asymptotic properties of the product limit estimate under random truncation on donne une description precise du comportement asymptotique de l estimateur limite produit incluant une forme explicite simple de la structure de covariance asymptotique

markov chain monte carlo method in bayesian reconstruction of dynamical systems from noisy chaotic time series the presence of a noise component in the time series generated by a dynamical system ds results in finite accuracy of reconstruction of the evolution operator eo any model that can be constructed will generally speaking differ from the original system one of the ways to take this fact into consideration is to describe parameters of the model eo as random quantities 1 two limiting cases may be distinguished 2 the perfect model scenario when the form of the operator describing the ds evolution is reliably known and the imperfect model scenario when eo is unknown the perfect model scenario is realized for instance when the problem of hidden information transmission is solved using chaotic time series ts generated by the known ds 3 in this case we are interested in the characteristics of the system perfect model parameters the most probable value mean dispersion distribution in investigations of many natural atmospheric oceanic tectonic biological systems the eo is unknown which corresponds to the imperfect model scenario then information about model parameters is of no value as the physical meaning of the parameters is unknown and we are interested in the properties of the model defined by these parameters and reflecting the properties of the reconstructed ds nevertheless in this case too evaluation of statistical characteristics of model parameters is the key element without which the problem of reconstructing a ds generating the original ts cannot be solved the mathematical body used to reconstruct the ds is determined by a specific application for example for finding the most probable set of model perfect or imperfect parameters it suffices to determine the maximum of posterior probability density of model parameters 4 6 however it should be remembered that in the presence of noise the inverse problem of reconstruction becomes ill posed i e it admits an infinite set of solutions selection of the most correct solutions demands regularization that is a physically justified constraint on admissible values of parameters based solely on a priori information 7 this approach is usually called bayesian within the bayesian approach there are methods which make it possible to estimate dispersions and mathematical expectations of the model parameters 8 a significant advantage of such methods is their relatively low computational resource requirements however due to the model nonlinearity the form of parameter distribution may differ strongly from the normal one in this case estimation of expectation and dispersion is insufficient to construct a correct model and one must use the bayesian approach in full in other words we must construct models which include distributions of parameters and take a priori information about the system into account correctly in this formulation the problem can be solved using the markov chain monte carlo mcmc algorithms 9 however in the case of reconstruction of dss by noisy chaotic time series computational resources required for these algorithms strongly depend on distribution dimensionality this limits applicability of the algorithms to a narrow class of problems e g the case of short ts 10 the method proposed in this paper makes it possible to expand the applicability domain of the mcmc algorithms to the case of arbitrarily long ts

parameter estimation through ignorance dynamical modeling lies at the heart of our understanding of physical systems its role in science is deeper than mere operational forecasting in that it allows us to evaluate the adequacy of the mathematical structure of our models despite the importance of model parameters there is no general method of parameter estimation outside linear systems a relatively simple method of parameter estimation for nonlinear systems is introduced based on variations in the accuracy of probability forecasts it is illustrated on the logistic map the henon map and the 12 dimensional lorenz96 flow and its ability to outperform linear least squares in these systems is explored at various noise levels and sampling rates as expected it is more effective when the forecast error distributions are non gaussian the method selects parameter values by minimizing a proper local skill score for continuous probability forecasts as a function of the parameter values this approach is easier to implement in practice than alternative nonlinear methods based on the geometry of attractors or the ability of the model to shadow the observations direct measures of inadequacy in the model the implied ignorance and the information deficit are introduced

nonparametric estimation of transition probabilities for a general progressive multi state model under cross sectional sampling nonparametric estimation of the transition probability matrix of a progressive multi state model is considered under cross sectional sampling two different estimators adapted to possibly right censored and left truncated data are proposed the estimators require full retrospective information before the truncation time which when exploited increases efficiency they are obtained as differences between two survival functions constructed for sub samples of subjects occupying specific states at a certain time point both estimators correct the oversampling of relatively large survival times by using the left truncation times associated with the cross sectional observation asymptotic results are established and finite sample performance is investigated through simulations one of the proposed estimators performs better when there is no censoring while the second one is strongly recommended with censored data the new estimators are applied to data on patients in intensive care units icus

