. Unfortunately, most of the hydrological indicators show a downward trend in the Habaleroud river flow. So that the average discharge has decreased in all months of the year. Base current values are reduced. Both the frequency and duration of minimum current pulses are increased. On the contrary, both the frequency and duration of maximum current pulses are reduced. For this reason, the frequency and magnitude of extreme events such as medium and large floods have decreased. The results of the analysis of the trend of several indicators of the environmental flow also indicate the regressive course in the ecohydrological conditions of the Hableroud watershed. So that the minimum monthly flows for all months of the year show a downward trend. On the one hand, the continuity and frequency of periods of water shortage has increased, and on the other hand, the frequency of high flow pulses has decreased. The consequence of these changes will be creating tension and threatening riverside plant and animal communities that live in the flood plains of rivers and provide many ecological services. On the other hand, with the destruction of these riverside communities, the hydraulic conditions of the floodplains have changed and the vulnerability of river ecosystems and infrastructure facilities around the river increases against possible floods and causes a lot of damage. With the continuation of the existing process of managing water resources of the basin, stakeholders and beneficiaries of the basin will face many challenges in the future. Due to the fact that the average annual rainfall of Hableroud basin does not show a decreasing trend, it seems that human interventions are one of the main factors affecting the hydrological changes of this basin. Therefore, it is suggested that the main focus of management policies and measures should be focused on the management and optimization of human interventions in Hableroud watershed. In other words, instead of focusing on the top-down management approach and (hard) structural engineering measures, the focus should be on the participatory management approach and (soft) management engineering measures, and the water and soil resources of this basin should be used optimally and in accordance with the principles of sustainable development, so that at the same time Reducing the conflicts between the beneficiaries and the stakeholders upstream and downstream of the watershed (social challenges and threats) which currently occurred on a larger scale between the two provinces of Tehran and Semnan, and also preventing these conflicts from occurring on a smaller scale between the smaller communities upstream and downstream in The extension of waterways and rivers in the basin prevented the occurrence and spread of diverse environmental challenges and threats and vulnerability to natural hazards such as sudden floods and droughts. Also, it is suggested that the future changes in discharge of the studied watershed should be predicted according to the results of climate change models and land use changes, and suitable solutions should be formulated and implemented in order to deal with or adapt to these changes.

The paper extends the results on the problem of change point detection for Markov processes generalizing the results contained in the publications [11], [15] and [8]. The short description are as follows. A random sequence having segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each process are known and joint a priori distribution of the disorder moments are given. The detection of the disorder rarely is precise. The decision maker accepts some deviation in estimation of the disorder moments. In this note the aim is to indicate the segment of given length between disorders with maximal probabilities. The case with various precision for over and under estimation of the middle point is analyzed including situation when the disorders do not appear with positive probability is also included. The observed sequence, when the change point i...

The stochastic component of the sensor signal in commercial semiconductor gas sensors during exposure to different gases has been studied. The resistance fluctuation measurements have been carried out using different concentrations of ethanol, CO, NO x , H 2 and SO 2 in dry synthetic air. The analysis of the stochastic resistance fluctuations in gas sensors during exposure to gases enables an enhanced sensitivity and selectivity. The normalized power spectrum is characteristic for each sensor, and each gas induces a new characteristic power spectrum. In many cases, sensors can be used even for different gases than the gas they were originally designed for.

Continual improvement in the quality of products, processes, and services has been facilitated by applying statistical methods. The statistical process control technique (SPC) provides enhanced results, as it utilizes statistical methods throughout all the developmental stages of a project and/or production. One of these techniques is control charts, which are powerful tools for viewing and understanding different types of process variations. Therefore, it is essential for professionals linked to engineering and technological fields to be familiar with these techniques and software programs, in order to facilitate the development process for creating control charts. The majority of these software programs designed for easy utilization and friendly interface for SPC applications are sold at high prices and thereby make access impossible to this computational resource for freelance professionals, small businesses, and especially students. The GNU R interface is open source and provides free access as one of the alternatives. So, for this purpose, this paper presents the description and application of control charts in three different R interfaces, as its objective is to use them for the teaching and learning process.

