necessary and sufficient conditions for near optimal harvesting control problem of stochastic age dependent system in this paper we consider a near optimal harvesting control problems for stochastic age structured population system we establish necessary and sufficient conditions for near optimality these conditions are described by adjoint equations and a nearly maximum condition on the hamiltonian the proof of the main result is based on ekeland s variational principle and the adjoint processes with respect to the control variable as is well known optimal controls may fail to exist even in simple cases this justifies the use of near optimal controls which exist under minimal assumptions and are sufficient in most practical cases at last an example is given for illustrating our results

some properties of the kaplan meier estimator for independent nonidentically distributed random variables in this paper we study the kaplan meier estimator in the case where survival and censoring times are not all i i d we prove several results which are analogous to those shown by van zuijlen in the complete data case

on using stratification in the analysis of linear regression models with right censoring we study two modified synthetic data least squares estimation methods for linear regression models with right censored response variables unspecified residual distributions and random censoring variables which may not be i i d these methods are the result of an investigation into the use of stratification we conclude that stratification should be used whether or not the censoring variables are dependent on the covariates we give the asymptotic results of the estimators and numerical results

a multiple imputation approach to cox regression with interval censored data we propose a general semiparametric method based on multiple imputation for cox regression with interval censored data the method consists of iterating the following two steps first from finite interval censored but not right censored data exact failure times are imputed using tanner and wei s poor man s or asymptotic normal data augmentation scheme based on the current estimates of the regression coefficient and the baseline survival curve second a standard statistical procedure for right censored data such as the cox partial likelihood method is applied to imputed data to update the estimates through simulation we demonstrate that the resulting estimate of the regression coefficient and its associated standard error provide a promising alternative to the nonparametric maximum likelihood estimate our proposal is easily implemented by taking advantage of existing computer programs for right censored data

modelling neuromotor ratings with floor effects associated movements ams are a classical diagnostic tool to assess differences between normal children and children with some motor dysfunction this paper presents a methodology to produce age and gender dependent reference curves for ams of normal children for various tasks of a test battery data available consist of separate ratings of duration and extent of ams which are ordinal quantities with few levels other problems are severe age and gender dependent floor effects as well as some ceiling effects leaving little information for analysis at older ages to get a better scale we combined the two ordinal ratings into one meaningful and quasi continuous quantity referred to as intensity of ams in order to solve problems due to floor effects ceiling effects and discreteness we assumed left right and interval censored values respectively we considered a censored regression problem and postulated a truncated normal distribution for the non censored values after an appropriate transformation of the data using wei and tanner s poor man s data augmentation algorithm together with the technique of linear mixed effects modelling useful reference curves could be produced in contrast to the cumulative probabilities approach for ordinal data our methodology allows the calculation of individual age and gender standardized values which puts us in a position to investigate numerous scientific questions

residual plots for the censored data linear regression model to be consistent censored data linear regression estimators typically require a correctly specified linear regression function and independent and identically distributed errors for uncensored data one can assess these model assumptions informally by examining plots of the residuals against the independent variables or fitted values in this paper i propose plots for censored data analogous to these uncensored data residual plots one can use such plots in the same way as their uncensored data counterparts for checking model assumptions if the model assumptions are correct then the plots should exhibit a random scatter i show that the proposed plots are useful in selecting a linear regression model for the stanford heart transplant data

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

a generalization of the product limit estimator with an application to censored regression the product limit estimator ple and weighted empirical processes are two important ingredients of almost any censored regression analysis a link between them is provided by the generalized ples introduced in this paper these generalized ples are the product limit integrals of the empirical cumulative hazard function estimators in which weighted empirical processes are used to replace the standard empirical processes the weak convergence and some large sample approximations of the generalized ples are established as an application these generalized ples are used to define some minimum distance estimators which are shown to be asymptotically normal these estimators are qualitatively robust in some submodels an optimal choice of the weight matrix is the covariate matrix and some of these estimators are quite efficient at a few common survival distributions to implement these estimators some computational aspects are discussed and an algorithm is given from a real data example and some preliminary simulation results these estimators seem to be very competitive to and more robust than some more traditional estimators such as the buckley james estimator