a numerical algorithm for the solution of signorini problems in this paper we propose a new iterative algorithm for the solution of a certain class of signorini problems such problems arise in the modelling of a variety of physical phenomena and usually involve the determination of an unknown free boundary here we describe a way of locating the free boundary directly and provide a proof that the algorithm converges when used with analytic methods the advantage of this algorithm is that it can be used in conjunction with any numerical method with minimal development of extra code we demonstrate its application with the boundary element method to some physical problems in both two and three dimensions

a semiparametric model for randomly truncated data abstract for randomly censored data it is known that the maximum likelihood estimate mle of the survival curve is not affected by parametric assumption on the censoring variable the kaplan meier 1958 estimate is the mle for both nonparametric and semiparametric models for randomly truncated data the truncation product limit estimate is the mle for nonparametric models this is not the case if the truncation mechanism is parameterized however specifically let x be a generic random variable and t be the truncation variable if the distribution of t is parameterized and the distribution of x is left unspecified it can be shown that the truncation product limit estimate is not the mle for this semiparametric model even though it is for the fully nonparametric model in this article the mle is characterized for the semiparametric model and the large sample properties of the estimate are established the results show that unlike censoring the parametric information from the truncation mechanism

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

two projection methods for the solution of signorini problems abstract two iterative methods based on projection and boundary element methods are considered for signorini problems the regularized problem with the projection boundary condition is first deduced from the signorini problem by using the equivalence between the signorini boundary condition and the projection fixed point problem our methods formulate the signorini boundary condition into a sequence of robin boundary conditions in the new boundary condition there is a penalty parameter the convergence speed of the first method is greatly influenced by the value of which is difficult to choose for individual problems to improve the performance of this method we present a self adaptive projection method which adjusts the parameter automatically per iteration based on the iterative data the main result of this work is to provide the convergence of the methods under mild assumptions as the iteration process is given by the potential and its derivative on the boundary of the domain the unknowns of the problem are computed explicitly by using the boundary element method both theoretical results and numerical experiments indicate efficiency of the methods proposed

inferential framework for nonstationary dynamics i theory a general bayesian framework is introduced for the inference of time varying parameters in nonstationary nonlinear stochastic dynamical systems its convergence is discussed the performance of the method is analyzed in the context of detecting signaling in a system of neurons modeled as fitzhugh nagumo fhn oscillators it is assumed that only fast action potentials for each oscillator mixed by an unknown measurement matrix can be detected it is shown that the proposed approach is able to reconstruct unmeasured hidden variables of the fhn oscillators to determine the model parameters to detect stepwise changes of control parameters for each oscillator and to follow continuous evolution of the control parameters in the adiabatic limit

testing the assumption of independence of truncation time and failure time summary for data subject to random censorship it is well known that the assumption of independence between censoring time and failure time cannot be tested nonparametrically for data subject to random truncation however it is possible to test independence of truncation time and failure time a statistic generalizing kendall s tau is proposed for testing the independence assumption and asymptotic properties under the null hypothesis are derived a conditional permutation test is also derived for small data sets generalization to allow right censoring and an application to truncated linear regression are also briefly discussed

nonparametric estimation from cross sectional survival data abstract in many follow up studies survival data are often observed according to a cross sectional sampling scheme data of this type are subject to left truncation in addition to the usual right censoring a number of characteristics and properties of the product limit estimate for left truncated and right censored data have been explored and found to be similar to those of the kaplan meier estimate under the stationarity assumption however it is believed that an alternative estimate has much better efficiency in this article the conditional maximum likelihood estimate mle property of the product limit estimate is visited the non parametric mle of the truncation distribution is derived use of this estimate includes testing the stationarity assumption estimating the proportion of truncated data and other applications in prevalent cohort studies the analysis of the estimation is based on a working data approach the asymptotic properties of the proposed estimates are developed through nonpar

better nonlinear models from noisy data attractors with maximum likelihood a new approach to nonlinear modelling is presented which by incorporating the global behaviour of the model lifts shortcomings of both least squares and total least squares parameter estimates although ubiquitous in practice a least squares approach is fundamentally flawed in that it assumes independent normally distributed ind forecast errors nonlinear models will not yield ind errors even if the noise is ind a new cost function is obtained via the maximum likelihood principle superior results are illustrated both for small data sets and infinitely long data streams

length biased sampling with right censoring when survival data arise from prevalent cases ascertained through a cross sectional study it is well known that the survivor function corresponding to these data is length biased and different from the survivor function derived from incident cases length biased data have been treated both unconditionally and conditionally in the literature in the latter case where length bias is viewed as being induced by random left truncation of the survival times the truncating distribution is assumed to be unknown conditioning on the observed truncation times hence causes very little loss of information in many instances however it can be supposed that the truncating distribution is uniform and it has been pointed out that under these circumstances an unconditional analysis will be more informative there are no results in the current literature that give the asymptotic properties of the unconditional nonparametric maximum likelihood estimator npmle of the unbiased survivor function in the presence of cen

evaluation of nonlinearity and validity of nonlinear modeling for complex time series even if an original time series exhibits nonlinearity it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria therefore we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria through numerical simulations we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model the measures are also robust against observational noises we also analyze some real time series the difference of the number of chickenpox and measles patients the number of sunspots five japanese vowels and the chaotic laser we can confirm that the nonlinear model is effective for the japanese vowel a the difference of the number of measles patients and the chaotic laser

a new formulation of signorini s type for seepage problems with free surfaces a new variational inequality formulation for seepage problems with free surfaces is presented in which a boundary condition of signorini s type is prescribed over the potential seepage surfaces this makes the singularity of seepage points eliminated and the location of seepage points determined easily compared to other variational formulations the proposed formulation can effectively overcome the mesh dependency and significantly improve the numerical stability a very challenging engineering example with complicated geometry aid strong inhomogeneity is investigated in detail

nonparametric analysis of truncated survival data with application to aids summary one source of data for the induction distribution of aids arises from persons infected by the aids virus from contaminated blood transfusions analyses of these data are complicated because the number of individuals infected by transfusion is unknown information is available only for those who are infected and develop aids within a certain chronologic time interval the statistical problem is one of making inferences about a stochastic process of infection and disease for which realizations are right truncated in chronologic time by considering the process in reverse time we transform the problem to one of analysing survival data that are left truncated in internal time we develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions of several groups an important feature of the natural history and population dynamics of aids is the induction period between infection with the aids virus and the onset of clinical aids this time is sometimes referred to as the latency period or incubation period follow up studies of individuals at risk of being infected will provide direct observations from the induction distribution but most of these studies will not be completed for several years one alternative source of information arises from persons infected with the aids virus from a contaminated blood transfusion of persons infected in this way only those who develop aids by a certain date can be identified the total number who are infected is not known a similar sampling distribution arises in the study of pediatric aids children who contract aids as a result of being infected in utero or at birth can be identified but the total number infected in this way is unknown the statistical problem is one of making inferences about a stochastic process of infection and subsequent disease in which realizations are right truncated in chronologic time by considering the process in reverse time the problem can be transformed to one of survival data that are left truncated in internal time we use this relationship to develop nonparametric methods for estimating and comparing the identifiable aspects of the induction distributions for

testing goodness of fit of a uniform truncation model several goodness of fit tests of a lifetime distribution have been suggested in the literature many take into account censoring and or truncation of event times in some contexts a goodness of fit test for the truncation distribution is of interest in particular better estimates of the lifetime distribution can be obtained when knowledge of the truncation law is exploited in cross sectional sampling for example there are theoretical justifications for the assumption of a uniform truncation distribution and several studies have used it to improve the efficiency of their survival estimates the duality of lifetime and truncation in the absence of censoring enables methods for testing goodness of fit of the lifetime distribution to be used for testing goodness of fit of the truncation distribution however under random censoring this duality does not hold and different tests are required in this article we introduce several goodness of fit tests for the truncation distribution and investigate their performance in the presence of censored event times using simulation we demonstrate the use of our tests on two data sets

failure of maximum likelihood methods for chaotic dynamical systems the maximum likelihood method is a basic statistical technique for estimating parameters and variables and is the starting point for many more sophisticated methods like bayesian methods this paper shows that maximum likelihood fails to identify the true trajectory of a chaotic dynamical system because there are trajectories that appear to be far more infinitely more likely than truth this failure occurs for unbounded noise and for bounded noise when it is sufficiently large and will almost certainly have consequences for parameter estimation in such systems the reason for the failure is rather simple in chaotic dynamical systems there can be trajectories that are consistently closer to the observations than the true trajectory being observed and hence their likelihood dominates truth the residuals of these truth dominating trajectories are not consistent with the noise distribution they would typically have too small standard deviation and many outliers and hence the situation may be remedied by using methods that examine the distribution of residuals and are not entirely maximum likelihood based

markov chain monte carlo estimation of nonlinear dynamics from time series abstract much of nonlinear time series analysis is concerned with inferring unmeasured quantities e g system parameters the shape of attractors in state space from a noisy measured time series from a bayesian perspective the time series is a vector sample picked at random from a probability density the density reflects the system dynamics and our subjective uncertainty about system parameters the measurement function dynamical noise and measurement noise the conditional probability density of the system parameters given the measured data is the basis of a bayesian estimate of the system parameters using illustrative chaotic systems with large amplitude dynamical and measurement noise we show here that it is feasible to use the markov chain monte carlo mcmc technique to generate the bayesian conditional probabilities the resulting parameter estimates are markedly superior to those based on conventional least squares methods the mcmc based estimates are unbiased and allow estimates of dynamical parameters on unmeasured components of the state vector in addition the mcmc method enables de noised attractors to be reconstructed not just in an embedding based on lags of measured variables but in the state space that includes unmeasured components of the dynamics state vector the general purpose mcmc technique effectively combines techniques of nonlinear noise reduction and nonlinear parameter estimation

nonlinear dynamical system identification with dynamic noise and observational noise in this paper we consider the problem of whether a nonlinear system has dynamic noise and then estimate the level of dynamic noise to add to any model we build the method we propose relies on a nonlinear model and an improved least squares method recently proposed on the assumption that observational noise is not large we do not need any a priori knowledge for systems to be considered and we can apply the method to both maps and flows we demonstrate with applications to artificial and experimental data the results indicate that applying the proposed method can detect presence or absence of dynamic noise from scalar time series and give a reliable level of dynamic noise to add to the model built in some cases

consistent nonlinear dynamics identifying model inadequacy empirical modelling often aims for the simplest model consistent with the data a new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space as is well known traditional statistics of nonlinear models like root mean square rms forecast error can prove misleading testing consistency is shown to overcome some of the deficiencies of rms error both within the perfect model scenario and when applied to data from several physical systems using previously published models in particular testing for consistent nonlinear dynamics provides insight towards i identifying when a delay reconstruction fails to be an embedding ii allowing state dependent model selection and iii optimising local neighbourhood size it also provides a more relevant state dependent threshold for identifying false nearest neighbours

a maximum pseudo profile likelihood estimator for the cox model under length biased sampling this paper considers semiparametric estimation of the cox proportional hazards model for right censored and length biased data arising from prevalent sampling to exploit the special structure of length biased sampling we propose a maximum pseudo profile likelihood estimator which can handle time dependent covariates and is consistent under covariate dependent censoring simulation studies show that the proposed estimator is more efficient than its competitors a data analysis illustrates the methods and theory

