additive change detection in nonlinear systems with unknown change parameters we study the change detection problem in partially observed nonlinear systems which satisfy the hidden markov model hmm property the change parameters are assumed unknown and the changes can be slow or sudden a partially observed system needs to be tracked first before changes can be detected sudden changes result in significant loss of track these can be detected easily using the increase in tracking error te or observation likelihood ol or using a cusum type method applied to either of these however slow changes which result in small loss of track often get missed we propose here a statistic that uses the tracked component of the change to detect it and hence detects slow changes faster than te or ol we show both analytically and through simulations that this statistic complements ol and te for change detection

stepwise signal extraction via marginal likelihood this article studies the estimation of a stepwise signal to determine the number and locations of change points of the stepwise signal we formulate a maximum marginal likelihood estimator which can be computed with a quadratic cost using dynamic programming we carry out an extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator we propose to treat each possible set of change points equally and adopt an empirical bayes approach to specify the prior distribution of segment parameters a detailed simulation study is performed to compare the effectiveness of this method with other existing methods we demonstrate our method on single molecule enzyme reaction data and on dna array comparative genomic hybridization cgh data our study shows that this method is applicable to a wide range of models and offers appealing results in practice supplementary materials for this article are available online

efficient recursive algorithms for detection of abrupt changes in signals and control systems this paper addresses a number of open problems concerning the generalized likelihood ratio glr rules for online detection of faults and parameter changes in control systems it is shown that with an appropriate choice of the threshold and window size these glr rules are asymptotically optimal the rules are also extended to non likelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing gaussian approximations to these statistics when the window size is chosen suitably recursive algorithms are developed for practical implementation of the procedure and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate

compact isospectral sets of surfaces on etudie des ensembles de surfaces qui sont isospectrales par rapport a l operateur de laplace beltrami

a dependent data extension of wald s identity and its application to sequential test performance computation the development of an exponential transformation of measure not restricted to independent identically distributed data is presented for a class of semi markov processes known as markov additive ma process the ma measure transformation is applied to obtain a new form of the wald identity to demonstrate the utility of this extension to ma processes the application of sequential tests with markov data to error probability performance analysis is investigated in particular it is demonstrated how previous work dealing with robust error probability evaluation in the presence of uncertain serial dependency can be applied to sequential tests

finding density functionals with machine learning machine learning is used to approximate density functionals for the model problem of the kinetic energy of noninteracting fermions in 1d mean absolute errors below 1 text text mathrm kcal mathrm mol on test densities similar to the training set are reached with fewer than 100 training densities a predictor identifies if a test density is within the interpolation region via principal component analysis a projected functional derivative finds highly accurate self consistent densities the challenges for application of our method to real electronic structure problems are discussed

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

arbitrarily varying channels with constrained inputs and states random coding theorems are proved for discrete memoryless arbitrarily varying channels avcs with constraints on the transmitted codewords and channel state sequences two types of constraints are considered peak i e required for each n length sequence almost surely and average over the message set or over an ensemble for peak constraints on the codewords and on the channel state sequences the avc is shown to have a strong random coding capacity if the codewords and or the channel state sequences are constrained in the average sense the avcs do not possess strong capacities only epsilon capacities are shown to exist

a nonlinear renewal theory soit t le premier instant auquel une marche aleatoire perturbee traverse une frontiere non lineaire on considere les approximations de la distribution de l exces au dela de la frontiere de l esperance du temps d arret et de la variance du temps d arret

asymptotic normality of the maximum likelihood estimator for general hidden markov models hidden markov models hmms have during the last decade become a widespread tool for modeling sequences of dependent random variables inference for such models is usually based on the maximum likelihood estimator mle and consistency of the mle for general hmms was recently proved by leroux in this paper we show that under mild conditions the mle is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the fisher information

information bounds and quick detection of parameter changes in stochastic systems by using information theoretic bounds and sequential hypothesis testing theory this paper provides a new approach to optimal detection of abrupt changes in stochastic systems this approach not only generalizes previous work in the literature on optimal detection far beyond the relatively simple models treated but also suggests alternative performance criteria which are more tractable and more appropriate for general stochastic systems in addition it leads to detection rules which have manageable computational complexity for on line implementation and yet are nearly optimal under the different performance criteria considered

sequential detection of markov targets with trajectory estimation the problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered assuming a markov evolution of the system in particular the pair signal observation forms a hidden markov model hmm a sequential procedure is proposed wherein the detection part is a sequential probability ratio test sprt and the estimation part relies upon a maximum a posteriori probability map criterion gated by the detection stage the parameter to be estimated is the trajectory of the state evolution of the system itself a thorough analysis of the asymptotic behavior of the test in this new scenario is given and sufficient conditions for its asymptotic optimality are stated i e for almost sure minimization of the stopping time and for first order minimization of any moment of its distribution an application to radar surveillance problems is also examined

asymptotic expansions for sums of weakly dependent random vectors it is shown that formal edgeworth expansions are valid for sums of weakly dependent random vectors the error of approximation has ordero n s 2 2 if the strong mixing coefficients in iii are decreasing at an exponential rate the above conditions can easily be checked and are often satisfied when the sequence of random vectors is a gaussian or a markov or an autoregressive process explicit formulas are given for the distribution of finite fourier transforms of a strictly stationary time series

unsupervised learning of phase transitions from principal component analysis to variational autoencoders we examine unsupervised machine learning techniques to learn features that best describe configurations of the two dimensional ising model and the three dimensional xy model the methods range from principal component analysis over manifold and clustering methods to artificial neural network based variational autoencoders they are applied to monte carlo sampled configurations and have a priori no knowledge about the hamiltonian or the order parameter we find that the most promising algorithms are principal component analysis and variational autoencoders their predicted latent parameters correspond to the known order parameters the latent representations of the models in question are clustered which makes it possible to identify phases without prior knowledge of their existence furthermore we find that the reconstruction loss function can be used as a universal identifier for phase transitions

minimax robust quickest change detection the popular criteria of optimality for quickest change detection procedures are the lorden criterion the pollak criterion and the bayesian criterion in this paper a robust version of these quickest change detection problems is considered when the pre change and post change distributions are not known exactly but belong to known uncertainty classes of distributions for uncertainty classes that satisfy a specific condition it is shown that one can identify least favorable distributions lfds from the uncertainty classes such that the detection rule designed for the lfds is optimal for the robust problem in a minimax sense the condition is similar to that required for the identification of lfds for the robust hypothesis testing problem originally studied by huber an upper bound on the delay incurred by the robust test is also obtained in the asymptotic setting under the lorden criterion of optimality this bound quantifies the delay penalty incurred to guarantee robustness when the lfds can be identified the proposed test is easier to implement than the cusum test based on the generalized likelihood ratio glr statistic which is a popular approach for such robust change detection problems the proposed test is also shown to give better performance than the glr test in simulations for some parameter values

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

inverse ising inference using all the data we show that a method based on logistic regression using all the data solves the inverse ising problem far better than mean field calculations relying only on sample pairwise correlation functions while still computationally feasible for hundreds of nodes the largest improvement in reconstruction occurs for strong interactions using two examples a diluted sherrington kirkpatrick model and a two dimensional lattice we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l 1 regularization is beneficial in this process pushing inference abilities further into low temperature regimes

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

universal classification for hidden markov models binary hypotheses testing using empirically observed statistics is studied in the neyman pearson formulation for the hidden markov model hmm an asymptotically optimal decision rule is proposed and compared to the generalized likelihood ratio test glrt which has been shown in earlier studies to be asymptotically optimal for simpler parametric families the proof of the main theorem is provided the result can be applied to several types of hmms commonly used in speech recognition and communication applications several applications are demonstrated

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

estimates and extremals for zeta function determinants on four manifolds leta be a positive integral power of a natural conformally covariant differential operator on tensor spinors in a riemannian manifold suppose thata is formally self adjoint and has positive definite leading symbol for example a could be the conformal laplacian yamabe operator l or the square of the dirac operator open image in new window within the conformal class left g e 2w g 0 w in c infty m right of an einstein locally symmetric background metricgo on a compact four manifoldm we use an exponential sobolev inequality of adams to show that bounds on the functional determinant ofa and the volume ofg imply bounds on thew2 2 norm of the conformal factorw provided that a certain conformally invariant geometric constantk k m g o a is strictly less than 32 2 we show for the operatorsl and open image in new window that indeedk 32 2 except when m g o is the standard sphere or a hyperbolic space form on the sphere a centering argument allows us to obtain a bound of the same type despite the fact thatk is exactly equal to 32 2 in this case finally we use an inequality of beckner to show that in the conformal class of the standard four sphere the determinant ofl or of open image in new window is extremized exactly at the standard metric and its images under the conformal transformation groupo 5 1

asymptotic optimality of mixture rules for detecting changes in general stochastic models the paper addresses a sequential changepoint detection problem for a general stochastic model assuming that the observed data may be non i i d i e dependent and non identically distributed and prior distribution of the change point is arbitrary tartakovsky and veeravalli 2005 baron and tartakovsky 2006 and more recently tartakovsky 2017 developed a general asymptotic theory of changepoint detection for non i i d stochastic models assuming certain stability of the log likelihood ratio process in the case of simple hypotheses when both pre change and post change models are completely specified however in most applications the post change distribution is not completely known in the present paper we generalize previous results to the case of parametric uncertainty assuming that the parameter of the post change distribution is unknown we introduce two detection rules based on mixtures the mixture shiryaev rule and the mixture shiryaev roberts rule and study their asymptotic properties in the bayesian context in particular we provide sufficient conditions under which these rules are first order asymptotically optimal minimizing moments of the delay to detection as the probability of false alarm approaches zero

statistical mechanics for natural flocks of birds flocking is a typical example of emergent collective behavior where interactions between individuals produce collective patterns on the large scale here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data we construct the minimally structured maximum entropy model consistent with experimental correlations in large flocks of starlings the maximum entropy model shows that local pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings with no free parameters we also find that the number of interacting neighbors is independent of flock density confirming that interactions are ruled by topological rather than metric distance finally by comparing flocks of different sizes the model correctly accounts for the observed scale invariance of long range correlations among the fluctuations in flight direction

input output properties of the page hinkley detector we consider the stochastic input output properties of a simple non linear dynamical system the so called page hinkley detector playing a key role in change detection and also in queuing theory we show that for l mixing inputs with negative expectation the output process of this system is l mixing the result is applied to get an upper bound for the false alarm rate the proof is then adapted to get a similar result for the case of random i i d inputs possible extensions and open problems are given in the discussion

vector field divergence of predictive model output as indication of phase transitions we introduce an alternative method to identify phase boundaries in physical systems it is based on training a predictive model such as a neural network to infer a physical system s parameters from its state the deviation of the inferred parameters from the underlying correct parameters will be most susceptible and diverge maximally in the vicinity of phase boundaries therefore peaks in the vector field divergence of the model s predictions are used as indication of phase transitions our method is applicable for phase diagrams of arbitrary parameter dimension and without prior information about the phases application to both the two dimensional ising model and the dissipative kuramoto hopf model show promising results

universal decoding for finite state channels universal decoding procedures for finite state channels are discussed although the channel statistics are not known universal decoding can achieve an error probability with an error exponent that for large enough block length or constraint length in case of convolutional codes is equal to the random coding error exponent associated with the optimal maximum likelihood decoding procedure for the given channel the same approach is applied to sequential decoding yielding a universal sequential decoding procedure with a cutoff rate and an error exponent that are equal to those achieved by the classical sequential decoding procedure

critical points of the determinant of the laplace operator abstract the determinant of the laplace operator det is a function on the set of metrics on a compact manifold generalizing the work of osgood phillips and sarnak on surfaces we consider one parameter variations of metrics of fixed volume in the conformal class of given metric by calculating the derivative of log det with respect to such variations we find the condition for a metric to be a critical point of the determinant function homogeneous manifolds satisfy this condition but we exhibit examples of locally homogeneous manifolds which are not critical points in dimensions 3 for 3 dimensional manifolds we derive a formula for the second derivative of log det with respect to such a variation at a critical point using this formula we show that the standard metric on the sphere s 3 and some flat metrics on three dimensional tori are local maxima of the determinant function

analysis of dynamic ising model by a variational approximate method estimation of transfer entropy transfer entropy is an important index for investigating the causal relationship between random variables it is known that a phase transition can be detected by transfer entropy in this work i propose a method for obtaining the transfer entropy by applying the variational approximation method to a dynamic ising model our method is also effective for dynamics that do not satisfy the detailed balance condition our method finds the transfer entropy by solving a transcendental equation when compared with the transfer entropy obtained by monte carlo sampling it was found that they qualitatively matched near the transition point moreover the match was obtained with good accuracy in the region deviated from the transition point

new method for parameter estimation in probabilistic models minimum probability flow fitting probabilistic models to data is often difficult due to the general intractability of the partition function we propose a new parameter fitting method minimum probability flow mpf which is applicable to any parametric model we demonstrate parameter estimation using mpf in two cases a continuous state space model and an ising spin glass in the latter case mpf outperforms current techniques by at least an order of magnitude in convergence time with lower error in the recovered coupling parameters

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

markovian structures in biological sequence alignments abstract the alignment of multiple homologous biopolymer sequences is crucial in research on protein modeling and engineering molecular evolution and prediction in terms of both gene function and gene product structure in this article we provide a coherent view of the two recent models used for multiple sequence alignment the hidden markov model hmm and the block based motif model to develop a set of new algorithms that have both the sensitivity of the block based model and the flexibility of the hmm in particular we decompose the standard hmm into two components the insertion component which is captured by the so called propagation model and the deletion component which is described by a deletion vector such a decomposition serves as a basis for rational compromise between biological specificity and model flexibility furthermore we introduce a bayesian model selection criterion that in combination with the propagation model genetic algorithm and other computational aspects forms the cor

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

specification testing in markov switching time series models this paper develops a series of specification tests of markov switching time series models tests for omitted autocorrelation omitted arch misspecification of the markovian dynamics and omitted explanatory variables are proposed all of the tests can be constructed as a natural byproduct of the routine used to calculate the smoothed probability that a given observation came from a particular regime and do not require estimation of additional parameters the paper performs monte carlo analysis of the tests and briefly illustrates their use with an empirical application

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

quickest change detection and kullback leibler divergence for two state hidden markov models in this paper the quickest change detection problem is studied in two state hidden markov models hmm where the vector parameter theta of the hmm changes from theta 0 to theta 1 at some unknown time and one wants to detect the true change as quickly as possible while controlling the false alarm rate it turns out that the generalized likelihood ratio glr scheme while theoretically straightforward is generally computationally infeasible for the hmm to develop efficient but computationally simple schemes for the hmm we first discuss a subtlety in the recursive form of the generalized likelihood ratio glr scheme for the hmm then we show that the recursive cusum scheme proposed in fuh ann statist 2003 can be regarded as a quasi glr scheme for pseudo post change hypotheses with certain dependence structure between pre and postchange observations next we extend the quasi glr idea to propose recursive score schemes in the scenario when the postchange parameter theta 1 of the hmm involves a real valued nuisance parameter finally the kullback leibler kl divergence plays an essential role in the quickest change detection problem and many other fields however it is rather challenging to numerically compute it in hmms here we develop a non monte carlo method that computes the kl divergence of two state hmms via the underlying invariant probability measure which is characterized by the fredholm integral equation numerical study demonstrates an unusual property of the kl divergence for hmm that implies the severe effects of misspecifying the postchange parameter for the hmm

probabilistic distances between finite state finite alphabet hidden markov models this note considers the problem of evaluating a probabilistic distance between discrete time homogeneous first order finite state finite alphabet hidden markov models hmms our approach is based on a correspondence between probability measures and hmms established in this note using a probability measure transformation technique we obtain recursive expressions for the relative entropy between the marginal probability distributions of two hmms under consideration also the relative entropy rate as the limit of the time averaged value of the above relative entropy is obtained these expressions are given in terms of the parameters of the given hmms furthermore we show that the probabilistic distance between hmms used in the existing literature admits a representation in terms of a conditional expectation given the observation sequence this representation allows us to evaluate this distance using an information state approach

an equation of monge ampere type in conformal geometry and four manifolds of positive ricci curvature we formulate natural conformally invariant conditions on a 4 manifold for the existence of a metric whose schouten tensor satisfies a quadratic inequality this inequality implies that the eigenvalues of the ricci tensor are positively pinched

extremal metrics of zeta function determinants on 4 manifolds in conformal geometry the sobolev inequality at a critical exponent has received much attention in particular the determination of the best constants has played a crucial role in the yamabe problem in dimension two the analogous problem deals with the moser trudinger inequality on a compact riemann surface m2 there exists a constant c c m so that f e47w2 c m if f ivw12 1 and f w 0 the connection of this inequality with geometry comes through the zeta functional determinant of the laplacian as defined by ray singer for a riemannian metric g let 0 a1 a2 be the spectrum

an algorithm for detecting a change in a stochastic process the problem of detecting a change from one given stationary and ergodic stochastic process to another such process is considered it is assumed that both stochastic processes are processes with memory and that they are mutually independent a sequential test is proposed and analyzed it is proved that the proposed test is asymptotically optimal in a mathematically precise sense

extremal metrics for spectral functions of dirac operators in even and odd dimensions abstract let m n g be a closed smooth riemannian spin manifold and denote by its atiyah singer dirac operator we study the variation of riemannian metrics for the zeta function and functional determinant of 2 and prove finiteness of the morse index at stationary metrics and local extremality at such metrics under general i e not only conformal change of metrics in even dimensions which is also a new case for the conformal laplacian the relevant stability operator is of log polyhomogeneous pseudodifferential type and we prove new results of independent interest on the spectrum for such operators we use this to prove local extremality under variation of the riemannian metric which in the important example when m n g is the round n sphere gives a partial verification of branson s conjecture on the pattern of extremals thus det 2 has a local max max min min when the dimension is 4 k 4 k 1 4 k 2 4 k 3 respectively

model parameter learning using kullback leibler divergence abstract in this paper we address the following problem for a given set of spin configurations whose probability distribution is of the boltzmann type how do we determine the model coupling parameters we demonstrate that directly minimizing the kullback leibler divergence is an efficient method we test this method against the ising and xy models on the one dimensional 1d and two dimensional 2d lattices and provide two estimators to quantify the model quality we apply this method to two types of problems first we apply it to the real space renormalization group rg we find that the obtained rg flow is sufficiently good for determining the phase boundary within 1 of the exact result and the critical point but not accurate enough for critical exponents the proposed method provides a simple way to numerically estimate amplitudes of the interactions typically truncated in the real space rg procedure second we apply this method to the dynamical system composed of self propelled particles where we extract the parameter of a statistical model a generalized xy model from a dynamical system described by the viscek model we are able to obtain reasonable coupling values corresponding to different noise strengths of the viscek model our method is thus able to provide quantitative analysis of dynamical systems composed of self propelled particles

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

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

a note on optimal detection of a change in distribution suppose x 1 x 2 dots x nu 1 are iid random variables with distribution f 0 and x nu x nu 1 dots are are iid with distributed f 1 the change point nu is unknown the problem is to raise an alarm as soon as possible after the distribution changes from f 0 to f 1 detect the change but to avoid false alarms pollak found a version of the shiryayev roberts procedure to be asymptotically optimal for the problem of minimizing the average run length to detection over all stopping times which satisfy a given constraint on the rate of false alarms here we find that this procedure is strictly optimal for a slight reformulation of the problem he considered explicit formulas are developed for the calculation of the average run length both before and after the change for the optimal stopping time

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

identifiability of hidden markov information sources and their minimum degrees of freedom if only a function of the state in a finite state markov chain is observed then the stochastic process is no longer markovian in general this type of information source is found widely and the basic problem of its identifiability remains open that is the problem of showing when two different markov chains generate the same stochastic process the identifiability problem is completely solved by linear algebra where a block structure of a markov transition matrix plays a fundamental role and from which the minimum degree of freedom for a source is revealed

quickest change detection of a markov process across a sensor array recent attention in quickest change detection in the multisensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption in this work a more general scenario is considered where the change propagates across the sensors and its propagation can be modeled as a markov process a centralized bayesian version of this problem is considered with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process the problem of minimizing the average detection delay subject to false alarm constraints is formulated in a dynamic programming framework insights into the structure of the optimal stopping rule are presented in the limiting case of rare disruptions it is shown that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened under a certain condition on the kullback leibler k l divergence between the post and the pre change densities it is established that the threshold test is asymptotically optimal in the vanishing false alarm probability regime it is shown via numerical studies that this low complexity threshold test results in a substantial improvement in performance over naive tests such as a single sensor test or a test that incorrectly assumes that the change propagates instantaneously

moduli space heights and isospectral sets of plane domains let q be a plane domain of finite connectivity n with smooth boundary and choose a fixed domain 2 of the same type then there exists a flat metric g on 2 such that q is isometric with 29g in what follows we do not distinguish between isometric domains by the spectrum of 29 we mean the spectrum of the laplace beltrami operator ag on 29 with dirichlet boundary conditions the height h eg log det ag is a spectral invariant and plays a central role in this paper among all suitably normalized flat metrics on 2 conformal to a given metric g there is a unique flat metric for which the height is a minimum this metric is characterized by the fact that d 2 has constant geodesic curvature we call such a metric uniform and denote it by u the set of all such metrics is denoted by u 2 we can therefore identify with the moduli space 2 of conformal structures on e for n 3 we introduce a special parametrization for mu 2 by means of which we show that h u oo as u approaches the boundary of fu 2 using this along with the heat invariants for the laplacian we then show that any isospectral set of plane domains is compact in the c topology similar results hold for n 1 and 2

critical metrics for the determinant of the laplacian in odd dimensions let m be a closed compact n dimensional manifold with n odd we calculate the first and second variations of the zeta regularized determinants det a and det l as the metric on m varies where a denotes the laplacian on functions and l denotes the conformal laplacian we see that the behavior of these functionals depends on the dimension indeed every critical metric for 1 n 1 2det a or 1 n 1 21 det l has finite index consequently there are no local maxima if n 4rm 1 and no local minima if n 4m 3 we show that the standard 3 sphere is a local maximum for det a while the standard 4m 3 sphere with m 1 2 is a saddle point by contrast for all odd n the standard n sphere is a local extremal for det l an important tool in our work is the canonical trace on odd class operators in odd dimensions this trace is related to the determinant by the formula det q tr log q and we prove some basic results on how to calculate this trace

optimality of cusum rule approximations in change point detection problems application to nonlinear state space systems the well known cumulative sum cusum sequential rule for abrupt model change detection in stochastic dynamic systems relies on the knowledge of the probability density functions of the system output variables conditional on their past values and on the system functioning mode at each time step this paper shows how to build an asymptotically optimal detection rule under the common average run length arl constraint when these densities are not available but can be consistently estimated this is the case for nonlinear state space systems observed through output variables for such systems a new class of particle filters based on convolution kernels allows to get consistent estimates of the conditional densities leading to an optimal cusum like filter detection rule fdr

examples of renormalization group transformations for image sets using the example of configurations generated with the worm algorithm for the two dimensional ising model we propose renormalization group rg transformations inspired by the tensor rg that can be applied to sets of images we relate criticality to the logarithmic divergence of the largest principal component we discuss the changes in link occupation under the rg transformation suggest ways to obtain data collapse and compare with the two state tensor rg approximation near the fixed point

order estimation and sequential universal data compression of a hidden markov source by the method of mixtures we consider first the estimation of the order i e the number of states of a discrete time finite alphabet stationary ergodic hidden markov source hms our estimator uses a description of the observed data in terms of a uniquely decodable code with respect to a mixture distribution obtained by suitably mixing a parametric family of distributions on the observation space this procedure avoids maximum likelihood calculations the order estimator is shown to be strongly consistent with the probability of underestimation decaying exponentially fast in the number n of observations while the probability of overestimation does not exceed cn sup 3 where c is a constant next we present a sequential algorithm for the uniquely decodable universal data compression of the hms which performs an on line estimation of source order followed by arithmetic coding this code asymptotically attains optimum average redundancy

nonparametric estimation of fisher information from real data the fisher information matrix fim is a widely used measure for applications including statistical inference information geometry experiment design and the study of criticality in biological systems the fim is defined for a parametric family of probability distributions and its estimation from data follows one of two paths either the distribution is assumed to be known and the parameters are estimated from the data or the parameters are known and the distribution is estimated from the data we consider the latter case which is applicable for example to experiments where the parameters are controlled by the experimenter and a complicated relation exists between the input parameters and the resulting distribution of the data since we assume that the distribution is unknown we use a nonparametric density estimation on the data and then compute the fim directly from that estimate using a finite difference approximation to estimate the derivatives in its definition the accuracy of the estimate depends on both the method of nonparametric estimation and the difference between the densities used in the finite difference formula we develop an approach for choosing the optimal parameter difference based on large deviations theory and compare two nonparametric density estimation methods the gaussian kernel density estimator and a novel density estimation using field theory method we also compare these two methods to a recently published approach that circumvents the need for density estimation by estimating a nonparametric f divergence and using it to approximate the fim we use the fisher information of the normal distribution to validate our method and as a more involved example we compute the temperature component of the fim in the two dimensional ising model and show that it obeys the expected relation to the heat capacity and therefore peaks at the phase transition at the correct critical temperature

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

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

efficient likelihood estimation in state space models motivated by studying asymptotic properties of the maximum likelihood estimator mle in stochastic volatility sv models in this paper we investigate likelihood estimation in state space models we first prove under some regularity conditions there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the fisher information as its variance with an extra assumption that the likelihood equation has a unique root for each n then there is a consistent sequence of estimators of the unknown parameters if in addition the supremum of the log likelihood function is integrable the mle exists and is strongly consistent edge worth expansion of the approximate solution of likelihood equation is also established several examples including markov switching models arma models g arch models and stochastic volatility sv models are given for illustration

sequential detection and identification of a change in the distribution of a markov modulated random sequence the problem of detection and identification of an unobservable change in the distribution of a random sequence is studied via a hidden markov model hmm approach the formulation is bayesian on line discrete time allowing both single and multiple disorder cases dealing with both independent and identically distributed i i d and dependent observations scenarios allowing for statistical dependencies between the change time and change type in both the observation sequence and the risk structure and allowing for general discrete time disorder distributions several of these factors provide useful new generalizations of the sequential analysis theory for change detection and or hypothesis testing taken individually in this paper a unifying framework is provided that handles each of these considerations not only individually but also concurrently optimality results and optimal decision characterizations are given as well as detailed examples that illustrate the myriad of sequential change detection and identification problems that fall within this new framework

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

critical behaviour of the 3d xy model a monte carlo study we present the results of a study of the three dimensional xy model on a simple cubic lattice using the single cluster updating algorithm combined with improved estimators we have measured the susceptibility and the correlation length for various couplings in the high temperature phase on lattices of size up to l 112 at the transition temperature we studied the fourth order cumulant and other cumulant like quantities on lattices of size up to l 64 from our numerical data we obtain for the critical coupling kc 0 45420 2 and for the static critical exponents v 1 976 6 and v 0 662 7