approximate bayesian analysis of censored survival data summary the bayesian analysis of data arising from a location scale regression model and which may include a number of right censored observations is considered the posterior distributions of the suitably normalized precision parameter and regression coefficient vector are shown to be well approximated by x2 and multivariate t distributions respectively the ideas are illustrated using some clinical survival data

numerical solutions to equations modelling nonlinearly interacting age dependent populations abstract a finite difference method for a system of hyperbolic partial differential integral equations describing nonlinearly interacting age dependent populations dynamics is discussed boundedness of the numerical approximations and unconditional convergence of the method are proved the proof is based on a discrete gronwall type inequality established in the paper

indexing and mining large scale neuron databases using maximum inner product search abstract morphological retrieval is an effective approach to explore large scale neuronal databases as the morphology is correlated with neuronal types regions functions etc in this paper we focus on the neuron identification and analysis via morphological retrieval in our proposed framework multiple features are extracted to represent 3d neuron data because each feature reflects different levels of similarity between neurons we group features into different hierarchies to compute the similarity matrix then compact binary codes are generated from hierarchical features for efficient similarity search since neuronal cells usually have tree topology structure it is hard to distinguish different types of neurons simply via traditional binary coding or hashing methods based on euclidean distance metric and or linear hyperplanes therefore we employ an asymmetric binary coding strategy based on the maximum inner product search mips which not only makes it easier to learn the binary coding functions but also preserves the non linear characteristics of the neuron morphological data we evaluate the proposed method on more than 17 000 neurons by validating the retrieved neurons with associated cell types and brain regions experimental results show the superiority of our approach in neuron morphological retrieval compared with other state of the art methods moreover we demonstrate its potential use cases in the identification and analysis of neuron characteristics from large neuron databases

convergence of numerical solutions to stochastic age structured population system with diffusion in this paper stochastic age structured population system with diffusion are studied in general most of stochastic age structured population system with diffusion do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties the main purpose of this paper is to develop a numerical scheme and show the convergence of the numerical approximation solution to the true solution

posterior computations for censored regression data abstract this article describes the computation of and sampling from the posterior density for censored regression problems with normal and generalized log gamma errors the data augmentation algorithm tanner and wong 1987 is facilitated in the normal error case because of the form of the augmented posterior in the generalized log gamma context this simplicity is absent the work of sweeting 1981 is used as a motivation to develop an importance sampling scheme to sample from an augmented posterior it is shown how the predictive distribution for a new observation may be computed and sampled from the methodology is illustrated with two examples

optimized product quantization product quantization pq is an effective vector quantization method a product quantizer can generate an exponentially large codebook at very low memory time cost the essence of pq is to decompose the high dimensional vector space into the cartesian product of subspaces and then quantize these subspaces separately the optimal space decomposition is important for the pq performance but still remains an unaddressed issue in this paper we optimize pq by minimizing quantization distortions w r t the space decomposition and the quantization codebooks we present two novel solutions to this challenging optimization problem the first solution iteratively solves two simpler sub problems the second solution is based on a gaussian assumption and provides theoretical analysis of the optimality we evaluate our optimized product quantizers in three applications i compact encoding for exhaustive ranking 1 ii building inverted multi indexing for non exhaustive search 2 and iii compacting image representations for image retrieval 3 in all applications our optimized product quantizers outperform existing solutions

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

renovated scatterplots for censored data summary in simple linear regression where the response variable has been subject to right censoring censored points in the scatterplot of observed data are moved vertically to create a renovated scatterplot where the bias of censoring is removed the relationship to least squares estimation and the effect on regression diagnostics are examined in the multiple regression context

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

modeling zero inflated count data using a covariate dependent random effect model in various medical related researches excessive zeros which make the standard poisson regression model inadequate often exist in count data we proposed a covariate dependent random effect model to accommodate the excess zeros and the heterogeneity in the population simultaneously this work is motivated by a data set from a survey on the dental health status of hong kong preschool children where the response variable is the number of decayed missing or filled teeth the random effect has a sound biological interpretation as the overall oral health status or other personal qualities of an individual child that is unobserved and unable to be quantified easily the overall measure of oral health status responsible for accommodating the excessive zeros and also the heterogeneity among the children is covariate dependent this covariate dependent random effect model allows one to distinguish whether a potential covariate has an effect on the conceived overall oral health condition of the children that is the random effect or has a direct effect on the magnitude of the counts or both we proposed a multiple imputation approach for estimation of the parameters we discussed the choice of the imputation size we evaluated the performance of the proposed estimation method through simulation studies and we applied the model and method to the dental data copyright 2012 john wiley sons ltd

