the em algorithm an old folk song sung to a fast new tune celebrating the 20th anniversary of the presentation of the paper by dempster laird and rubin which popularized the em algorithm we investigate after a brief historical account strategies that aim to make the em algorithm converge faster while maintaining its simplicity and stability e g automatic monotone convergence in likelihood first we introduce the idea of a working parameter to facilitate the search for efficient data augmentation schemes and thus fast em implementations second summarizing various recent extensions of the em algorithm we formulate a general alternating expectation conditional maximization algorithm aecm that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations we illustrate these methods using multivariate t models with known or unknown degrees of freedom and poisson models for image reconstruction we show through both empirical and theoretical evidence the potential for a dramatic reduction in computational time with little increase in human effort we also discuss the intrinsic connection between em type algorithms and the gibbs sampler and the possibility of using the techniques presented here to speed up the latter the main conclusion of the paper is that with the help of statistical considerations it is possible to construct algorithms that are simple stable and fast

a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

a markov chain monte carlo em algorithm for analyzing interval censored data under the cox proportional hazards model summary this paper proposes a monte carlo em mcem algorithm for fitting the proportional hazards model for interval censored failure time data the algorithm generates orderings of the failures from their probability distribution under the model we maximize the average of the log likelihoods from these completed data sets to obtain updated parameter estimates as with the standard cox model this algorithm does not require the estimation of the baseline hazard function the performance of the algorithm is evaluated using simulations and the method is applied to data from aids and cancer studies our results indicate that our method produced more precise and unbiased estimates than methods of right and midpoint imputation

applying the cox proportional hazards model when the change time of a binary time varying covariate is interval censored this paper develops methodology for estimation of the effect of a binary time varying covariate on failure times when the change time of the covariate is interval censored the motivating example is a study of cytomegalovirus cmv disease in patients with human immunodeficiency virus hiv disease we are interested in determining whether cmv shedding predicts an increased hazard for developing active cmv disease since a clinical screening test is needed to detect cmv shedding the time that shedding begins is only known to lie in an interval bounded by the patient s last negative and first positive tests in a cox proportional hazards model with a time varying covariate for cmv shedding the partial likelihood depends on the covariate status of every individual in the risk set at each failure time due to interval censoring this is not always known to solve this problem we use a monte carlo em algorithm with a gibbs sampler embedded in the e step we generate multiple completed data sets by drawing imputed exact shedding times based on the joint likelihood of the shedding times and event times under the cox model the method is evaluated using a simulation study and is applied to the data set described above

orbital stability of spatially synchronized solitary waves of an m coupled nonlinear schrodinger system in this paper we investigate the orbital stability of solitary wave solutions for an m coupled nonlinear schrodinger system i tuj 2 x2uj i 1mbijui2uj 0 j 1 m where m 2 uj are complex valued functions of x t 2 bjj j 1 2 m and bij i j are positive coupling constants satisfying bij bji it will be shown that spatially synchronized solitary wave solutions of the m coupled nonlinear schrodinger system exist and are orbitally stable here by synchronized solutions we mean solutions in which the components are proportional to one another our results completely settle the question on the existence and stability of synchronized solitary waves for the m coupled system while only partial results were known in the literature for the cases of m 3 heretofore furthermore the conditions imposed on the symmetric matrix b bij satisfied here are both sufficient and necessary for the m coupled nonlinear schrodinger system to admit synchronized ground state solutions

stability of standing waves for the fractional schrodinger choquard equation abstract in this paper we consider the stability of standing waves for the fractional schrodinger choquard equation with an l 2 critical nonlinearity by using the profile decomposition of bounded sequences in h s and variational methods we prove that the standing waves are orbitally stable we extend the study of bhattarai for a single equation bhattarai 2017 to the l 2 critical case

analysis of failure time data with dependent interval censoring summary this article develops a method for the analysis of screening data for which the chance of being screened is dependent on the event of interest informative censoring because not all subjects make all screening visits the data on the failure of interest is interval censored we propose a model that will properly adjust for the dependence to obtain an unbiased estimate of the nonparametric failure time function and we provide an extension for applying the method for estimation of the regression parameters from a discrete time proportional hazards regression model the method is applied on a data set from an observational study of cytomegalovirus shedding in a population of hiv infected subjects who participated in a trial conducted by the aids clinical trials group

a joint model for survival and longitudinal data measured with error the relationship between a longitudinal covariate and a failure time process can be assessed using the cox proportional hazards regression model we consider the problem of estimating the parameters in the cox model when the longitudinal covariate is measured infrequently and with measurement error we assume a repeated measures random effects model for the covariate process estimates of the parameters are obtained by maximizing the joint likelihood for the covariate process and the failure time process this approach uses the available information optimally because we use both the covariate and survival data simultaneously parameters are estimated using the expectation maximization algorithm we argue that such a method is superior to naive methods where one maximizes the partial likelihood of the cox model using the observed covariate values it also improves on two stage methods where in the first stage empirical bayes estimates of the covariate process are computed and then used as time dependent covariates in a second stage to find the parameters in the cox model that maximize the partial likelihood

sharp thresholds of global existence and blowup for a system of schrodinger equations with combined power type nonlinearities in this paper we consider the cauchy problem of a nonlinear schrodinger system through establishing a sharp weighted vector valued gagliardo nirenberg s inequality we find that the best constant in this inequality can be regarded as the criterion of blowup and global existence of the solutions when p 4 n and we prove that the solutions of this system will always exist globally if p 4 n the sharp thresholds for blowup and global existence are also obtained when 4 n p 4 n 2

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

relation of pooled logistic regression to time dependent cox regression analysis the framingham heart study a standard analysis of the framingham heart study data is a generalized person years approach in which risk factors or covariates are measured every two years with a follow up between these measurement times to observe the occurrence of events such as cardiovascular disease observations over multiple intervals are pooled into a single sample and a logistic regression is employed to relate the risk factors to the occurrence of the event we show that this pooled logistic regression is close to the time dependent covariate cox regression analysis numerical examples covering a variety of sample sizes and proportions of events display the closeness of this relationship in situations typical of the framingham study a proof of the relationship and the necessary conditions are given in the appendix

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

existence and orbital stability of standing waves for nonlinear schrodinger systems abstract in this paper we investigate the existence of solutions in h 1 r n h 1 r n for nonlinear schrodinger systems of the form u 1 1 u 1 1 u 1 p 1 2 u 1 r 1 u 1 r 1 2 u 1 u 2 r 2 u 2 2 u 2 2 u 2 p 2 2 u 2 r 2 u 1 r 1 u 2 r 2 2 u 2 under the constraints r n u 1 2 d x a 1 0 r n u 2 2 d x a 2 0 here n 1 0 i 0 r i 1 2 p i 2 4 n for i 1 2 and r 1 r 2 2 4 n this problem is motivated by the search of standing waves for an evolution problem appearing in several physical models our solutions are obtained as constrained global minimizers of an associated functional note that in the system 1 and 2 are unknown and will correspond to the lagrange multipliers our main result is the precompactness of the minimizing sequences up to translation assuming the local well posedness of the associated evolution problem we then obtain the orbital stability of the standing waves associated to the set of minimizers

global existence for a coupled system of schrodinger equations with power type nonlinearities in this manuscript we consider the cauchy problem for a schrodinger system with power type nonlinearitiesi tuj uj k 1majk uk p uj p 2uj 0 uj x 0 j0 x where uj rn r c j0 rn c for j 1 2 m and ajk akj are positive real numbers global existence for the cauchy problem is established for a certain range of p a sharp form of a vector valued gagliardo nirenberg inequality is deduced which yields the minimal embedding constant for the inequality using this minimal embedding constant global existence for small initial data is shown for the critical case p 1 2 n finite time blow up as well as stability of solutions in the critical case is discussed

stability and instability of standing waves to a system of schrodinger equations with combined power type nonlinearities abstract we obtain the existence of standing wave solutions to a coupled nonlinear schrodinger system i u 1 t u 1 u 1 p k 1 m k u 1 p k 2 u 2 q k u 1 in r n 0 t i u 2 t u 2 u 2 p k 1 m k u 1 p k u 2 q k 2 u 2 in r n 0 t u 1 x 0 u 10 x u 2 x 0 u 20 x in r n where 0 p 4 n 2 and k k p k q k are real constants with 1 p k p 1 1 q k p 1 p k q k p 2 and k q k k p k k 1 m we also discuss the stability and instability of the standing wave solutions

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

stability of solitary waves for the vector nonlinear schrodinger equation in higher order sobolev spaces abstract in this manuscript a sharp form of orbital stability for the schrodinger system also known as the vector nls i t u j 2 x x u j 2 i 1 m u i 2 u j 0 where u j are complex valued functions of x t r 2 j 1 2 m is established in l 2 based sobolev classes of arbitrarily high order the result means practically that not only does the bulk of what emanates from the perturbed solitary wave stay close in shape and propagation and phase speeds to the original solitary wave but emerging residual oscillations must also be very small and not only in the energy norm

erratum to sharp thresholds of global existence and blowup for a system of schrodinger equations with combined power type nonlinearities j math phys 51 033509 2010

a score test for association of a longitudinal marker and an event with missing data often clinical studies periodically record information on disease progression as well as results from laboratory studies that are believed to reflect the progressing stages of the disease a primary aim of such a study is to determine the relationship between the lab measurements and a disease progression if there were no missing or censored data these analyses would be straightforward however often patients miss visits and return after their disease has progressed in this case not only is their progression time interval censored but their lab test series is also incomplete in this article we propose a simple test for the association between a longitudinal marker and an event time from incomplete data we derive the test using a very intuitive technique of calculating the expected complete data score conditional on the observed incomplete data conditional expected score test cest the problem was motivated by data from an observational study of patients with diabetes

orbital stability of solitary waves of a 3 coupled nonlinear schrodinger system abstract in this paper consideration is given to the 3 coupled nonlinear schrodinger system i t u j 2 x 2 u j i 1 3 b i j u i 2 u j 0 where u j are complex valued functions of x t r 2 j 1 2 3 and b i j are positive constants satisfying b i j b j i it will be shown first that if the symmetric matrix b b i j satisfies certain conditions then ground state solutions of the 3 coupled nonlinear schrodinger system exist and moreover they are orbitally stable the theory is then extended to include solitary waves as well in particular it will be shown that when a solitary wave is perturbed the perturbed solution must stay close to a solitary wave profile in which the translation and phase parameters are prescribed functions of time properties of these functions are then studied this is a continuous work of our previous paper where the 2 coupled nonlinear schrodinger system was considered

lyapunov stability of ground states of nonlinear dispersive evolution equations on presente une nouvelle demonstration de la stabilite orbitale des solitons d etat fondamental de l equation de schrodinger non lineaire pour une grande classe de non linearites on demontre la stabilite de l onde solitaire pour l equation de korteweg de vries generalisee

log linear analysis of censored survival data with partially observed covariates abstract log linear models provide a flexible means of extending life table techniques for the analysis of censored survival data with categorical covariates as discussed by holford 1980 and laird and olivier 1981 we extend this methodology to incorporate cases in which one or more of the categorical covariates are sometimes missing maximum likelihood estimates of the parameters are calculated using data from all cases this can result in large gains in efficiency over standard methods that require the exclusion of cases with incomplete data with this approach we assume that the hazard function conditional on the covariates is a stepwise function over disjoint intervals of time the model has two parts a log linear model describing the hazard parameters and a multinomial model describing the probabilities in the contingency table defined by the covariates the main interest is in the model for the hazard parameters we show how to calculate maximum likelihood estimates of parameters of the mo

servocompensation of disturbances in robotic systems robot manipulators are susceptible to external disturbances that may alter their behaviour so significantly that certain specifications cannot be maintained additive signals that satisfy a linear differential equation with constant coefficients are the type of disturbance that may enter a manipulator and corrupt its behaviour from linear servocompensator theory one knows that linear disturbances can be asymptotically rejected if the linear plant satisfies certain criteria however for robot manipulators which are extremely non linear the former criteria cannot be applied it is shown here that linear disturbances can be asymptotically rejected by employing a standard linear servocompensator in linear system theory the proof that the error e 0 as t is shown via the laplace transform the volterra series is utilized here to verify the asymptotic convergence of the error digital computer simulations are carried out on a two link planar robot to demonstrate the effectiveness of the linear servoco

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented