a robust surveillance scheme for stochastically ordered alternatives we sequentially observe independent observations x 1 x 2 such that initially they have distribution g 0 at some unknown time v they become stochastically larger having distribution g 1 neither g 0 nor g 1 is fully specified we wish to detect that a change has taken place as soon as possible after its occurrence subject to a constraint on the rate of false alarms we derive a family of nonparametric sequential procedures based on ranks with noncontiguous alternatives in mind large sample approximations to the operating characteristics are obtained analytically the proposed procedures all possess robustness of validity because they are based on ranks near optimal sensitivity can be obtained for specific alternatives by choosing an appropriate procedure for example when observations are normally distributed with one standard deviation shift in mean postchange an appropriate nonparametric surveillance scheme yields 97 asymptotic relative efficiency as compared to the optimal procedure when all distributional parameters are known our procedures are computationally feasible monte carlo experiments confirm the applicability of the asymptotic calculations including high levels of efficiency for sample sizes met in practice

wiener disorder problem with observations at fixed discrete time epochs suppose that a wiener process gains a known drift rate at some unobservable disorder time with some zero modified exponential distribution the process is observed only at known fixed discrete time epochs which may not always be spaced in equal distances the problem is to detect the disorder time as quickly as possible by means of an alarm that depends only on the observations of wiener process at those discrete time epochs we show that bayes optimal alarm times which minimize expected total cost of frequent false alarms and detection delay time always exist optimal alarms may in general sound between observation times and when the space time process of the odds that disorder happened in the past hits a set with a nontrivial boundary the optimal stopping boundary is piecewise continuous and explodes as time approaches from left to each observation time on each observation interval if the boundary is not strictly increasing everywhere then it first decreases and then increases it is strictly monotone wherever it does not vanish its decreasing portion always coincides with some explicit function we develop numerical algorithms to calculate nearly optimal detection algorithms and their bayes risks and we illustrate their use on numerical examples the solution of wiener disorder problem with discretely spaced observation times will help reduce risks and costs associated with disease outbreak and production quality control where the observations are often collected and or inspected periodically

sequential change point detection when unknown parameters are present in the pre change distribution in the sequential change point detection literature most research specifies a required frequency of false alarms at a given pre change distribution f and tries to minimize the detection delay for every possible post change distribution g in this paper motivated by a number of practical examples we first consider the reverse question by specifying a required detection delay at a given post change distribution and trying to minimize the frequency of false alarms for every possible pre change distribution f we present asymptotically optimal procedures for one parameter exponential families next we develop a general theory for change point problems when both the pre change distribution f and the post change distribution g involve unknown parameters we also apply our approach to the special case of detecting shifts in the mean of independent normal observations

non restarting cumulative sum charts and control of the false discovery rate cumulative sum or cusum charts are typically used to detect a change in the distribution of a sequence of observations e g shifts in the mean usually after signalling the chart is restarted by setting it to some value below the signalling threshold we propose a non restarting cusum chart which is able to detect periods during which the stream is out of control further we advocate an upper boundary to prevent the cusum chart rising too high which helps to detect a change back into control we present an algorithm to control the false discovery rate when considering cusum charts based on multiple streams of data we consider two definitions of a false discovery signalling out of control when the observations have been in control since the start and signalling out of control when the observations have been in control since the last time the chart was at zero we prove that the false discovery rate is controlled under both these definitions simultaneously simulations reveal the difference in false discovery rate control when using these and other desirable definitions of a false discovery copyright 2013 oxford university press

a dynamic sampling approach for detecting a change in distribution the problem of detecting a change in drift of brownian motion is considered in the bayesian framework with the time of change having a prior exponential distribution to the well known problem of finding an optimal stopping rule for declaring a change we add the option of continuously controlling the sampling rates resulting in controlling the variance coefficient of the process the combined problem of finding an optimal rate function dynamic sampling together with an optimal stopping rule is solved and explicit expressions for the quantities of interest are derived the dynamic sampling procedure is shown to be significantly superior to constant rate sampling the comparison is most favorable when the expected time until change tends to infinity where the relative efficiency between the two procedures tends to infinity

average run length to false alarm for surveillance schemes designed with partially specified pre change distribution observations are taken independently and sequentially detection of a change in distribution is studied when the problem has an invariance structure the prechange distribution is assumed to be a member of a specified family and is assumed known up to a nuisance parameter we provide a general method of constructing surveillance schemes in the presence of a nuisance parameter and give sufficient conditions for approximating their average run lengths to false alarm applications include detecting a change in scale of i i d gamma variates with unknown initial scale detecting a change in location of i i d normal variates with unknown initial mean and a non parametric scheme based on ranks for detecting a change to a stochastically larger distribution

on the exponential decay in thermoelasticity without energy dissipation and of type iii in presence of an absorbing boundary we study the asymptotic behavior of the solution of a 3d hyperbolic system arising in the green naghdi models of thermoelasticity of type ii and iii with a dissipative boundary condition for the displacement and prove that the energy exponentially decays in time

phase space green s functions for modeling time harmonic scattering from smooth inhomogeneous objects the paper deals with inhomogeneous medium green s functions in the phase space domain by which the phase space local spectral distributions of the field scattered by a high contrast object due a genetic time harmonic incidence are evaluated two forms of phase space green s functions are considered one that links induced sources in the configuration space to phase space distributions of the scattered field while the other one directly links the phase space distribution of the incident field to phase space distributions of the scattered field the scattering mechanism is described in terms of local samplings of the object function which are localized in the object domain according to the scattered and incidence processing parameters applications in the field of inverse scattering may be expected to yield fast and efficient algorithms due to the capability of analytically evaluating forward scattering green s functions

asymptotically optimal prediction for time varying data generating processes we develop a methodology referred to as kinetic prediction for predicting time series undergoing unknown changes in their data generating distributions based on kolmogorov tikhomirov s varepsilon entropy we propose a concept called varepsilon predictability that quantifies the size of a model class which can be parametric or nonparametric and the maximal number of abrupt structural changes that guarantee the achievability of asymptotically optimal prediction moreover for parametric distribution families we extend the aforementioned kinetic prediction with discretized function spaces to its counterpart with continuous function spaces and propose a sequential monte carlo based implementation we also extend our methodology for predicting smoothly varying data generating distributions under reasonable assumptions we prove that the average predictive performance converges almost surely to the oracle bound which corresponds to the case that the data generating distributions are known in advance the results also shed some light on the so called prediction inference dilemma various examples and numerical results are provided to demonstrate the wide applicability of our methodology

a phase space beam summation formulation for ultrawide band radiation a new discrete phase space gaussian beam gb summation representation for ultrawide band uwb radiation from an aperture source distribution is presented the formulation is based on the theory of the windowed fourier transform wft frames wherein we introduce a novel relation between the frequency and the frame overcompleteness with this procedure the discrete lattice of beams that are emitted by the aperture satisfies the main requirement of being frequency independent so that only a single set of beams needs to be traced through the medium for all the frequencies in the band it is also shown that a properly tuned class of iso diffracting id gaussian windows provides the snuggest frame representation for all frequencies thus generating stable and localized expansion coefficients furthermore due to the id property the resulting gbs propagators are fully described by frequency independent matrices whose calculation in the ambient environment need to be done only once for all frequencies consequently the theory may also be expressed directly in the time domain as will be presented elsewhere the localization implied by the new formulation is demonstrated numerically for an uwb focused aperture it is shown that the algorithm extracts the local radiation properties of the aperture source and enhances only those beams that conform with these properties i e those residing near the phase space lagrange manifold further localization is due to the fact the algorithm accounts only for beams that pass within a few beamwidths vicinity of the observation point it is thus shown that the total number of beams is much smaller than the landau pollak bound on the aperture s degrees of freedom

on the average run length to false alarm in surveillance problems which possess an invariance structure surveillance can be based in some change point detection problems on a sequence of invariant statistics gordon and pollak prove that under 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

non orthogonal domain parabolic equation and its tilted gaussian beam solutions a non orthogonal coordinate system which is a priori matched to localized initial field distributions for time harmonic wave propagation is presented applying in addition a rigorous paraxial asymptotic approximation results in a novel parabolic wave equation for beam type field propagation in 3d homogeneous media localized solutions to this equation that exactly match linearly phased gaussian aperture distributions are termed tilted gaussian beams these beams serve as the building blocks for various beam type expansion schemes application of the scalar waveobjects to electromagnetic field beam type expansion as well as reflection and transmission of these waveobjects by planar velocity dielectric discontinuity are presented a numerical example which demonstrates the enhanced accuracy of the tilted gaussian beams over the conventional ones concludes the paper

quantization effect on the log likelihood ratio and its application to decentralized sequential detection it is well known that quantization cannot increase the kullback leibler divergence which can be thought of as the expected value or first moment of the log likelihood ratio in this paper we investigate the quantization effects on the second moment of the log likelihood ratio it is shown via the convex domination technique that quantization may result in an increase in the case of the second moment but the increase is bounded above by 2 e the result is then applied to decentralized sequential detection problems not only to provide simpler sufficient conditions for asymptotic optimality theories in the simplest models but also to shed new light on more complicated models in addition some brief remarks on other higher order moments of the log likelihood ratio are also provided

optimal sequential detection in multi stream data consider a large number of detectors each generating a data stream the task is to detect online distribution changes in a small fraction of the data streams previous approaches to this problem include the use of mixture likelihood ratios and sum of cusums we provide here extensions and modifications of these approaches that are optimal in detecting normal mean shifts we show how the optimal detection delay depends on the fraction of data streams undergoing distribution changes as the number of detectors goes to infinity there are three detection domains in the first domain for moderately large fractions immediate detection is possible in the second domain for smaller fractions the detection delay grows logarithmically with the number of detectors with an asymptotic constant extending those in sparse normal mixture detection in the third domain for even smaller fractions the detection delay lies in the framework of the classical detection delay formula of lorden we show that the optimal detection delay is achieved by the sum of detectability score transformations of either the partial scores or cusum scores of the data streams

surveillance of a simple linear regression this article considers an important aspect of the general sequential analysis problem where a process is in control up to some unknown point i 1 after which the distribution from which the observations are generated changes an extensive sequential analytic literature assumes that the change in distribution is abrupt for example from n 0 1 to n 1 there is also an extensive literature that deals with a gradual change in the case where the decision whether or not a change has occurred is based on a fixed set of observations rather than an ongoing process of decision making every time a new observation is obtained however there is virtually no literature on the practical case of sequentially detecting a gradual change in distribution visualize a machine deteriorating gradually this article considers solutions to this problem as a first approximation the gradual change problem can be modeled as a change from a fixed distribution to a model of simple linear regression with respect to ti

decision theoretic optimality of the cusum procedure suppose x 1 x 2 are independent random variables such that for some unknown each of x 1 x 1 is distributed according to f 0 while x x 1 are all distributed according to f 1 we prove a result of moustakides that claims that the cusum procedures are optimal in the sense of lorden we do that by proving that the procedures are bayes for some stochastic mechanism of generating

information bounds and quickest change detection in decentralized decision systems the quickest change detection problem is studied in decentralized decision systems where a set of sensors receive independent observations and send summary messages to the fusion center which makes a final decision in the system where the sensors do not have access to their past observations the previously conjectured asymptotic optimality of a procedure with a monotone likelihood ratio quantizer mlrq is proved in the case of additive gaussian sensor noise if the signal to noise ratios snr at some sensors are sufficiently high this procedure can perform as well as the optimal centralized procedure that has access to all the sensor observations even if all snrs are low its detection delay will be at most pi 2 1ap 57 larger than that of the optimal centralized procedure next in the system where the sensors have full access to their past observations the first asymptotically optimal procedure in the literature is developed surprisingly the procedure has the same asymptotic performance as the optimal centralized procedure although it may perform poorly in some practical situations because of slow asymptotic convergence finally it is shown that neither past message information nor the feedback from the fusion center improves the asymptotic performance in the simplest model

asymptotic minimax robust quickest change detection for dependent stochastic processes with parametric uncertainty in this paper we consider the problem of quickly detecting an unknown change in the conditional densities of a dependent stochastic process in contrast to the existing quickest change detection approaches for dependent stochastic processes we propose minimax robust versions of the popular lorden pollak and bayesian criteria for when there is uncertainty about the parameter of the post change conditional densities under an information theoretic pythagorean inequality condition on the uncertainty set of possible post change parameters we identify asymptotic minimax robust solutions to our lorden pollak and bayesian problems finally through simulation examples we illustrate that asymptotically minimax robust rules can provide detection performance comparable to the popular but more computationally expensive generalized likelihood ratio rule

a mathematical framework for new fault detection schemes in nonlinear stochastic continuous time dynamical systems in this work a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous time dynamical systems is developed these schemes are based on a stochastic process called the residual which reflects the system behavior and whose changes are to be detected a quickest detection scheme for the residual is proposed which is based on the computed likelihood ratios for time varying statistical changes in the ornstein uhlenbeck process several expressions are provided depending on a priori knowledge of the fault which can be employed in a proposed cusum type approximated scheme this general setting gathers different existing fault detection schemes within a unifying framework and allows for the definition of new ones a comparative simulation example illustrates the behavior of the proposed schemes

optimal stopping times for detecting changes in distributions it is shown that page s stopping time is optimal for the detection of changes in distributions in a well defined sense this work is a generalization of an existing result where it was shown that page s stopping time is optimal asymptotically

data efficient quickest change detection in minimax settings the classical problem of quickest change detection is studied with an additional constraint on the cost of observations used in the detection process the change point is modeled as an unknown constant and minimax formulations are proposed for the problem the objective in these formulations is to find a stopping time and an on off observation control policy for the observation sequence to minimize a version of the worst possible average delay subject to constraints on the false alarm rate and the fraction of time observations are taken before change an algorithm called de cusum is proposed and is shown to be asymptotically optimal for the proposed formulations as the false alarm rate goes to zero numerical results are used to show that the de cusum algorithm has good tradeoff curves and performs significantly better than the approach of fractional sampling in which the observations are skipped using the outcome of a sequence of coin tosses independent of the observation process this study is guided by the insights gained from an earlier study of a bayesian version of this problem

performance analysis of sequential tests between poisson processes the problem of performance computation for sequential tests between poisson processes is considered the average sample numbers and error probabilities of the sequential probability ratio test sprt between two homogeneous poisson processes are known to solve certain delay differential equations ddes exact numerically stable solutions to these ddes are developed here and their asymptotic properties are explored these solutions are seen to be superior to earlier solutions of dvoretsky kiefer and wolfowitz 1953 which suffer from severe numerical instability in some ranges of parameters of interest in applications the application of these results is illustrated in the problem of performance approximation for the cumulative sum cusum quickest detection procedure

a pulsed beam summation formulation for short pulse radiation based on windowed radon transform wrt frames a new time domain td representation for radiation from apertures wherein the field is expanded in a discrete lattice of shifted tilted and retarded pulsed beam pb propagators is proposed the pb representation provides a uniformly accurate systematic framework for ray based tracking of ultrawide band transient fields in complex configurations e g slowly or abruptly varying inhomogeneous media the excitation coefficients of the pbs are extracted from the aperture source distribution via a new discretized local slant stack transform the formulation is structured upon a new class of frames termed windowed radon transform frames the sets of expansion and analysis functions are shown to be dual frames thus facilitating representation of arbitrary bandlimited source fields explicit expressions for the processing windows the analysis frame set and for the pb propagators the expansion set are provided for the class of isodiffracting pbs accuracy of the pb expansion technique is demonstrated for a focusing aperture case that tends to fail the conventional ray shooting schemes

detecting a suddenly arriving dynamic profile of finite duration this paper addresses the detection of a suddenly arriving dynamic profile of a finite duration often called a transient change in contrast to the traditional abrupt change detection where the post change period is assumed to be infinitely long the detection of a suddenly arriving transient change should be done before it disappears the detection of transient changes after their disappearance is considered as missed hence the traditional quickest change detection criterion minimizing the average detection delays provided a prescribed false alarm rate is compromised the proposed optimality criterion minimizes the worst case probability of missed detection provided that the worst case probability of false alarm during a certain period is upper bounded a suboptimal cusum type transient change detection algorithm based on a subclass of truncated sequential probability ratio tests is proposed the optimization of the proposed algorithm in this subclass leads to a specially designed finite moving average test the proposed method is analyzed theoretically and by simulation a special attention is paid to the case of gaussian observations with a dynamic profile

a diffusion process and its applications to detecting a change in the drift of brownian motion abstract the purpose of the present paper is to make a quantitative comparison of the shiryayev roberts and page procedures we do this in the context of continuous time in order to use the machinery of diffusion processes to perform explicitly certain calculations which seem impossible in discrete time although the continuous time results are not especially good approximations to the corresponding quantities in discrete time they provide very useful comparative information on which to base selection of a stopping rule this paper is organized as follows the shiryayev roberts process is defined and shown to be a novel diffusion process with some surprising properties we also specify more precisely the basis for our comparison of the two procedures and give the results of some elementary calculations these developments contain an asymptotic evaluation we define a modification of our basic procedure and give an asymptotic evaluation of its average run length numerical comparisons and a discussion of their significance are contained next our conclusions are roughly these in simple situations where the two procedures can be directly compared neither seems dramatically superior to the other however the shiryayev roberts procedure is more easily adapted to complex circumstances and consequently warrants additional study

existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary in this article we study the degenerate system r 1 r 2 0 subject to memory conditions on the boundary given email protected 1 x u t email protected email protected u v email protected 0 r 2 x v t email protected a u v email protected 0 email protected 0 email protected 0 tg 1 t s email protected email protected s email protected 1x 0 email protected 0 email protected 0 tg 2 t s email protected email protected s email protected 1x 0 u 0 v 0 u 0 v 0 r 1u t 0 r 2v t 0 r 1u 1 r 2v 1 email protected where w is a bounded region in r n whose boundary is partitioned into disjoint sets c 0 c 1 we prove that the dissipations given by the memory terms are strong enough to guarantee exponential or polynomial decay provided the relaxation functions also decay exponentially or polynomially and with the same rate of decay

second order asymptotic optimality in multisensor sequential change detection a generalized multisensor sequential change detection problem is considered in which a number of possibly correlated sensors monitor an environment in real time the joint distribution of their observations is determined by a global parameter vector and at some unknown time there is a change in an unknown subset of components of this parameter vector the goal is to detect the change as soon as possible while controlling the rate of false alarms we establish the second order asymptotic optimality with respect to lorden s criterion of various generalizations of the cusum rule that is we show that their additional expected worst case detection delay relative to the one that could be achieved if the affected subset was known remains bounded as the rate of false alarm goes to 0 for any possible subset of affected components this general framework incorporates the traditional multisensor setup in which only an unknown subset of sensors is affected by the change the latter problem has a special structure which we exploit in order to obtain feasible representations of the proposed schemes we present the results of a simulation study where we compare the proposed schemes with scalable detection rules that are only first order asymptotically optimal finally in the special case that the change affects exactly one sensor we consider the scheme that runs in parallel the local cusum rules and study the problem of specifying the local thresholds

an adi pe approach for modeling radio transmission loss in tunnels alternate direction implicit adi method is used to study radio wave propagation in tunnels using the parabolic equation pe we formulate the adi technique for use in tunnels with rectangular circular and arched cross sections and with lossy walls the electrical parameters of the lossy walls are characterized by an equivalent surface impedance a vector pe is also formulated for use in tunnels with lossy walls it is shown that the adi is more computationally efficient than the crank nicolson method however boundary conditions become more difficult to model the boundary conditions of the adi intermediate planes are given the same boundary conditions as the physical plane and the overall accuracy is reduced also when implementing the adi in tunnels with circular cross sections the order at which the line by line decomposition occurs becomes important to validate the adi pe we show simulation results for tunnel test cases with known analytical solutions furthermore the adi pe is used to simulate real tunnels in order to compare with experimental data it is shown that the pe models the electric fields most accurately in real tunnels at large distances where the lower order modes dominate

propagation modeling over terrain using the parabolic wave equation we address the numerical solution of the parabolic wave equation over terrain using the fourier split step approach the method referred to as a shift map generalizes that of beilis and tappert 1979 who introduced a coordinate transformation technique to flatten the boundary this technique is extended to a wide angle form allowing larger propagation angles with respect to the horizon a new impedance boundary condition is derived for electromagnetic waves incident on a finitely conducting surface that enables solution of the parabolic wave pwe using the previously developed mixed fourier transform it is also shown by example that in many cases of interest the boundary may be approximated by discrete piecewise linear segments without affecting the field solution a more accurate shift map solution of the pwe for a piecewise linear boundary is therefore developed for modeling propagation over digitally sampled terrain data the shift map solution is applied to various surface types including ramps wedges curved obstacles and actual terrain where possible comparisons are made between the numerical solution and an exact analytical form the examples demonstrate that the shift map performs well for surface slopes as large as 10 15 spl deg and discontinuous slope changes on the order of 15 20 spl deg to accommodate a larger range of slopes it is suggested that the most viable solution for general terrain modeling is a hybrid of the shift map with the well known terrain masking knife edge diffraction approximation

sequential detection of a change in a normal mean when the initial value is unknown three stopping rules are proposed to detect a change in a normal mean when the initial value of the mean is unknown but an estimate obtained from a training sample is available asymptotic approximations are given for the average run length when there is no change under certain hypotheses about the length of time before the change occurs and the magnitude of the change we obtain asymptotic approximations for the expected delay in detection in terms of the corresponding expected delay in the much simpler case of a known initial value the results of a monte carlo experiment supplement our asymptotic theory to yield some general conclusions about the relative merits of the three stopping rules and guidelines for choosing the size of the training sample

sequential changepoint detection in quality control and dynamical systems after a brief survey of a large variety of sequential detection procedures that are widely scattered in statistical references on quality control and engineering references on fault detection and signal processing we study some open problems concerning these procedures and introduce a unified theory of sequential changepoint detection this theory leads to a class of sequential detection rules which are not too demanding in computational and memory requirements for on line implementation and yet are nearly optimal under several performance criteria

nonanticipating estimation applied to sequential analysis and changepoint detection suppose a process yields independent observations whose distributions belong to a family parameterized by theta e theta when the process is in control the observations are i i d with a known parameter value theta 0 when the process is out of control the parameter changes we apply an idea of robbins and siegmund proc sixth berkeley symp math statist probab 4 1972 37 41 to construct a class of sequential tests and detection schemes whereby the unknown post change parameters are estimated this approach is especially useful in situations where the parametric space is intricate and mixture type rules are operationally or conceptually difficult to formulate we exemplify our approach by applying it to the problem of detecting a change in the shape parameter of a gamma distribution in both a univariate and a multivariate setting

optimal design of second order linear filters for control charting in many common control charting situations the statistic to be charted can be viewed as the output of a linear filter applied to the sequence of process measurement data in recent work that has generalized this concept the charted statistic is the output of a general linear filter in impulse response form and the filter is designed by selecting its impulse response coefficients to optimize its average run length performance in this work we restrict attention to the class of all second order linear filters applied to the residuals of a time series model of the process data we present an algorithm for optimizing the design of the second order filter that is more computationally efficient and robust than the algorithm for optimizing the general linear filter we demonstrate that the optimal second order filter performs almost as well as the optimal general linear filter in many situations both methods share a number of interesting characteristics and are tuned to detect any distinct features of the p

optimal detection of a change in distribution abstract document discusses a stopping rule that is a limit of bayes rules derived then an almost minimax rule is presented

tracking stopping times through noisy observations a novel quickest detection setting is proposed generalizing the well known bayesian change point detection model suppose xi yi i ges 1 is a sequence of pairs of random variables and that s is a stopping time with respect to xi i ges 1 the problem is to find a stopping time t with respect to yi i ges 1 that optimally tracks s in the sense that t minimizes the expected reaction delay bbe t s while keeping the false alarm probability p t s e t s below a given threshold alpha isin 0 1 this problem formulation applies in several areas such as in communication detection forecasting and quality control

nonparametric sequential change point detection by a vertically trimmed box method this paper examines a new method for sequential detection of a sudden and unobservable change in a sequence of independent observations with completely unspecified distribution functions a nonparametric detection rule is proposed which relies on the concept of a moving vertically trimmed box as such it will be coined as the vertical box control chart v box chart its implementation requires merely to count the number of data points which fall into the box attached to the last available observation no a priori knowledge of data distributions is required and proper tuning of the box size provides a quick detection technique this is supported by establishing statistical properties of the method which explain the role of the tuning parameters used in the v box chart these theoretical results are verified by simulation studies which indicate that the v box chart may provide quick detection with zero delay for jumps of moderate sizes its averaged run length to detection is more favorable than the one for the classical ewma method by comparison with the classical shewhart chart which was optimized for normal errors our method provides comparable or better performance

detecting a change in regression first order optimality 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

two strategies in the problem of change detection and isolation the comparison between optimal sequential and nonsequential fixed size sample strategies in the problem of abrupt change detection and isolation is discussed in particular we show that sometimes a simple fixed size sample algorithm is almost as efficient as an optimal sequential algorithm which leads to a burdensome number of arithmetical operations

average run lengths of an optimal method of detecting a change in distribution abstract suppose one accumulates independent observations from a certain process initially the process is at state 0 at some unknown point in time something occurs e g a breakdown which puts the process in state 1 and consequently the stochastic behavior of the observations changes it is of interest to declare that a change took place to raise an alarm as soon as possible after its occurrence subject to a restriction on the rate of false detections it is assumed that the aforementioned observations are the only information one has about the process and the problem is to construct a good detection scheme practical examples of this problem arise in areas such as health quality control ecological monitoring etc for instance consider surveillance for congenital malformations in newborn infants under normal circumstances the percentage of babies born with a certain type of malformation has a known value should something occur such as an environmental change the introduction of a new drug to the market etc the percentage may increase one would want to raise an alarm as quickly as possible after a change would have taken place subject to an acceptable rate of false alarms

efficient scalable schemes for monitoring a large number of data streams the sequential changepoint detection problem is studied in the context of global online monitoring of a large number of independent data streams we are interested in detecting an occurring event as soon as possible but we do not know when the event will occur nor do we know which subset of data streams will be affected by the event a family of scalable schemes is proposed based on the sum of the local cumulative sum cusum statistics from each individual data stream and is shown to asymptotically minimize the detection delays for each and every possible combination of affected data streams subject to the global false alarm constraint the usefulness and limitations of our asymptotic optimality results are illustrated by numerical simulations and heuristic arguments the appendices contain a probabilistic result on the first epoch to simultaneous record values for multiple independent random walks

misspecified and asymptotically minimax robust quickest change detection we investigate the quickest detection of an unknown change in the distribution of a stochastic process generating independent and identically distributed observations we develop new bounds on the performance of misspecified cumulative sum cusum rules and pose minimax robust versions of the popular lorden and pollak criteria with polynomial or higher order moment detection delay penalties by exploiting our results for misspecified cusum rules we identify solutions to our robust quickest change detection problems in the asymptotic regime of few false alarms in contrast to previous robust quickest change detection treatments our asymptotic results hold under relaxed conditions on the uncertainty sets of possible prechange and postchange distributions we illustrate our results in simulations and apply them to the problem of detecting target manoeuvres in low signal to noise ratio settings i e dim target manoeuvre detection

risk adjusted monitoring of time to event recently there has been interest in risk adjusted cumulative sum charts cusums to monitor the performance of e g hospitals taking into account the heterogeneity of patients even though many outcomes involve time only conventional regression models are commonly used in this article we investigate how time to event models may be used for monitoring purposes we consider monitoring using cusums based on the partial likelihood ratio between an out of control state and an in control state we consider both proportional and nonproportional alternatives as well as a head start against proportional alternatives we present an analytic method of computing the expected number of observed events before stopping or the probability of stopping before a given observed number of events in a stationary set up the former is roughly proportional to the average run length in calendar time adding a head start changes the threshold only slightly if the expected number of events until hitting is used as a criterion however it changes the threshold substantially if a false alarm probability is used in simulation studies charts based on survival analysis perform better than simpler monitoring schemes we present one example from retail finance and one medical application

on optimality of the shiryaev roberts procedure for detecting a change in distribution in 1985 for detecting a change in distribution pollak introduced a specific minimax performance metric and a randomized version of the shiryaev roberts procedure where the zero initial condition is replaced by a random variable sampled from the quasi stationary distribution of the shiryaev roberts statistic pollak proved that this procedure is third order asymptotically optimal as the mean time to false alarm becomes large the question of whether pollak s procedure is strictly minimax for any false alarm rate has been open for more than two decades and there were several attempts to prove this strict optimality in this paper we provide a counterexample which shows that pollak s procedure is not optimal and that there is a strictly optimal procedure which is nothing but the shiryaev roberts procedure that starts with a specially designed deterministic point

sprt and cusum in hidden markov models in this paper we study the problems of sequential probability ratio tests for parameterized hidden markov models we investigate in some detail the performance of the tests and derive corrected brownian approximations for error probabilities and expected sample sizes asymptotic optimality of the sequential probability ratio test for testing simple hypotheses based on hidden markov chain data is established next we consider the cumulative sum cusum procedure for change point detection in this model based on the renewal property of the stopping rule cusum can be regarded as a repeated one sided sequential probability ratio test asymptotic optimality of the cusum procedure is proved in the sense of lorden 1971 motivated by the sequential analysis in hidden markov models wald s likelihood ratio identity and wald s equation for products of markov random matrices are also given we apply these results to several types of hidden markov models i i d hidden markov models switch gaussian regression and switch gaussian autoregression which are commonly used in digital communications speech recognition bioinformatics and economics

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

a note on ritov s bayes approach to the minimax property of the cusum procedure 1 introduction page 1954 proposed the cusum procedures as a solu tion to the problem of sequential detection of a change in distribution lorden 1971 introduced a notion of minimax optimality for change point models andshowed that the cusum procedures are asymptotically optimal in his sense moustakides 1986 then showed the minimax optimality of the cusum pro cedures when the initial and nal distribution are both known ritov 1990 used a bayes approach and gave an interesting argument for moustakides result similar to that of lehmann 1959 on the optimality of the sequentialprobability ratio test we transfer his approach to a continuous time modeland discuss the structure of the bayes risk let be an arbitrary but known constant we will consider a process wwithw

quickest detection with exponential penalty for delay the problem of detecting a change in the probability distribution of a random sequence is considered stopping times are derived that optimize the tradeoff between detection delay and false alarms within two criteria in both cases the detection delay is penalized exponentially rather than linearly as has been the case in previous formulations of this problem the first of these two criteria is to minimize a worst case measure of the exponential detection delay within a lower bound constraint on the mean time between false alarms expressions for the performance of the optimal detection rule are also developed for this case it is seen for example that the classical page cusum test can be arbitrarily unfavorable relative to the optimal test under exponential delay penalty the second criterion considered is a bayesian one in which the unknown change point is assumed to obey a geometric prior distribution in this case the optimal stopping time effects an optimal trade off between the expected exponential detection delay and the probability of false alarm finally generalizations of these results to problems in which the penalties for delay may be path dependent are also considered

asymptotic operating characteristics of an optimal change point detection in hidden markov models let 0 1 1 be observations from the hidden markov model with probability distribution p 0 and let 1 be observations from the hidden markov model with probability distribution p 1 the parameters 0 and 1 are given while the change point is unknown the problem is to raise an alarm as soon as possible after the distribution changes from p 0 to p 1 but to avoid false alarms specifically we seek a stopping rule n which allows us to observe the s sequentially such that e n is large and subject to this constraint sup k e k n k n k is as small as possible here e k denotes expectation under the change point k and e denotes expectation under the hypothesis of no change whatever in this paper we investigate the performance of the shiryayev roberts pollak srp rule for change point detection in the dynamic system of hidden markov models by making use of markov chain representation for the likelihood function the structure of asymptotically minimax policy and of the bayes rule and sequential hypothesis testing theory for markov random walks we show that the srp procedure is asymptotically minimax in the sense of pollak ann statist 13 1985 206 227 next we present a second order asymptotic approximation for the expected stopping time of such a stopping scheme when w 1 motivated by the sequential analysis in hidden markov models a nonlinear renewal theory for markov random walks is also given

using the generalized likelihood ratio statistic for sequential detection of a change point we study sequential detection of a change point using the generalized likelihood ratio statistic for the special case of detecting a change in a normal mean with known variance we give approximations to the average run lengths and compare our procedure to standard cusum tests and combined cusum shewhart tests several examples indicating extensions to problems involving multiple parameters are discussed

systematic study of fields due to extended apertures by gaussian beam discretization gaussian beams are used as basis elements in field representations to gain insight into how the choice of beam parameters affects the final representation a systematic study for the simple test case of a one dimensional linearly phased cosine aperture distribution has been undertaken by successively adding individual displaced and or tilted beams with large narrow or matched waists one can assess how the elements in various portions of the lattice contribute to the build up of the actual field in the aperture near zone and far zone adding enough beams always guarantees homing in on the exact solution as is verified here by independent comparison different beam choices imply different modeling of the radiation process the understanding gained thereby is helpful for selecting beam parameters in subsequent applications where it is necessary to balance requirements of good convergence ease of computation and ability to track the beams through perturbing environments like a radome indications are that the narrow beams provide the most robust and versatile formulation to deal with these generalized conditions

comparison of ewma cusum and shiryayev roberts procedures for detecting a shift in the mean pollak and siegmund compared the shiryayev roberts procedure with the cusum procedure for detecting a change in the drift of a brownian motion based on the conditional average delay time in this paper the exponentially weighted moving average ewma procedure proposed by roberts is compared with the shiryayev roberts and cusum procedures the comparison is based on the stationary average delay time as advocated by shiryayev the optimal design for the ewma procedure and its asymptotic properties are studied when the average in control run length is large the results show that the ewma procedure is less efficient than the other two procedures

time dependent tilted pulsed beams and their properties novel time dependent wavepacket equation and its pulsed field solutions are obtained by utilizing a non orthogonal coordinate system which is a priori matched to the field s planar linearly delayed pulsed localized aperture distributions these waveobjects that serve as the building blocks for various time dependent beam expansion schemes are termed tilted pulsed beams iso axial pulsed beams are parameterized in term of beam widths waist locations collimation lengths wave front radii of curvature and other features emphasis is placed on a direct time domain derivation a numerical example is presented in which the enhanced accuracy of the tilted pulsed beams over the conventional orthogonal coordinates ones in the well collimated zone is demonstrated

input design for detection of abrupt changes in dynamical systems the detection and diagnosis of changes in stationary dynamical systems via statistical methods and using input design to improve detection performance are discussed a cumulative sum test to detect a change towards one of several hypotheses is obtained by exploiting connections with the sequential probability ratio test for input design the objectives are taken to be to decrease the detection time and at the same time to ensure a tolerable false alarm rate both off line auxiliary inputs and on line generation of the input signal by a linear output feedback are considered the problem is first introduced for the two hypotheses case and then the design techniques are extended to the general multiple hypotheses case

data efficient minimax quickest change detection with composite post change distribution the problem of quickest change detection is studied where there is an additional constraint on the cost of observations used before the change point and where the post change distribution is composite minimax formulations are proposed for this problem it is assumed that the post change family of distributions has a member which is least favorable in a well defined sense an algorithm is proposed in which on off observation control is employed using the least favorable distribution and a generalized likelihood ratio based approach is used for change detection under additional conditions on the post change family of distributions it is shown that the proposed algorithm is asymptotically optimal uniformly for all possible post change distributions

a linearized inverse boundary value problem for maxwell s equations abstract in this paper we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body we study the full set of maxwell s equations that govern time harmonic electric and magnetic fields we seek to reconstruct the magnetic permeability the electric permitivity and the electric conductivity in the interior of the body from measurements made on the surface we exhibit appropriate boundary measurements in the form of a boundary mapping specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field this data can be used to reconstruct and approximately provided they deviate only slightly from known constants we also estimate the reconstruction errors

exponential decay for maxwell equations with a boundary memory condition abstract we study the asymptotic behavior of the solution of the maxwell equations with the following boundary condition of memory type 0 1 e t 0 h t n 0 s h t s n d s we consider a graffi type free energy and we prove that if the kernel satisfies the condition 0 and the domain is strongly star shaped then the energy of the solution exponentially decays we also prove that the exponential decay of is a necessary condition for the exponential decay of the solution

grouped data sequential probability ratio tests and cumulative sum control charts methodology is proposed for the design of sequential methods when data are obtained by gauging articles into groups exact expressions are obtained for the operating characteristics and average sampling number of wald sequential probability ratio tests and for the average run length of cumulative sum cusum schemes based on grouped data step by step design algorithms are provided to assist the practitioner the methodology is illustrated assuming a normal process with known standard deviation in which we wish to detect shifts in the mean an example from a progressive die operation is presented the methods proposed are simple to implement and are an economical alternative to variables data based sequential sampling plans and cusum control charts

an efficient sequential nonparametric scheme for detecting a change of distribution ble and remarkably efficient the method is based on the sequential vectors of signs and ranks of the observations the methodology is one of likelihood ratio a sequence of likelihood ratios for these vectors is computed and the shiryayev roberts approach to changepoint detection is then applied to yield a class of statistics and associated stopping rules inequalities and asymptotic approximations for the operating characteristics of these rules are developed these are found to be valid also for small average run lengths and early changepoints as well the relative efficiency of these schemes with respect to a normal parametric shift detection policy is very high making them a robust alternative to parametric methof s