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

the ordinal relation preserving binary codes hashing algorithm has been widely used for efficient approximate nearest neighbor ann search learning optimal hashing functions has been given focus and it is still a challenge this paper aims to effectively and efficiently generate relative similarity preserving binary codes most existing hashing methods try to preserve the locality similarity by preserving direct distance similarity while ignoring the relative similarity which advantages in ann search in this paper this issue is solved by proposing the relative error which emphasizes that the ordinal relations in hamming space and euclidean space should be consistent with each other we learn hashing projection functions via two steps the first step adopts the lookup based mechanism to find the optimal binary codes of training data which can preserve the relative similarity and simultaneously adapt to data distribution the binary codes in the first step are considered as supervision information in the second step the objective of the second step is to learn hashing projection functions which can efficiently regenerate the binary codes in the first step aim to be in accordance with the property of data distribution the hyper internal tangent planes of two specified spheres are chosen as hashing projection functions assisted by these projection functions the time complexity of encoding process is greatly reduced experimental results on four public data sets demonstrate that our method outperforms many other state of the art methods author highlightsan effective and efficient binary coding framework which enjoys the merits of lookup based and hamming based methods is proposed relative error is proposed to preserve the relative sensitivity the effective tangent planes are adopted as hashing functions to avoid computing the complex classification problem the encoding error guarantees that the selected hashing functions have good performance

regression m estimators with doubly censored data the m estimators are proposed for the linear regression model with random design when the response observations are doubly censored the proposed estimators are constructed as some functional of a campbell type estimator f n for a bivariate distribution function based on data which are doubly censored in one coordinate we establish strong uniform consistency and asymptotic normality of f n and derive the asymptotic normality of the proposed regression m estimators through verifying their hadamard differentiability property as corollaries we show that our results on the proposed m estimators also apply to other types of data such as uncensored observations bivariate observations under univariate right censoring bivariate right censored observations and so on computation of the proposed regression m estimators is discussed and the method is applied to a doubly censored data set which was encountered in a recent study on the age dependent growth rate of primary breast cancer

analysis of accelerated failure time data with dependent censoring using auxiliary variables via nonparametric multiple imputation we consider the situation of estimating the marginal survival distribution from censored data subject to dependent censoring using auxiliary variables we had previously developed a nonparametric multiple imputation approach the method used two working proportional hazards ph models one for the event times and the other for the censoring times to define a nearest neighbor imputing risk set this risk set was then used to impute failure times for censored observations here we adapt the method to the situation where the event and censoring times follow accelerated failure time models and propose to use the buckley james estimator as the two working models besides studying the performances of the proposed method we also compare the proposed method with two popular methods for handling dependent censoring through the use of auxiliary variables inverse probability of censoring weighted and parametric multiple imputation methods to shed light on the use of them in a simulation study with time independent auxiliary variables we show that all approaches can reduce bias due to dependent censoring the proposed method is robust to misspecification of either one of the two working models and their link function this indicates that a working proportional hazards model is preferred because it is more cumbersome to fit an accelerated failure time model in contrast the inverse probability of censoring weighted method is not robust to misspecification of the link function of the censoring time model the parametric imputation methods rely on the specification of the event time model the approaches are applied to a prostate cancer dataset copyright 2015 john wiley sons ltd

functional form diagnostics for cox s proportional hazards model summary we propose a new type of residual and an easily computed functional form test for the cox proportional hazards model the proposed test is a modification of the omnibus test for testing the overall fit of a parametric regression model developed by stute gonzalez manteiga and presedo quindimil 1998 journal of the american statistical association93 141 149 and is based on what we call censoring consistent residuals in addition we develop residual plots that can be used to identify the correct functional forms of covariates we compare our test with the functional form test of lin wei and ying 1993 biometrika80 557 572 in a simulation study the practical application of the proposed residuals and functional form test is illustrated using both a simulated data set and a real data set