comparing estimation approaches for the illness death model under left truncation and right censoring left truncated data arise when lifetimes are observed only if they are larger than independent truncation times for example in a cross sectional sampling only individuals who live long enough to be present on the sampling day are observed there are several ways to perform statistical inference under this setting one can do the following i use an unconditional approach ii condition on the value of the truncation variable or iii condition on all the history up to the time of truncation the latter two approaches are equivalent when analyzing univariate survival outcomes but differ under the multi state framework in this paper we consider the illness death model and compare between the three estimation approaches in a parametric regression framework we show that approach ii is more efficient than the standard approach iii although it requires more computational effort approach i is the most efficient approach but it requires knowledge on the distribution of the truncation variable and hence is less robust the methods are compared using a theoretical example and simulations and are applied to intensive care units data collected in a cross sectional design where the illness state corresponds to a bloodstream infection

pseudo partial likelihood for proportional hazards models with biased sampling data we obtain a pseudo partial likelihood for proportional hazards models with biased sampling data by embedding the biased sampling data into left truncated data the log pseudo partial likelihood of the biased sampling data is the expectation of the log partial likelihood of the left truncated data conditioned on the observed data in addition asymptotic properties of the estimator that maximize the pseudo partial likelihood are derived applications to length biased data biased samples with right censoring and proportional hazards models with missing covariates are discussed

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

finite element analysis of contact problems in thermoelasticity the semi coercive case abstract numerical analysis of the signorini problem with friction in two dimensional quasi coupled linear thermoelasticity is investigated piecewise linear finite elements on the triangulation of the given domain r 2 with polygonal boundary are used in this contribution we establish the rate of convergence of the finite element approximate solution u h provided the exact solution is smooth enough in general the problem represents the model problem of a great number of branches such as the model problem of a high level radioactive waste disposal system as well as the model problem of geodynamcis and biomechanics etc

meshless projection iterative analysis of signorini problems using a boundary element free method this paper presents a meshless method based on coupling a boundary element free method befm with a new projection iterative scheme for signorini problems using the new iterative scheme the nonlinear complementary signorini boundary conditions are transformed into neumann boundary conditions then mixed elliptic problems are formed and are solved by the befm in this method only a nodal data structure on the boundary is required and the coefficient matrices of the discrete system equations only have to be computed once in the whole iterative process convergence of the iterative scheme is discussed theoretically numerical examples involving beach percolation and an electropaint process are given to illustrate the convergence rate and high computational efficiency of the method

choice of dynamical variables for global reconstruction of model equations from time series the success of modeling from an experimental time series is determined to a significant extent by the choice of dynamical variables we propose a method for preliminary investigation of a time series whose purpose is to find out whether a global dynamical model with smooth functions can be constructed for the chosen variables the method consists in the estimation of single valuedness and continuity of relations between dynamical variables and variables to enter left hand sides of model equations the method is explained with numerical examples its efficiency is demonstrated by modeling a real nonlinear electric circuit

projection and self adaptive projection methods for the signorini problem with the bem abstract we propose two new projection methods for solving the signorini problem and study the relationship between them since the signorini boundary condition is equivalent to a projection fixed point problem the methods formulate the signorini boundary condition into a sequence of robin boundary conditions and only require solving a variational problem with simple boundary conditions at each iterative step the convergence speed of the first method depends on the parameter heavily and it is difficult to choose a proper for individual problems to improve the efficiency of the method we propose an adaptive projection method which adjusts the parameter automatically per iteration we establish the convergence analysis of the methods because the signorini boundary condition is given in an iterative form by the potential and its derivative on the boundary of the domain we can easily provide the boundary element approximation of the problem finally we present some numerical simulations which illustrate the performance of the methods