Head start values -that is, non-zero initial values for the summary statistics of Markovtype control schemes such as the well known CUSUM schemes -are throughly recommended in the literature and used by quality control practitioners. The rationale of it is as follows: if the process is operating in-control, the summary statistic of the control scheme is soon brought to zero, so that the expected effect of the head start is minimal; otherwise, the operator is alerted to the out-of-control situation much sooner, which may prevent start-up problems. This paper emphasizes on the assessment of the impact of the adoption of a head start on the run length, the indisputedly popular performance measure of control schemes. It also brings the issue of stochastically monotone matrices into focus in the statistical process control setting and investigates their influence on the alarm rate function, the ageing character and the equilibrium rate function of the run length of one-sided Markov-type control schemes.

Head start values -that is, non-zero initial values for the summary statistics of Markovtype control schemes such as the well known CUSUM schemes -are throughly recommended in the literature and used by quality control practitioners. The rationale of it is as follows: if the process is operating in-control, the summary statistic of the control scheme is soon brought to zero, so that the expected effect of the head start is minimal; otherwise, the operator is alerted to the out-of-control situation much sooner, which may prevent start-up problems. This paper emphasizes on the assessment of the impact of the adoption of a head start on the run length, the indisputedly popular performance measure of control schemes. It also brings the issue of stochastically monotone matrices into focus in the statistical process control setting and investigates their influence on the alarm rate function, the ageing character and the equilibrium rate function of the run length of one-sided Markov-type control schemes.

The multi-arm bandit problem is widely used in scheduling of traffic in broadband networks, manufacturing systems and robotics. This paper presents a finite dimensional optimal solution to the multi-arm bandit problem for Hidden Markov Models. The key to solving any multi-arm bandit problem is to compute the Gittins index. In this paper a finite dimensional algorithm is presented which exactly computes the Gittins index. Suboptimal algorithms for computing the Gittins index are also presented and experimentally shown to perform almost as well as the optimal method. Finally an application of the algorithms to tracking multiple targets with a single intelligent sensor is presented.

Whilst musical transients are generally acknowledged as holding much of the perceptual information within musical tones, most research in sound analysis and synthesis tends to focus on the steady state components of signals. A method is presented which separates the noisy transient information from the slowly time varying steady state components of musical audio. Improvements of using adaptive thresholding, and multiresolution analysis methods are then illustrated. It is shown that by analyzing the resulting transient information only, current onset detection algorithms can be improved considerably, especially for those instruments with noisy attack information, such as plucked or struck strings. The idea is then applied to audio processing techniques to enhance or decrease the strength of note attack information. Finally, the transient extraction algorithm (TSS) is applied to time-scaling implementation, where the transient and noise information is analyzed so that only steady state regions are stretched, yielding considerably improved results.

This paper presents a software tool that was developed for the transformation of audio signals, be it short sounds or whole songs. This can subsequently be used to synthesize music from audio signal fragments ("Concatenative Sound Synthesis"). It is attempted to use timbre-related features to re-synthesize audio signals. As in a mosaic, an existing song is newly constructed from small parts ("frames") of other songs already stored in a database. Suitable database frames are found by feature similarity analysis. The length of the frames corresponds to musically meaningful units. For the implementation suitable onset-and beat tracking methods are evaluated. The selection of suitable parameters describing the subjective semantic similarities is determined by listening tests.

Surveillance can be based, in some change-point detection problems, on a sequence of invariant statistics. Gordon and Pollak prove that, under Ž . certain conditions, the average run length ARL to false alarm of invariance-based Shiryayev᎐Roberts detection schemes is asymptotically the same as that of the dual classical scheme that is based on the original sequence of observations. In this paper we give alternative conditions under which the two ARLs coincide and demonstrate that these conditions are satisfied in cases where Gordon and Pollak's conditions are difficult to check.

Given a set of aligned sequences of independent noisy observations, we are concerned with detecting intervals where the mean values of the observations change simultaneously in a subset of the sequences. The intervals of changed means are typically short relative to the length of the sequences, the subset where the change occurs, the "carriers," can be relatively small, and the sizes of the changes can vary from one sequence to another. This problem is motivated by the scientific problem of detecting inherited copy number variants in aligned DNA samples. We suggest a statistic based on the assumption that for any given interval of changed means there is a given fraction of samples that carry the change. We derive an analytic approximation for the false positive error probability of a scan, which is shown by simulations to be reasonably accurate. We show that the new method usually improves on methods that analyze a single sample at a time and on our earlier multi-sample method, which is most efficient when the carriers form a large fraction of the set of sequences. The proposed procedure is also shown to be robust with respect to the assumed fraction of carriers of the changes.

We address the sequential change-point detection problem for the Gaussian model where baseline distribution is Gaussian with variance σ 2 and mean µ such that σ 2 = aµ, where a > 0 is a known constant; the change is in µ from one known value to another. First, we carry out a comparative performance analysis of four detection procedures: the CUSUM procedure, the Shiryaev-Roberts (SR) procedure, and two its modifications -the Shiryaev-Roberts-Pollak and Shiryaev-Roberts-r procedures. The performance is benchmarked via Pollak's maximal average delay to detection and Shiryaev's stationary average delay to detection, each subject to a fixed average run length to false alarm. The analysis shows that in practically interesting cases the accuracy of asymptotic approximations is "reasonable" to "excellent". We also consider an application of change-point detection to cybersecurity -for rapid anomaly detection in computer networks. Using real network data we show that statistically traffic's intensity can be well-described by the proposed Gaussian model with σ 2 = aµ instead of the traditional Poisson model, which requires σ 2 = µ. By successively devising the SR and CUSUM procedures to "catch" a low-contrast network anomaly (caused by an ICMP reflector attack), we then show that the SR rule is quicker. We conclude that the SR procedure is a better cyber "watch dog" than the popular CUSUM procedure.

Model Selections in Bayesian Statistics are primarily made with statistics known as Bayes Factors, which are directly related to Posterior Probabilities of models. Bayes Factors require a careful assessment of prior distributions as in the Intrinsic Priors of Berger and Pericchi (1996a) and integration over the parameter space, which may be highly dimensional. Recently researchers have been proposing alternatives to Bayes Factors that require neither integration nor specification of priors. These developments are still in a very early stage and are known as Prior-free Bayes Factors, Cross-Validation Bayes Factors (CVBF), and Bayesian "Stacking." This kind of method and Intrinsic Bayes Factor (IBF) both avoid the specification of prior. However, this Prior-free Bayes factor might need a careful choice of a training sample size. In this article, a way of choosing training sample sizes for the Prior-free Bayes factor based on Geometric Intrinsic Bayes Factors (GIBFs) is propo...

In this paper 1 , we propose a new Spectrum Sensing technique for spectrum distribution discontinuities detection using algebraic detection (AD). The presented mathematical background leading to such technique is based on operational calculus and differential algebra which offers a new stand point in sensing theory. Even if this background is quite heavy, the sensing algorithm related to this technique is nevertheless very simple and remains with extremely low complexity, comparable even to the Energy Detection technique (ED). Simulations results show good performance of the proposed technique in terms of reliability and accuracy with low complexity and good robustness in noisy context.

This work addresses the fundamental problem of distinguishing between a driver and passenger using a mobile phone, which is the critical input to enable numerous safety and interface enhancements. Our detection system leverages the existing car stereo infrastructure, in particular, the speakers and Bluetooth network. Our acoustic approach has the phone send a series of customized high frequency beeps via the car stereo. The beeps are spaced in time across the left, right, and if available, front and rear speakers. After sampling the beeps, we use a sequential change-point detection scheme to time their arrival, and then use a differential approach to estimate the phone's distance from the car's center. From these differences a passenger or driver classification can be made. To validate our approach, we experimented with two kinds of phones and in two different cars. We found that our customized beeps were imperceptible to most users, yet still playable and recordable in both cars. Our customized beeps were also robust to background sounds such as music and wind, and we found the signal processing did not require excessive computational resources. In spite of the cars' heavy multi-path environment, our approach had a classification accuracy of over 90%, and around 95% with some calibrations. We also found we have a low false positive rate, on the order of a few percent.

In defining selection bias, we have considered only the parallel universe of the treated group or the untreated group rather than including the parallel universe of the untreated group or the treated group. This makes causal inference theories unbalanced because they were developed on one side of treated or untreated group while the other side remained static. In this paper, we redefined selection bias by considering all four existing universes in the real and hypothetical worlds, and we provided sufficient statistics for estimating the effects of treatment with Quadruple Randomized Controlled Trials (QRCT)

An event encountered for the first time can become a common phenomenon in a population through transmission over time. This study focuses on nonparametric partially sequential test statistics in order to early detect such events. For this purpose, firstly, the partially sequential test statistic given in Mukherjee [1] is considered. Then, with a modification of this statistic, a new nonparametric partially sequential test statistic that works at almost the desired α level of significance is revealed. Also, based on Monte-Carlo simulations, the proposed test statistic is shown to be more powerful than Mukherjee's statistic. Lastly, two illustrative numerical examples are also given.

A distribution on Ω is a continuous linear form on D(Ω). The set of distribution is denoted D (Ω) and is a vector space. If T is a distribution, we denote by T, ϕ the result of evaluating the distribution T at the test function ϕ. We hence have the following properties: Distributions generalize the notion of measure defined a linear forms on the space D0 of continuous functions with compact support.

A distribution on Ω is a continuous linear form on D(Ω). The set of distribution is denoted D (Ω) and is a vector space. If T is a distribution, we denote by T, ϕ the result of evaluating the distribution T at the test function ϕ. We hence have the following properties: Distributions generalize the notion of measure defined a linear forms on the space D0 of continuous functions with compact support.

The railway infrastructure is a perfect blend of all branches of engineering. Technology has drastically increased, mainly in the Signalling, Civil, Electrical and Mechanical engineering streams. In the field of Signalling, it has leaped from Mechanical to Electronics Interlocking. Civil engineering has gone from manual track maintenance to high-end mechanized tools. In the field of mechanical engineering, it has progressed from wooden coaches to modern designed (LHB)coaches. In electrical engineering, the technology changed from steam loco to diesel and later electrically powered loco design. Nowadays, the loco is powered by nonconventional sources (like solar or wind). Hence, the maintenance of rail infrastructure with traditional methods of physical supervision is sluggish and prone to frequent failures. However, condition monitoring through manual verification by railwaymen helps in the upkeep of railway assets, but it is prone to human errors and subsequent failure of systems, which may result in disasters like derailments or head-on collisions. Signalling components (Point, Tracks, Signals, OFC, DNS, Dataloggers, EI, Block-working instruments etc.), Mechanical rolling stock (Carriage and Wagon), Electrical fitments (OHE, AT, DG, TSS/SP/SSP, locomotive etc.) and Civil Structures (Bridges, Culverts, rail-tracks, rail beds) all require regular maintenance. This paper introduces a “condition monitoring method Enhanced with Wireless Sensor Network” for railway infrastructure. It also clearly distinguishes the typical category of sensors, which are best suitable for condition monitoring of various types of railway assets. The proposed WSN-based technology will improve railway subsystem reliability, effectively reducing failure time and improving the operating ratio.

Continual improvement in the quality of products, processes, and services has been facilitated by applying statistical methods. The statistical process control technique (SPC) provides enhanced results, as it utilizes statistical methods throughout all the developmental stages of a project and/or production. One of these techniques is control charts, which are powerful tools for viewing and understanding different types of process variations. Therefore, it is essential for professionals linked to engineering and technological fields to be familiar with these techniques and software programs, in order to facilitate the development process for creating control charts. The majority of these software programs designed for easy utilization and friendly interface for SPC applications are sold at high prices and thereby make access impossible to this computational resource for freelance professionals, small businesses, and especially students. The GNU R interface is open source and provides free access as one of the alternatives. So, for this purpose, this paper presents the description and application of control charts in three different R interfaces, as its objective is to use them for the teaching and learning process.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Multivariate abrupt change detectors Sarra Houidi, F. Auger, Houda Ben Attia Sethom, Laurence Miègeville, Dominique Fourer

This paper deals with the minimax quickest detection problem of a drift change for the Brownian motion. The following minimax risks are studied: C(T) = inf τ ∈M T sup θ E θ (τ − θ | τ θ) and C(T) = inf τ ∈M T sup θ E θ (τ − θ | τ θ), where M T is the set of stopping times τ such that E∞τ = T and M T is the set of randomized stopping times τ such that E∞τ = T. The goal of this paper is to obtain for these risks estimates from above and from below. Using these estimates we prove the existence of stopping times, which are asymptotically optimal of the first and second orders as T → ∞ (for C(T) and C(T), respectively).

This work addresses the fundamental problem of distinguishing between a driver and passenger using a mobile phone, which is the critical input to enable numerous safety and interface enhancements. Our detection system leverages the existing car stereo infrastructure, in particular, the speakers and Bluetooth network. Our acoustic approach has the phone send a series of customized high frequency beeps via the car stereo. The beeps are spaced in time across the left, right, and if available, front and rear speakers. After sampling the beeps, we use a sequential change-point detection scheme to time their arrival, and then use a differential approach to estimate the phone's distance from the car's center. From these differences a passenger or driver classification can be made. To validate our approach, we experimented with two kinds of phones and in two different cars. We found that our customized beeps were imperceptible to most users, yet still playable and recordable in both cars. Our customized beeps were also robust to background sounds such as music and wind, and we found the signal processing did not require excessive computational resources. In spite of the cars' heavy multi-path environment, our approach had a classification accuracy of over 90%, and around 95% with some calibrations. We also found we have a low false positive rate, on the order of a few percent.

We study the problem of private stochastic multi-arm bandits. Our notion of privacy is the same as some of the earlier works in the general area of private online learning [13, 17, 24]. We design algorithms that are i) differentially private, and ii) have regret guarantees that (almost) match the regret guarantees for the best non-private algorithms (e.g., upper confidence bound sampling and Thompson sampling). Moreover, through our experiments, we empirically show the effectiveness of our algorithms.

In this paper we study the problem of private stochastic multi-arm bandits. Our notion of privacy is the same as some of the earlier works in the general area of private online learning (Dwork et al., 2010; Jain et al., 2012; Smith and Thakurta, 2013). We design algorithms that are i) differentially private, and ii) have regret guarantees that (almost) match the regret guarantees for the best non-private algorithms (e.g., upper confidence bound sampling). Moreover, through our experiments on simulated and real-world data sets, we empirically show the effectiveness of our algorithms.

Abstract. Control charts are used to distinguish between chance and assignable causes in the variability of quality characteristics. When a control chart signals that an assignable cause is present, process engineers must initiate a search for the assignable cause of the process disturbance. Identifying the time of a process change could lead to simplifying the search for the assignable cause and less process down time, as well as help to reduce the probability of incorrectly identifying the assignable cause. The change point estimation by likelihood theory and the built-in change point estimation in a control chart have been discussed until now. In this article, we discuss two kinds of process change point estimation when the CUSUM ( ,)x s control chart for monitoring process mean and variance simultaneously is operated. Throughout some numerical experiments about the performance of the change point estimation, the change point estimation techniques in the CUSUM ( ,)x s control cha...

This paper studies the autoregressive integrated moving average (ARIMA) state space model combined with Kalman smoothing to impute missing values in a univariate time series before detecting change points. We estimate a scale-dependent time-average variance constant that depends on the length of the data section and is robust to mean shifts under serial dependence. The consistency of the proposed estimator is shown under the assumption allowing heavy tailedness. Integrating the proposed estimator with the moving sum and wild binary segmentation procedures to determine the number and locations of change points is discussed. Furthermore, the performance of the proposed methods is evaluated through extensive simulation studies and applied to the Beijing multi-site air quality dataset to impute missing values and detect mean changes in the data.
Keywords: ARIMA; Kalman smoothing; time-average variance constant; robust estimation; moving sum; wild binary segmentation
MSC: 62F35; 62M10

Multi-armed bandit problem is a classic example of the exploration vs. exploitation dilemma in which a collection of one-armed bandits, each with unknown but fixed reward probability, is given. The key idea is to develop a strategy, which results in the arm with the highest reward probability to be played such that the total reward obtained is maximized. Although seemingly a simplistic problem, solution strategies are important because of their wide applicability in a myriad of areas such as adaptive routing, resource allocation, clinical trials, and more recently in the area of online recommendation of news articles, advertisements, coupons, etc. to name a few. In this dissertation, we present different types of Bayesian Inference based bandit algorithms for Two and Multiple Armed Bandits which use Order Statistics to select the next arm to play. The Bayesian strategies, also known in literature as "Thompson Method" are shown to function well for a whole range of values, including very small values, outperforming UCB and other commonly used strategies. Empirical analysis results show a significant improvement in both synthetic and real

We propose new tests to detect a change in the mean of a time series. Like many existing tests, the new ones are based on the CUSUM process. Existing CUSUM tests require an estimator of a scale parameter to make them asymptotically distribution free under the no change null hypothesis. Even if the observations are independent, the estimation of the scale parameter is not simple since the estimator for the scale parameter should be at least consistent under the null as well as under the alternative. The situation is much more complicated in case of dependent data, where the empirical spectral density at 0 is used to scale the CUSUM process. To circumvent these difficulties, new tests are proposed which are ratios of CUSUM functionals. We demonstrate the applicability of our method to detect a change in the mean when the errors are AR(1) and GARCH(1,1) sequences.

The literature displays change point detection problems in the context of one of the key issues that belong to testing statistical hypotheses. The main focus in this article is to review recent retrospective change point policies and propose new relevant procedures. Commonly applied practical quality control purposes have declared statements of the change point problems. Various biostatistical and engineering applications cause consideration of an extended form of the change point problem. In this article, we consider parametric and distribution free generalized change point detection policies, attending to different contexts of optimality and robustness of the procedures. We conducted a broad Monte Carlo study to compare various parametric and nonparametric tests, also investigating a sensitivity of the change point detection policies with respect to assumptions required for correct executions of the procedures. An example based on real biomarker measurements is provided to judge our conclusions.

The estimation of the lifetime distribution of a technical item is an important issue in reliability. Since the assumption of i.i.d. failure cycles is questionable if the item is subject to a repair rather than a renewal at failure time, considerable efforts have been made to develop a flexible general repair model. A repairable system with general repairs introduced by Last and Szekli (1998) is considered. Apart from simple special cases, this model leads to a strong dependency among the observed failure times. The aim of this paper is to estimate the underlying failure time distribution and its cumulative hazard given that the failure process has been observed up to the nth failure. Non-parametric estimators of Kaplan-Meier and Nelson-Aalen type are used. Strong uniform consistency of the estimators is proved as n tends to infinity. Further results on weak convergence are derived. Neither stationarity nor mixing conditions are required. Reviewed by P. Rochus (Liège)

We investigate the possibility of using a combination of a smartphone and a smartwatch, carried by a shopper, to get insights into the shopper's behavior inside a retail store. The proposed IRIS framework uses standard locomotive and gestural micro-activities as building blocks to define novel composite features that help classify different facets of a shopper's interaction/experience with individual items, as well as attributes of the overall shopping episode or the store. Besides defining such novel features, IRIS builds a novel segmentation algorithm, which partitions the duration of an entire shopping episode into atomic item-level interactions, by using a combination of feature-based landmarking, change point detection and variable-order HMMbased sequence prediction. Experiments with 50 real-life grocery shopping episodes, collected from 25 shoppers, we show that IRIS can demarcate item-level interactions with an accuracy of approx. 91%, and subsequently characterize item-and-episode level shopper behavior with accuracies of over 90%.

Inferential statistics is the scientific method for evidence-based knowledge acquisition. The underlying logic is difficult and the mathematical methods created for this purpose are based on advanced concepts of probability, combined with different epistemological positions. Many different approaches have been developed over the years. Following the classical significance tests of Fisher and the statistical tests by Neyman and Pearson, and decision theory, two more approaches are considered here using qualitative scientific argument: the Bayesian approach, which is linked to a contested conception of probability, and the rerandomization and bootstrap strand, which is bound to simulation. While Barnett (1982) analysed statistical inference from a mathematical/philosophical perspective to shed light on the various approaches, we analyse from the grand scenario of statistics education and investigate the relative merits of each approach. Some thoughts are developed to reconsider inform...

The three-parameter exponentiated-Weibull distribution has been widely used especially in the modelling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. Bayesian estimation procedures are considered for estimating the reliability function R(t)=P(X>t) and P=P(X>Y) for three-parameter exponentiated-Weibull distribution under type II censoring. Considerations are given to squared-error loss. Approach: A new technique of obtaining Bayes estimators of these parametric functions is introduced in which major role is played by the estimators of the powers of the parameter and the functional forms of the parametric functions to be estimated are not needed. Simulation studied is performed. Reliability theory is mainly concerned with the and engineering, in the field of medical, in the field of determination of the probability th...

This paper describes a formal feedback-control algorithm for dynamic voltage/frequency scaling (DVS) in a portable multimedia system to save power while maintaining a desired playback rate. Our algorithm is similar in complexity to the previously-proposed change-point detection algorithm but does a better job of maintaining stable throughput and is not dependent on the assumption of an exponential distribution of the frame decoding rate. For approximately the same energy savings as reported by , our controller is able to keep the average frame delay within 10% of the target more than 90% of the time, whereas the change-point detection algorithm kept the average frame delay with 10% of the target only 70% or less of the time executing the same workload.

This licentiate thesis contains two articles. 1. Tools to estimate the first passage time to a convex barrier 2. A large deviation estimate of the first passage time to a convex barrier ∗Postal address: Mathematical Statistics, Stockholm University, SE-106 91, Sweden. E-mail: olah@math.su.se. Mathematical Statistics Stockholm University Research Report 2003:6, http://www.math.su.se/matstat Tools to estimate the first passage time to a convex barrier Ola Hammarlid∗

Background: Rainfall variation is a clear indicator of climate change. IPCC in its multiple assessment reports has raised concerns over the changing climate and rising global average temperatures which could lead to widespread and catastrophic impacts on natural and human systems. The study of long-term patterns is crucial in establishing evidence of shifting climate and informing policy decisions. Objectives: This study examines the rainfall trend and variability of the semi-arid Agra district and assesses rainfall in the region. Annual rainfall for 101 years from 18 grid data points was statistically analysed for the same. Methodology: For the projection and analysis of data points, a Thiessen network polygon was drawn using QGIS 3.28.4. Each grid data point was assigned a Thiessen polygon. According to the area each Thiessen polygon covers, it was assigned weights. Then according to the weight of each polygon, annual rain in that area was calculated. Next, the data were tested for homogeneity and breakpoints using the Standard Normal Homogeneity test, Buishand's Range test, Buishand's U test and Pettitt's test. After this the trend of the data was identified using Mann-Kendall and the magnitude was calculated using Theil-Sen's estimator. R-studio was used for all the statistical analysis and graph plotting. Results: Upon conducting the Standard Normal Homogeneity test, Buishand's Range test, Buishand's U test and Pettitt's test it was found that the data was nonhomogeneous with the breakpoint in the year 1967. The Mann-Kendall test revealed a declining trend in the annual rainfall and the Theil-Sen estimator calculated the magnitude of this declining trend to be-1.63 for the last century. Conclusion: The findings suggest that climate change is having a significant impact on rainfall in the semi-arid Agra district. The declining trend in rainfall could have several negative consequences for the region, including water scarcity, crop failure, and increased risk of droughts.

Water resources management in the Sahel region, West Africa, is extremely difficult because of high inter-annual rainfall variability. Unexpected floods and droughts often lead to severe humanitarian crises. Seasonal rainfall forecasting is one possible way to increase resilience to climate variability by providing information in advance about the amount of rainfall expected in each upcoming rainy season. Rainfall forecasting models often arbitrarily assume that rainfall is linked to predictors by a multiple linear regression with parameters that are independent of time and of predictor magnitude. Two probabilistic methods based on change point detection that allow the relationship to change according to time or rainfall magnitude were developed in this paper using normalized Bayes factors. Each method uses one of the following predictors: sea level pressure, air temperature and relative humidity. Method M1 allows for change in model parameters according to annual rainfall magnitude, while M2 allows for changes in model parameters with time. M1 and M2 were compared to the classical linear model with constant parameters (M3) and to the climatology (M4). New hydrological insights for the region: The model that allows a change in the predictor-predictand relationship according to rainfall amplitude (M1) and uses air temperature as predictor is the best model for seasonal rainfall forecasting in the study area.

Control charts are used to distinguish between chance and assignable causes in the variability of quality characteristics. When a control chart signals that an assignable cause is present, process engineers must initiate a search for the assignable cause of the process disturbance. Identifying the time of a process change could lead to simplifying the search for the assignable cause and less process down time, as well as help to reduce the probability of incorrectly identifying the assignable cause. The change point estimation by likelihood theory and the built-in change point estimation in a control chart have been discussed until now. In this article, we discuss two kinds of process change point estimation when the CUSUM (,) x s control chart for monitoring process mean and variance simultaneously is operated. Throughout some numerical experiments about the performance of the change point estimation, the change point estimation techniques in the CUSUM (,) x s control chart are considered.

Control charts are used to distinguish between chance and assignable causes in the variability of quality characteristics. When a control chart signals that an assignable cause is present, process engineers must initiate a search for the assignable cause of the process disturbance. Identifying the time of a process change could lead to simplifying the search for the assignable cause and less process down time, as well as help to reduce the probability of incorrectly identifying the assignable cause. The change point estimation by likelihood theory and the built-in change point estimation in a control chart have been discussed until now. In this article, we discuss two kinds of process change point estimation when the CUSUM (,) x s control chart for monitoring process mean and variance simultaneously is operated. Throughout some numerical experiments about the performance of the change point estimation, the change point estimation techniques in the CUSUM (,) x s control chart are considered.