exponential stability of numerical solutions for a class of stochastic age dependent capital system with poisson jumps recently numerical solutions of stochastic differential equations have received a great deal of attention numerical approximation schemes are invaluable tools for exploring their properties in this paper we introduce a class of stochastic age dependent vintage capital system with poisson jumps we also give the discrete approximate solution with an implicit euler scheme in time discretization using gronwall s lemma and barkholder davis gundy s inequality some criteria are obtained for the exponential stability of numerical solutions to the stochastic age dependent capital system with poisson jumps it is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions where information on the order of approximation is provided these error bounds imply strong convergence as the timestep tends to zero a numerical example is used to illustrate the theoretical results

linear regression for bivariate censored data via multiple imputation bivariate survival data arise for example in twin studies and studies of both eyes or ears of the same individual often it is of interest to regress the survival times on a set of predictors in this paper we extend wei and tanner s multiple imputation approach for linear regression with univariate censored data to bivariate censored data we formulate a class of censored bivariate linear regression methods by iterating between the following two steps 1 the data is augmented by imputing survival times for censored observations 2 a linear model is fit to the imputed complete data we consider three different methods to implement these two steps in particular the marginal independence approach ignores the possible correlation between two survival times when estimating the regression coefficient to improve the efficiency we propose two methods that account for the correlation between the survival times first we improve the efficiency by using generalized least squares regression in step 2 second instead of generating data from an estimate of the marginal distribution we generate data from a bivariate log spline density estimate in step 1 through simulation studies we find that the performance of the two methods that take the dependence into account is close and that they are both more efficient than the marginal approach the methods are applied to a data set from an otitis media clinical trial copyright 1999 john wiley sons ltd

applications of multiple imputation to the analysis of censored regression data the first part of the article reviews the data augmentation algorithm and presents two approximations to the data augmentation algorithm for the analysis of missing data problems the poor man s data augmentation algorithm and the asymptotic data augmentation algorithm these two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology the performances of the censored regression algorithms are examined in a simulation study it is found up to the precision of the study that the bias of both the poor man s and asymptotic data augmentation estimators as well as the buckley james estimator does not appear to differ from zero however with regard to mean squared error over a wide range of settings examined in this simulation study the two data augmentation estimators have a smaller mean squared error than does the buckley james estimator in addition associated with the two data augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters it is shown how this device can be used to estimate the standard error of either data augmentation estimate of any parameter e g the correlation coefficient associated with the model in the simulation study the estimated standard error of the asymptotic data augmentation estimate of the regression parameter is found to be congruent with the monte carlo standard deviation of the corresponding parameter estimate the algorithms are illustrated using the updated stanford heart transplant data set

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

an application of imputation to an estimation problem in grouped lifetime analysis tanner and wang in press have introduced the data augmentation algorithm for the analysis of parametric missing data problems in this article this paradigm is used to develop an algorithm for the nonparametric estimation of the hazard function from grouped and censored lifetime data this algorithm makes use of the notions of cross validation and multiple imputation to prescribe the appropriate degree of smoothing for the nonparametric hazard estimate a procedure for estimating the variance of the estimator is also proposed the nonparametric hazard estimate and corresponding variance formula are shown to perform well in a simulation study the algorithm is illustrated with a numerical example

prediction in censored survival data a comparison of the proportional hazards and linear regression models although the analysis of censored survival data using the proportional hazards and linear regression models is common there has been little work examining the ability of these estimators to predict time to failure this is unfortunate since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a kaplan meier plot obtained by discretizing the variable in this paper the predictive power of the cox 1972 journal of the royal statistical society series b 34 187 202 proportional hazards estimator and the buckley james 1979 biometrika 66 429 436 censored regression estimator are compared using computer simulations and heuristic arguments it is shown that the choice of method depends on the censoring proportion strength of the regression the form of the censoring distribution and the form of the failure distribution several examples are provided to illustrate the usefulness of the methods

correlation coefficient estimation involving a left censored laboratory assay variable when assessing a correlation between two exposure or biological marker variables one sometimes encounters the problem of indeterminate values for one of the variables due to an assay detection limit in this event investigators often report correlation coefficients computed after removing the pairs involving non detectable values or after substituting some small constant for those values these ad hoc practices can lead to bias in both point and confidence interval estimates of the true correlation coefficient to address this issue we consider two parametric techniques for estimating the correlation in the presence of left censoring for one of the variables the first is a maximum likelihood approach and the second is an adaptation of multiple imputation motivated primarily by potential benefits in confidence interval coverage both of the estimators studied reduce to the standard pearson s correlation coefficient in the event of no censoring and hence are valid in cases where this measure would be appropriate for the complete data we assess these approaches empirically and contrast them with ad hoc methods for estimating the correlation between cervicovaginal human immunodeficiency virus hiv viral load measurements and cd4 lymphocyte counts from hiv positive women enrolled in a clinical trial conducted in bangkok thailand

age distribution dynamics with stochastic jumps in mortality while deterministic age distribution models have been extensively studied and applied in various disciplines little work has been devoted to understanding the role of stochasticity in birth and mortality terms in this paper we analyse a stochastic m kendrick von foerster equation in which jumps in mortality represent intense losses of population due to external events we present explicit solutions for the probability density functions of the age distribution and the total population and for the temporal dynamics of their moments we also derive the dynamics of the mean age of the population and its harmonic mean the framework is then used to calculate the age distribution of salt in the soil root zone where the accumulation of salt by atmospheric deposition is counteracted by plant uptake and by jump losses due to percolation events

a note on the analysis of censored regression data by multiple imputation wei and tanner 1991 biometrics 47 1297 1309 considered two approximations to the data augmentation algorithm for the analysis of semiparametric linear regression models with censored response and unspecified residual distribution on the basis of a simulation study they concluded that the approximations have smaller mean squared errors than the buckley james estimator over a range of settings we show that these conclusions result from the particular choice of censoring mechanism starting value and stopping rule for the iterations and that they do not appear to hold in general even in the cases considered by wei and tanner one appears to do at least as well with the same starting values and stopping rule using the buckley james iterations

approximate inference in location scale regression models abstract it is shown that 2 and multivariate t distributions provide good approximations to posterior distributions arising in location scale regression models in the case of a linear regression model bayesian inferences based on an improper prior have conditional frequency as well as fiducial structural interpretation so the results are also applicable in a non bayesian context numerical support for the approximations is presented for the case of a weibull regression model and a regression with t distributed errors

modeling the shape of the scene a holistic representation of the spatial envelope in this paper we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions the procedure is based on a very low dimensional representation of the scene that we term the spatial envelope we propose a set of perceptual dimensions naturalness openness roughness expansion ruggedness that represent the dominant spatial structure of a scene then we show that these dimensions may be reliably estimated using spectral and coarsely localized information the model generates a multidimensional space in which scenes sharing membership in semantic categories e g streets highways coasts are projected closed together the performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category

numerical analysis for stochastic age dependent population equations a numerical method proposed to approximate the solution of a class of stochastic age dependent populations we show that under certain conditions weaker than linear growth and global lips chits the euler scheme applied to stochastic age dependent population converges to the analytic solution and provide information on the order of approximation

existence uniqueness and exponential stability for stochastic age dependent population in this paper we introduce a class of stochastic age dependent population dynamic system existence and uniqueness of strong solution are proved for stochastic age dependent population dynamic system in hilbert space using klmogorou s inequality and barkholder davis gundy s lemma some criteria are obtained for the exponential stability of stochastic age dependent population dynamic system

product quantization for nearest neighbor search this paper introduces a product quantization based approach for approximate nearest neighbor search the idea is to decompose the space into a cartesian product of low dimensional subspaces and to quantize each subspace separately a vector is represented by a short code composed of its subspace quantization indices the euclidean distance between two vectors can be efficiently estimated from their codes an asymmetric version increases precision as it computes the approximate distance between a vector and a code experimental results show that our approach searches for nearest neighbors efficiently in particular in combination with an inverted file system results for sift and gist image descriptors show excellent search accuracy outperforming three state of the art approaches the scalability of our approach is validated on a data set of two billion vectors

scale parameters a bayesian treatment a definition of a scale parameter is given which includes the usual definition of a scale parameter in the exponential family some suggestions for the estimation of and approximations to the marginal posterior distribution of a vector valued parameter of primary interest are made in particular the possibility of a 2 approximation to the posterior distribution of leading to h p d regions for based on the f distribution is explored two examples are discussed where observations are from a normal and gamma distribution

censored median regression using weighted empirical survival and hazard functions abstract for median regression models that regress the median of the survival time or a transform thereof on the covariates some semi parametric estimators that include the intercept component are introduced when the survival time may be censored these new median regression estimators do not require estimating the censoring distributions they can be viewed as an extension of the sample median to the censored regression model these estimators are based on some weighted empirical survival and hazard functions and are shown to be consistent and asymptotically normal they performed very well in various numerical studies the proposed procedures are illustrated in some real data examples

a partial differential equation for the characteristic function of the response of non linear systems to additive poisson white noise abstract a method has been developed for finding the characteristic function u t e exp i u x t of the solution x t of a non linear stochastic differential equation driven by poisson white noise poisson white noise can be viewed as a sequence of independent identically distributed pulses arriving at poisson times if the drift is a polynomial of x t and the diffusion is independent of this process u t satisfies a partial differential equation that can be solved numerically two approaches are used to establish the partial differential equation of the characteristic function of x t the first approach is based on a generalized version of the ito differentiation formula for stochastic differential equations with poisson white noise the second approach uses elementary arguments to determine the rate of change of u t in time linear and non linear systems subjected to poisson white noise are used to demonstrate and evaluate the proposed method the solution x t of a linear differential equation with poisson white noise is a filtered poisson process and the characteristic function for this type of process is available in closed form it is shown that the characteristic function of the filtered poisson process x t satisfies the partial differential equation of u t because the characteristic function of the state x t of a non linear system subjected to poisson white noise is not known numerical solutions of the partial differential equation of u t are compared with estimates of this characteristic function calculated from independent realization of x t obtained by monte carlo simulation these comparisons show that the proposed method for calculating the characteristic function of x t as the solution of a partial differential equation is accurate

correlating two viral load assays with known detection limits summary a timely objective common to many hiv studies involves assessing the correlation between two different measures of viral load obtained from each of a sample of patients this correlation has scientific utility in a number of contexts including those aimed at a comparison of competing assays for quantifying virus and those aimed at determining the level of association between viral loads in two different reservoirs using the same assay a complication for the analyst seeking valid point and interval estimates of such a correlation is the fact that both variables may be subject to left censoring due to values below assay detection limits we address this problem using a bivariate normal likelihood that accounts for left censoring of two variables that may have different detection limits we provide simulation results to evaluate sampling properties of the resulting correlation estimator and compare it with ad hoc estimators in the presence of nondetects in an effort to obtain improved confidence interval properties relative to the wald approach we evaluate and compare profile likelihood based intervals we apply the methods to hiv viral load data on women and infants from a trial in bangkok thailand and we discuss an extension of the original model to accommodate interval censoring arising due to the study design

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

convergence of numerical solutions for a class of stochastic age dependent capital system with random jump magnitudes in stochastic differential equations sdes there is a class of stochastic functional differential equations with random jump magnitudes which aries in many financial models in general most equations of stochastic age dependent capital system do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties in this paper the numerical approximation is established for a class of stochastic age dependent capital system with random jump magnitudes the main aim of this paper is to investigate the convergence of the numerical approximation for a class of stochastic age dependent capital system with random jump magnitudes it is proved that the numerical approximate solutions converge to the analytical solutions of the equations under given conditions the numerical approximate results in zhang et al 2011 2 are improved an example is given for illustration

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

numerical analysis of semilinear stochastic evolution equations in banach spaces the solution of stochastic evolution equations generally relies on numerical computation here usually the main idea is to discretize the spde spatially obtaining a system of sdes that can be solved by e g the euler scheme in this paper we investigate the discretization error of semilinear stochastic evolution equations in lp spaces resp banach spaces the space discretization may be done by galerkin approximation for the time discretization we consider the implicit euler the explicit euler scheme and the crank nicholson scheme in the last section we give some examples i e we consider an spdes driven by nuclear wiener noise approximated by wavelets and delay equation approximated by finite differences

multiple imputation for interval censored data with auxiliary variables we propose a non parametric multiple imputation scheme npmle imputation for the analysis of interval censored survival data features of the method are that it converts interval censored data problems to complete data or right censored data problems to which many standard approaches can be used and that measures of uncertainty are easily obtained in addition to the event time of primary interest there are frequently other auxiliary variables that are associated with the event time for the goal of estimating the marginal survival distribution these auxiliary variables may provide some additional information about the event time for the interval censored observations we extend the imputation methods to incorporate information from auxiliary variables with potentially complex structures to conduct the imputation we use a working failure time proportional hazards model to define an imputing risk set for each censored observation the imputation schemes consist of using the data in the imputing risk sets to create an exact event time for each interval censored observation in simulation studies we show that the use of multiple imputation methods can improve the efficiency of estimators and reduce the effect of missing visits when compared to simpler approaches we apply the approach to cytomegalovirus shedding data from an aids clinical trial in which cd4 count is the auxiliary variable

exponential stability of numerical solutions to a stochastic age structured population system with diffusion the main aim of this paper is to investigate the exponential stability of the euler method for a stochastic age structured population system with diffusion the definition of exponential mean square stability of numerical method is introduced it is proved that the euler scheme is exponentially stable in mean square sense an example is given for illustration

ldahash improved matching with smaller descriptors sift like local feature descriptors are ubiquitously employed in computer vision applications such as content based retrieval video analysis copy detection object recognition photo tourism and 3d reconstruction feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations in particular affine and intensity scale transformations however real transformations that an image can undergo can only be approximately modeled in this way and thus most descriptors are only approximately invariant in practice second descriptors are usually high dimensional e g sift is represented as a 128 dimensional vector in large scale retrieval and matching problems this can pose challenges in storing and retrieving descriptor data we map the descriptor vectors into the hamming space in which the hamming metric is used to compare the resulting representations this way we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples we show extensive experimental validation demonstrating the advantage of the proposed approach

convergence of numerical solutions to stochastic age structured system of three species abstract in general most of stochastic age structured system of three species do not have explicit solutions thus numerical approximation schemes are invaluable tools for exploring their properties the aim of this paper is to investigate the convergence of numerical approximation solution to the true solution for stochastic age structured system of three species

bayes inference in the tobit censored regression model we consider the bayes estimation of the tobit censored regression model with normally distributed errors a simple condition for the existence of posterior moments is provided suitable versions of monte carlo procedures based on symmetric multivariate t distributions and laplacian approximations in a certain parametrization are developed and illustrated ideas involving data augmentation and gibbs sampling cf tanner and wong 1987 and gelfand and smith 1990 are also developed the methods are compared in two examples with diffuse priors and various combinations of sample sizes and degrees of censoring

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

a two sample test with interval censored data via multiple imputation interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be recorded as having occurred between two examination times in this paper we consider the problem of comparing two interval censored samples we propose to impute exact failure times from interval censored observations to obtain right censored data then apply existing techniques such as harrington and fleming s g rho tests to imputed right censored data to appropriately account for variability a multiple imputation algorithm based on the approximate bayesian bootstrap abb is discussed through simulation studies we find that it performs well the advantage of our proposal is its simplicity to implement and adaptability to incorporate many existing two sample comparison techniques for right censored data the method is illustrated by reanalysing the breast cosmesis study data set

image segmentation using hidden markov gauss mixture models image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing we develop a multiclass image segmentation method using hidden markov gauss mixture models hmgmms and provide examples of segmentation of aerial images and textures hmgmms incorporate supervised learning fitting the observation probability distribution given each class by a gauss mixture estimated using vector quantization with a minimum discrimination information mdi distortion we formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation we estimate both the hidden markov parameter and hidden states using a stochastic expectation maximization algorithm our results demonstrate that hmgmm provides better classification in terms of bayes risk and spatial homogeneity of the classified objects than do several popular methods including classification and regression trees learning vector quantization causal hidden markov models hmms and multiresolution hmms the computational load of hmgmm is similar to that of the causal hmm

a comparison of estimators for regression with a censored response variable summary several methods of estimating parameters in a linear regression when the response variable is censored are compared the estimator of buckley james 1979 is preferred further it is shown that the strength of the regression the support and distribution of the censoring variable and the magnitude of the slope all have an effect on the relative performance of the estimators

nonparametric estimation and regression analysis with left truncated and right censored data abstract in many prospective and retrospective studies survival data are subject to left truncation in addition to the usual right censoring for left truncated data without covariates only the conditional distribution of the survival time y given y can be estimated nonparametrically where is the lower boundary of the support of the left truncation variable t if the data are also right censored then the conditional distribution can be consistently estimated only at points not larger than where is the upper boundary of the support of the right censoring variable c in this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of y with the trimming inside the observable range between and we then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variable y asymptotic normality of m estimators of the regression parameters derived from this approach is

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea