accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation the em method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography pet the result is an iterative algorithm for image reconstruction that is finding increasing use in pet due to its attractive theoretical and practical properties its major disadvantage is the large amount of computation that is often required due to the algorithm s slow rate of convergence this paper presents an accelerated form of the em algorithm for pet in which the changes to the image as calculated by the standard algorithm are multiplied at each iteration by an overrelaxation parameter the accelerated algorithm retains two of the important practical properties of the standard algorithm namely the selfnormalization and nonnegativity of the reconstructed images experimental results are presented using measured data obtained from a hexagonal detector system for pet the likelihood function and the norm of the data residual were monitored during the iterative process according to both of these measures the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm for two different sets of data important theoretical properties remain to be investigated namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator

alternative c means clustering algorithms abstract in this paper we propose a new metric to replace the euclidean norm in c means clustering procedures on the basis of the robust statistic and the influence function we claim that the proposed new metric is more robust than the euclidean norm we then create two new clustering methods called the alternative hard c means ahcm and alternative fuzzy c means afcm clustering algorithms these alternative types of c means clustering have more robustness than c means clustering numerical results show that ahcm has better performance than hcm and afcm is better than fcm we recommend afcm for use in cluster analysis recently this afcm algorithm has successfully been used in segmenting the magnetic resonance image of ophthalmology to differentiate the abnormal tissues from the normal tissues

estimating rate constants in hidden markov models by the em algorithm the em algorithm e g the baum welch 1970 re estimation is an important tool for parameter estimation in discrete time hidden markov models we present a direct re estimation of rate constants for applications in which the underlying markov process is continuous in time previous estimation of discrete time transition probabilities is not necessary

estimation of parameters in latent class models using fuzzy clustering algorithms abstract a mixture approach to clustering is an important technique in cluster analysis a mixture of multivariate multinomial distributions is usually used to analyze categorical data with latent class model the parameter estimation is an important step for a mixture distribution described here are four approaches to estimating the parameters of a mixture of multivariate multinomial distributions the first approach is an extended maximum likelihood ml method the second approach is based on the well known expectation maximization em algorithm the third approach is the classification maximum likelihood cml algorithm in this paper we propose a new approach using the so called fuzzy class model and then create the fuzzy classification maximum likelihood fcml approach for categorical data the accuracy robustness and effectiveness of these four types of algorithms for estimating the parameters of multivariate binomial mixtures are compared using real empirical data and samples drawn from the multivariate binomial mixtures of two classes the results show that the proposed fcml algorithm presents better accuracy robustness and effectiveness overall the fcml algorithm has the superiority over the ml em and cml algorithms thus we recommend fcml as another good tool for estimating the parameters of mixture multivariate multinomial models

multilinear estimates for periodic kdv equations and applications we prove an endpoint multilinear estimate for the xs b spaces associated to the periodic airy equation as a consequence we obtain sharp local well posedness results for periodic generalized kdv equations as well as some global well posedness results below the energy norm

optimality test for generalized fcm and its application to parameter selection in cluster analysis the fuzzy c means fcm clustering algorithm is the best known and most widely used method it was proven to converge to either a local minimum or saddle points by bezdek et al wei and mendel produced efficient optimality tests for fcm fixed points recently a weighting exponent selection for fcm was proposed by yu et al inspired by these results we unify several alternative fcm algorithms into one model called the generalized fuzzy c means gfcm this gfcm model presents a wide variation of fcm algorithms and can easily lead to new and interesting clustering algorithms moreover we construct a general optimality test for gfcm fixed points this is applied to theoretically choose the parameters in the gfcm model the experimental results demonstrate the precision of the theoretical analysis

fronts pulses sources and sinks in generalized complex ginzberg landau equations an important clement in the long time dynamics of pattern forming systems is a class of solutions we will call coherent structures these are states that are either themselves localized or that consist of domains of regular patterns connected by localized defects or interfaces this paper summarizes and extends recent work on such coherent structures in the one dimensional complex ginzburg landau equation and its generalizations for which rather complete information can be obtained on the existence and competition of fronts pulses sources and sinks for the special subclass of uniformly translating structures the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three dimensional phase space fixed points of the flow correspond to the two basic building blocks of coherent structures uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero a study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures the dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts and is expressed in terms of a set of conjectures for front propagation that generalize the marginal stability and pinch point approaches of earlier authors these rules together with an exact front solution whose dynamics plays an important role in the selection of patterns yield an analytic expression for the upper limit of the range of existence of pulse solutions as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses in the parameter ranges where no uniformly translating fronts can exist examples are shown of irregularly spreading fronts that generate strongly chaotic regions as well as nonuniformly translating fronts that lead to uniform amplitude states recent perturbative treatments based on expansions about the nonlinear schr6dinger equation are generalized to perturbations of the cubic quintic and derivative schr idinger equations for which both pulses and fronts exist in the unperturbed system comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions nevertheless those that are obtained are found to be consistent with the general conjectures and in particular they provide an analytic demonstration of front pulse competition while the discussion of the competition between fronts and pulses focusses on the complex ginzburg landau equation with quintic terms and a subcritical bifurcation a number of results are also presented for the cubic equation in particular the existence of a family of moving source solutions derived by bekki and nozaki for this equation contradicts the naive counting arguments we attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits

on the derivative nonlinear schro dinger equation abstract in this paper we discuss the cauchy problem for the derivative nonlinear schrodinger equation i t 2i x 2 0 0 x x where 0 under an explicit smallness condition of the initial data we prove the unique global existence of solutions to this problem in the usual sobolev spaces in the weighted sobolev spaces and in the schwartz class we describe the smoothing effect in detail furthermore for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction

general c means clustering model partitional clustering is an important part of cluster analysis based on various theories numerous clustering algorithms have been developed and new clustering algorithms continue to appear in the literature it is known that occam s razor plays a pivotal role in data based models and partitional clustering is categorized as a data based model however no relation had previously been discovered between occam s razor and partitional clustering as we discuss in this paper the three main contributions of this paper can be summarized as follows 1 according to a novel definition of the mean a unifying generative framework for partitional clustering algorithms called a general c means clustering model gcm is presented and studied and 2 based on the local optimality test of the gcm the connection between occam s razor and partitional clustering is established for the first time as its application a comprehensive review of the existing objective function based clustering algorithms is presented based on gcm 3 under a common assumption about partitional clustering a theoretical guide for devising and implementing clustering algorithm is discovered these conclusions are verified by numerical experimental results

a disaggregate negative binomial regression procedure for count data analysis various research areas face the methodological problems presented by nonnegative integer count data drawn from heterogeneous populations we present a disaggregate negative binomial regression procedure for analysis of count data observed for a heterogeneous sample of cross sections possibly over some fixed time periods this procedure simultaneously pools or groups cross sections while estimating a separate negative binomial regression model for each group an e m algorithm is described within a maximum likelihood framework to estimate the group proportions the group specific regression coefficients and the degree of overdispersion in event rates within each derived group the proposed procedure is illustrated with count data entailing nonnegative integer counts of purchases events for a frequently bought consumer good

global well posedness of the derivative nonlinear schrodinger equation with periodic boundary condition in h12 abstract we establish the global well posedness of the derivative nonlinear schrodinger equation with periodic boundary condition in the sobolev space h 1 2 provided that the mass of initial data is less than 4 this result matches the one by miao wu and xu and its recent mass threshold improvement by guo and wu in the non periodic setting below h 1 2 we show that the uniform continuity of the solution map on bounded subsets of h s does not hold for any gauge equivalent equation

regression analysis of interval censored survival data with covariates using log linear models we considered the regression analysis of the event time data with left right or interval censored observations we extended life table techniques for censored survival data using log linear models to incorporate interval censored failures the em algorithm was used to calculate maximum likelihood estimates for the parameters we assumed that the hazard function was a stepwise function over disjoint intervals of time thus the nonparametric model the parametric exponential model and the semiparametric cox proportional hazard model were easily implemented as special cases we adapted the restricted em algorithm to test hypotheses and to construct confidence intervals for the parameters these methods were applied in an analysis of the recurrence time for treated melanoma patients

maximum likelihood variance components estimation for binary data abstract we consider a class of probit normal models for binary data and describe ml and reml estimation of variance components for that class as well as best prediction for the realized values of the random effects ml estimates are calculated using an em algorithm for complicated models em includes a gibbs step the computations are illustrated through two examples

estimation of allocation rates in a cluster analysis context abstract a sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations the mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the maximum of these posterior probabilities the estimates of the correct allocation rates provide a means of assessing the performance of the mixture approach to clustering the bootstrap technique is investigated for its effectiveness in reducing the bias of the estimates so obtained results are reported for three real data sets and a simulation study it is demonstrated that the proposed estimates generally provide useful information on the unobservable allocation rates of the mixture approach encouraging results are obtained for

clustering construction on a multimodal probability model in 2009 yu et al proposed a multimodal probability model mpm for clustering this paper makes advanced clustering constructions on the mpm we first reconstruct most existing clustering algorithms such as the k means fuzzy c means possibilistic c means mean shift classification maximum likelihood and latent class methods by establishing the relationships between these clustering algorithms and the mpm under our clustering construction we find that the mpm can be seen as a basic probability model for most existing clustering algorithms we then construct new clustering frameworks based on the mpm one of the frameworks develops new penalized type clustering algorithms another one induces entropy type clustering algorithms especially with sample weighted clustering several numerical and real data sets are made for comparisons these experimental results show that our clustering constructions based on the mpm can produce useful and effective clustering algorithms

a quick method for estimation of parameters of individual pulses in a multipath signal abstract consider a multipath signal whose individual signals are deterministic known increasing or decreasing pulses the problem is to estimate the amplitudes and delay times of individual signals several methods have been devoted to the solution of these unknown parameters the maximum likelihood ml estimation and the estimate maximize em algorithm are commonly used but they are computationally intensive and still insufficient to obtain accurate estimations the method can provide a quick and accurate estimate of the amplitudes and arrival delay times even in the closely spaced multipaths and heavy noise

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

maximum likelihood estimation and likelihood ratio test for square tables with missing data missing data complicate the analysis of paired categorical data this paper considers with the use of the em algorithm the maximum likelihood estimation and likelihood ratio test for incomplete square tables with missing data an example involving the susceptibility of micro organisms to antimicrobial drugs illustrates the procedure

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

optimal small data scattering for the generalized derivative nonlinear schrodinger equations abstract in this work we consider the following generalized derivative nonlinear schrodinger equation i t u x x u i u 2 x u 0 t x r r we prove that when 2 the solution is global and scattering when the initial data is small in h s r 1 2 s 1 moreover we show that when 0 2 there exist a class of solitary wave solutions c satisfying c h 1 r 0 when c tends to some endpoint which is against the small data scattering statement therefore in this model the exponent 2 is optimal for small data scattering we remark that this exponent is larger than the short range exponent and the strauss exponent

global well posedness for schrodinger equation with derivative in h 1 2 r abstract in this paper we consider the cauchy problem of the cubic nonlinear schrodinger equation with derivative in h s r this equation was known to be the local well posedness for s 1 2 takaoka 1999 27 ill posedness for s 1 2 biagioni and linares 2001 1 etc and global well posedness for s 1 2 i team 2002 10 in this paper we show that it is global well posedness in the endpoint space h 1 2 r which remained open previously the main approach is the third generation i method combined with a new resonant decomposition technique the resonant decomposition is applied to control the singularity coming from the resonant interaction

an incomplete data approach to the analysis of covariance structures in this paper linear structural equation models with latent variables are considered it is shown how many common models arise from incomplete observation of a relatively simple system subclasses of models with conditional independence interpretations are also discussed using an incomplete data point of view the relationships between the incomplete and complete data likelihoods assuming normality are highlighted for computing maximum likelihood estimates the em algorithm and alternatives are surveyed for the alternative algorithms simplified expressions for computing function values and derivatives are given likelihood ratio tests based on complete and incomplete data are related and an example on using their relationship to improve the fit of a model is given

signal modeling with filtered discrete fractional noise processes filtered versions of fractionally differenced gaussian noise fdgn processes are studied fractionally differenced gaussian noise is a discrete time equivalent of fractional brownian motion filtered versions of such processes are ideally suited for modeling signals with different short term and long term correlation structure two iterative algorithms for estimating the parameters of filtered fdgn processes are described the first technique is based on the expectation maximization algorithm it converges to a stationary point of the log likelihood function corresponding to the parameters of the model the second technique is a computationally efficient approximate approach it is found to converge experimentally but no proof of its convergence is given the usefulness of filtered fdgn models and the performance of the proposed iterative algorithms are illustrated by fitting filtered fdgn models to speech waveforms and other data corresponding to natural phenomena

optimal local well posedness for the periodic derivative nonlinear schrodinger equation we prove local well posedness for the periodic derivative nonlinear schrodinger equation which is l 2 critical in fourier lebesgue spaces which scale like h s mathbb t for s 0 our result is optimal in the sense that it covers the full subcritical regime in particular we close the existing gap in the subcritical theory by improving the result of grunrock and herr siam j math anal 39 6 1890 1920 2008 which established local well posedness in fourier lebesgue spaces which scale like h s mathbb t for s frac 1 4 we achieve this result by a delicate analysis of the structure of the solution and the construction of an adapted nonlinear submanifold of a suitable function space together these allow us to construct the unique solution to the given subcritical data this constructive procedure is inspired by the theory of para controlled distributions developed by gubinelli et al forum math pi 3 75 2015 and catellier and chouk ann probab 46 5 2621 2679 2018 in the context of stochastic pde our proof and results however are purely deterministic

statistical mechanics of the nonlinear schrodinger equation we investigate the statistical mechanics of a complex fieldo whose dynamics is governed by the nonlinear schrodinger equation such fields describe in suitable idealizations langmuir waves in a plasma a propagating laser field in a nonlinear medium and other phenomena their hamiltonian h phi int omega frac 1 2 nabla phi 2 1 p phi p dx is unbounded below and the system will under certain conditions develop self focusing singularities in a finite time we show that when is the circle and thel 2 norm of the field which is conserved by the dynamics is bounded byn the gibbs measure obtained is absolutely continuous with respect to wiener measure and normalizable if and only ifp andn are such that classical solutions exist for all time no collapse of the solitons this measure is essentially the same as that of a one dimensional version of the more realisitc zakharov model of coupled langmuir and ion acoustic waves in a plasma we also obtain some properties of the gibbs state by both analytic and numerical methods asn and the temperature are varied

a canonical space time state space model state and parameter estimation the maximum likelihood estimation of a dynamic spatiotemporal model is introduced centred around the inclusion of a prior arbitrary spatiotemporal neighborhood description the neighborhood description defines a specific parameterization of the state transition matrix chosen on the basis of prior knowledge about the system the model used is inspired by the spatiotemporal arma starma model but the representation used is based on the standard state space model the inclusion of the neighborhood into an expectation maximization based joint state and parameter estimation algorithm allows for accurate characterization of the spatiotemporal model the process of including the neighborhood and the effect it has on the maximum likelihood parameter estimate is described and demonstrated in this paper

vector quantization in dct domain using fuzzy possibilistic c means based on penalized and compensated constraints in this paper fuzzy possibilistic c means fpcm approach based on penalized and compensated constraints are proposed to vector quantization vq in discrete cosine transform dct for image compression these approaches are named penalized fuzzy possibilistic c means pfpcm and compensated fuzzy possibilistic c means cfpcm the main purpose is to modify the fpcm strategy with penalized or compensated constraints so that the cluster centroids can be updated with penalized or compensated terms iteratively in order to 4nd near global solution in optimal problem the information transformed by dct was separated into dc and ac coe5cients then the ac coe5cients are trained by using the proposed methods to generate better codebook based on vq the compression performances using the proposed approaches are compared with fpcm and conventional vq method from the experimental results the promising performances can be obtained using the proposed approaches 2002 pattern recognition society published by elsevier science ltd all rights reserved

on a class of fuzzy classification maximum likelihood procedures classification maximum likelihood cml procedure is a remarkable mixture of maximum likelihood approach to clustering this has been well documented in the book of mclachlan and basford in this paper we make the fuzzy extension of the cml procedure based on this class of fuzzy cml procedures we extend the fuzzy clustering algorithms of trauwaert kaufman and rousseeuw by adding a penalty term especially we derive a generalized type of fuzzy c means fcm clustering algorithms called the penalized fcm clustering algorithms then we create some asymptotic behaviors of these penalized fcm procedures by doing some numerical examples we find that the penalized fcm is more meaningful and effective than fcm

on convergence properties of the em algorithm for gaussian mixtures we build up the mathematical connection between the expectation maximization em algorithm and gradient based approaches for maximum likelihood learning of finite gaussian mixtures we show that the em step in parameter space is obtained from the gradient via a projection matrix p and we provide an explicit expression for the matrix we then analyze the convergence of em in terms of special properties of p and provide new results analyzing the effect that p has on the likelihood surface based on these mathematical results we present a comparative discussion of the advantages and disadvantages of em and other algorithms for the learning of gaussian mixture models

instability of solitary wave solutions for the nonlinear schrodinger equation of derivative type in degenerate case abstract we study the stability theory of solitary wave solutions for a type of derivative nonlinear schrodinger equation i t u x 2 u i u 2 x u b u 4 u 0 b 0 the equation has a two parameter family of solitary wave solutions of the form u c x t exp i t i c 2 x c t i 4 x c t c 2 d c x c t here c is some suitable function and 2 c 2 the stability in the frequency region of 2 c 2 for some 0 1 and the instability in the frequency region of 2 c 2 were proved by ohta 2014 recently in the endpoint case c 2 the instability of u c was proved by ning et al 2017 then the stability and instability region has been established except the degenerate case c 2 in this paper we address the problem and prove its instability in the degenerate case

a note on the paper combination of interval valued fuzzy set and soft set comput math appl 58 2009 521 527 yang the second author of this paper et al 2009 3 established the distributive law of interval valued fuzzy soft sets in this article it is pointed that it is not true in general but in order to establish the distributive law of interval valued fuzzy soft sets more general notions than interval valued fuzzy soft sets and interval valued fuzzy soft equal are considered using such notions the generalized distributive law of interval valued fuzzy soft sets is established

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

maximum likelihood parameter estimation from incomplete data via the sensitivity equations the continuous time case this paper deals with maximum likelihood ml parameter estimation of continuous time nonlinear partially observed stochastic systems via the expectation maximization em algorithm it is shown that the em algorithm can be executed efficiently provided the unnormalized conditional density of nonlinear filtering is either explicitly solvable or numerically implemented the methodology exploits the relationships between incomplete and complete data log likelihood and its gradient

information theoretic image formation the emergent role of information theory in image formation is surveyed unlike the subject of information theoretic communication theory information theoretic imaging is far from a mature subject the possible role of information theory in problems of image formation is to provide a rigorous framework for defining the imaging problem for defining measures of optimality used to form estimates of images for addressing issues associated with the development of algorithms based on these optimality criteria and for quantifying the quality of the approximations the definition of the imaging problem consists of an appropriate model for the data and an appropriate model for the reproduction space which is the space within which image estimates take values each problem statement has an associated optimality criterion that measures the overall quality of an estimate the optimality criteria include maximizing the likelihood function and minimizing mean squared error for stochastic problems and minimizing squared error and discrimination for deterministic problems the development of algorithms is closely tied to the definition of the imaging problem and the associated optimality criterion algorithms with a strong information theoretic motivation are obtained by the method of expectation maximization related alternating minimization algorithms are discussed in quantifying the quality of approximations global and local measures are discussed global measures include the mean squared error and discrimination between an estimate and the truth and probability of error for recognition or hypothesis testing problems local measures include fisher information

publication bias and meta analysis for 2x2 tables an average markov chain monte carlo em algorithm summary a major difficulty in meta analysis is publication bias studies with positive outcomes are more likely to be published than studies reporting negative or inconclusive results correcting for this bias is not possible without making untestable assumptions in this paper a sensitivity analysis is discussed for the meta analysis of 2 2 tables using exact conditional distributions a markov chain monte carlo em algorithm is used to calculate maximum likelihood estimates a rule for increasing the accuracy of estimation and automating the choice of the number of iterations is suggested

orthogonalizing em a design based least squares algorithm we introduce an efficient iterative algorithm intended for various least squares problems based on a design of experiments perspective the algorithm called orthogonalizing em oem works for ordinary least squares ols and can be easily extended to penalized least squares the main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework we establish several attractive theoretical properties concerning oem for the ols with a singular regression matrix an oem sequence converges to the moore penrose generalized inverse based least squares estimator for ordinary and penalized least squares with various penalties it converges to a point having grouping coherence for fully aliased regression matrices convergence and the convergence rate of the algorithm are examined finally we demonstrate that oem is highly efficient for large scale least squares and penalized least squares proble

variable selection in penalized model based clustering via regularization on grouped parameters penalized model based clustering has been proposed for high dimensional but small sample sized data such as arising from genomic studies in particular it can be used for variable selection a new regularization scheme is proposed to group together multiple parameters of the same variable across clusters which is shown both analytically and numerically to be more effective than the conventional l 1 penalty for variable selection in addition we develop a strategy to combine this grouping scheme with grouping structured variables simulation studies and applications to microarray gene expression data for cancer subtype discovery demonstrate the advantage of the new proposal over several existing approaches

noise covariance identification for nonlinear systems using expectation maximization and moving horizon estimation in order to estimate states from a noise driven state space system the state estimator requires a priori knowledge of both process and output noise covariances unfortunately noise statistics are usually unknown and have to be determined from output measurements current expectation maximization em based algorithms for estimating noise covariances for nonlinear systems assume the number of additive process and output noise signals are the same as the number of states and outputs respectively however in some applications the number of additive process noises could be less than the number of states in this paper a more general nonlinear system is considered by allowing the number of process and output noises to be smaller or equal to the number of states and outputs respectively in order to estimate noise covariances a semi definite programming solver is applied since an analytical solution is no longer easy to obtain the expectation step in current em algorithms rely on state estimates from the extended kalman filter ekf or smoother however the instability and divergence problems of the ekf could cause the em algorithm to converge to a local optimum that is far away from true values we use moving horizon estimation instead of the ekf smoother so that the accuracy of the covariance estimation in nonlinear systems can be significantly improved

nonparametric estimation of the distribution of time to onset for specific diseases in survival sacrifice experiments this paper concerns the analysis of an animal survival sacrifice experiment designed to investigate the incidence of a particular disease of interest the disease is assumed to be irreversible and detectable only at death for example by a necropsy each observation can be of one of three types i death caused by the disease ii death from a competing cause such as sacrifice with the disease present or iii death with the disease absent a two dimensional em algorithm is proposed for the nonparametric maximum likelihood estimation of the distributions of the time to onset and of the time to death from the disease these can be compared with nonparametric estimators recently proposed by kodell shaw and johnson 1982 biometrics 38 43 58 and by dinse and lagakos 1982 biometrics 38 921 932 a slight modification of the algorithm permits the construction of likelihood based interval estimates of quantiles of the distributions some extensions and generalizations are indicated

on some new operations in soft set theory molodtsov introduced the theory of soft sets which can be seen as a new mathematical approach to vagueness in this paper we first point out that several assertions proposition 2 3 iv vi proposition 2 4 and proposition 2 6 iii iv in a previous paper by maji et al p k maji r biswas a r roy soft set theory comput math appl 45 2003 555 562 are not true in general by counterexamples furthermore based on the analysis of several operations on soft sets introduced in the same paper we give some new notions such as the restricted intersection the restricted union the restricted difference and the extended intersection of two soft sets moreover we improve the notion of complement of a soft set and prove that certain de morgan s laws hold in soft set theory with respect to these new definitions

combination of interval valued fuzzy set and soft set the soft set theory proposed by molodtsov can be used as a general mathematical tool for dealing with uncertainty by combining the interval valued fuzzy set and soft set models the purpose of this paper is to introduce the concept of the interval valued fuzzy soft set the complement and and or operations are defined on the interval valued fuzzy soft sets the demorgan s associative and distribution laws of the interval valued fuzzy soft sets are then proved finally a decision problem is analyzed by the interval valued fuzzy soft set some numerical examples are employed to substantiate the conceptual arguments

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

an em algorithm for fitting two level structural equation models maximum likelihood is an important approach to analysis of two level structural equation models different algorithms for this purpose have been available in the literature in this paper we present a new formulation of two level structural equation models and develop an em algorithm for fitting this formulation this new formulation covers a variety of two level structural equation models as a result the proposed em algorithm is widely applicable in practice a practical example illustrates the performance of the em algorithm and the maximum likelihood statistic

a probabilistic and statistical view of fuzzy methods fuzzy set theory has primarily been associated with control theory and with the representation of uncertainty in applications in artificial intelligence more recently fuzzy methods have been proposed as alternatives to traditional statistical methods in statistical quality control linear regression and forecasting among other areas we review some basic concepts of fuzzy methods point out some philosophical and practical problems and offer simpler alternatives based on traditional probability and statistical theory applications in control theory and statistical quality control serve as our primary examples

soft subsets and soft product operations molodtsov s soft set theory provides a general mathematical framework for dealing with uncertainty it is known that soft subsets and soft equal relations are of vital importance in soft set theory this paper aims to give a systematic study on several types of soft subsets and various soft equal relations induced by them we give some equivalent characterizations of different soft subsets and endeavor to ascertain the interrelations among these notions illustrated by a number of concrete examples we also consider ontology based soft sets and show that soft l subsets generalize both soft m subsets and ontology based soft subsets moreover by means of soft l subsets and some related notions we give a theoretical study concerning soft product operations such as products and products we consummate some incomplete results concerning soft product operations existing in the literature and investigate the algebraic properties of soft product operations in detail finally we consider free soft algebras associated with soft product operations it is shown that soft l equal relations are congruence relations over free soft algebras and the corresponding quotient structures form commutative semigroups

maximum likelihood estimation under a successive sampling discovery model a common problem encountered in the analysis of discovery data is the size bias phenomenon in which the larger units tend to be discovered first one approach to account for this bias is to model the discovery process as sampling successively from a finite population without replacement and with probability proportional to size we consider in this article a generalized version of this model for analyzing multivariate data with any given measure of size we assume a superpopulation framework and develop procedures for maximum likelihood estimation of the parameters of the distribution the use of the em algorithm for computing the maximum likelihood estimates associated computational issues and relationships to regression estimators in survey sampling are discussed oil discovery data from the rimbey meadowbrook reef play are used to illustrate the techniques

em based joint data detection and channel estimation of ds cdma signals we present two efficient iterative receiver structures of tractable complexity for joint multiuser detection and multichannel estimation jde of direct sequence code division multiple access signals the schemes result from an application of the expectation maximization em and the space alternating generalized expectation maximization sage algorithms respectively the em jde receiver updates the data bit sequences in parallel while the sage jde receiver reestimates them successively the channel parameters are updated in parallel in both schemes the em algorithm provides a set of free parameters called weight coefficients which can be selected to optimize its performance two optimality criteria are defined and analytical expressions for the corresponding optimized weight coefficients are given monte carlo simulations of a synchronous scenario show that the proposed jde receivers have excellent multiuser efficiency and are robust against errors in the estimation of the channel parameters moreover very short training sequences are required for the jde schemes to converge simulation results further demonstrate that the sage jde receiver exhibits a better performance when the users bit sequences are updated in the order of increasing signal strength i e the bit sequence of the user with the weakest signal strength is updated first at each stage

a priori estimates and weak solutions for the derivative nonlinear schrodinger equation on torus below h 1 2 abstract we propose a priori estimates for a weak solution to the derivative nonlinear schrodinger equation dnls on torus with small l 2 norm datum in low regularity sobolev spaces these estimates allow us to show the existence of solutions in h s t with some s 1 2 in a relatively weak sense furthermore we make some remarks on the error estimates arising from the finite dimensional approximation solutions of dnls using the fourier lesbesgue type as auxiliary spaces despite the fact that nahmod oh rey bellet and staffilani 12 have already seen them

global solvability of the derivative nonlinear schrodinger equation the derivative nonlinear schrodinger equation dnls iqt qxx q q2 x i q x t i a77xr z jffjt was first derived by plasma physicists 9 10 this equation was used to in terpret the propagation of circular polarized nonlinear alfven waves in plasma kaup and newell obtained the soliton solutions of dnls in 1978 5 the au thor obtained the local solvability of dnls in his dissertation 6 in this paper we obtain global existence in time of schwartz class solutions of dnls if the z 2 norm of the generic initial data q x 0 is bounded

image classification by a two dimensional hidden markov model for block based classification an image is divided into blocks and a feature vector is formed for each block by grouping statistics extracted from the block conventional block based classification algorithms decide the class of a block by examining only the feature vector of this block and ignoring context information in order to improve classification by context an algorithm is proposed that models images by two dimensional 2 d hidden markov models hmms the hmm considers feature vectors statistically dependent through an underlying state process assumed to be a markov mesh which has transition probabilities conditioned on the states of neighboring blocks from both horizontal and vertical directions thus the dependency in two dimensions is reflected simultaneously the hmm parameters are estimated by the em algorithm to classify an image the classes with maximum a posteriori probability are searched jointly for all the blocks applications of the hmm algorithm to document and aerial image segmentation show that the algorithm outperforms cart sup tm lvq and bayes vq

convergence of an alternating maximization procedure we derive two convergence results for a sequential alternating maximization procedure to approximate the maximizer of random functionals such as the realized log likelihood in mle estimation we manage to show that the sequence attains the same deviation properties as shown for the profile m estimator by andresen and spokoiny 2013 that means a finite sample wilks and fisher theorem further under slightly stronger smoothness constraints on the random functional we can show nearly linear convergence to the global maximizer if the starting point for the procedure is well chosen

robust continuous time smoothers without two sided stochastic integrals we consider the problem of fixed interval smoothing of a continuous time partially observed nonlinear stochastic dynamical system existing results for such smoothers require the use of two sided stochastic calculus the main contribution of the paper is to present a robust formulation of the smoothing equations under this robust formulation the smoothing equations are nonstochastic parabolic partial differential equations with random coefficients and hence the technical machinery associated with two sided stochastic calculus is not required furthermore the robust smoothed state estimates are locally lipschitz in the observations which is useful for numerical simulation as examples finite dimensional robust versions of the benes and hidden markov model smoothers and smoothers for piecewise linear dynamics are derived these finite dimensional smoothers do not involve stochastic integrals

invariant measures for the periodic derivative nonlinear schrodinger equation we construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear schrodinger equation dnls for small data in l 2 and we show these measures to be absolutely continuous with respect to the gaussian measure the key ingredient of the proof is the analysis of the gauge group of transformations associated to dnls as an intermediate step for our main result we prove quasi invariance with respect to the gauge maps of the gaussian measure on l 2 with covariance mathbb i delta k 1 for any k geqslant 2

asymptotics frequency modulation and low regularity ill posedness for canonical defocusing equations in a recent paper kenig ponce and vega study the low regularity behavior of the focusing nonlinear schrodinger nls focusing modified korteweg de vries mkdv and complex korteweg de vries kdv equations using soliton and breather solutions they demonstrate the lack of local well posedness for these equations below their respective endpoint regularities in this paper we study the defocusing analogues of these equations namely defocusing nls defocusing mkdv and real kdv all in one spatial dimension for which suitable soliton and breather solutions are unavailable we construct for each of these equations classes of modified scattering solutions which exist globally in time and are asymptotic to solutions of the corresponding linear equations up to explicit phase shifts these solutions are used to demonstrate lack of local well posedness in certain sobolev spaces in the sense that the dependence of solutions upon initial data fails to be uniformly continuous in particular we show that the mkdv flow is not uniformly continuous in the l 2 topology despite the existence of global weak solutions at this regularity finally we investigate the kdv equation at the endpoint regularity h and construct solutions for both the real and complex kdv equations the construction provides a nontrivial time interval t t and a locally lipschitz continuous map taking the initial data in h to a distributional solution u c 0 t t h which is uniquely defined for all smooth data the proof uses a generalized miura transform to transfer the existing endpoint regularity theory for mkdv to kdv

asymptotic convergence rate of the em algorithm for gaussian mixtures it is well known that the convergence rate of the expectation maximization em algorithm can be faster than those of convention first order iterative algorithms when the overlap in the given mixture is small but this argument has not been mathematically proved yet this article studies this problem asymptotically in the setting of gaussian mixtures under the theoretical framework of xu and jordan 1996 it has been proved that the asymptotic convergence rate of the em algorithm for gaussian mixtures locally around the true solution is o e0 5 e where e 0 is an arbitrarily small number o x means that it is a higher order infinitesimal as x 0 and e is a measure of the average overlap of gaussians in the mixture in other words the large sample local convergence rate for the em algorithm tends to be asymptotically superlinear when e tends to zero

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

an expert system for predicting nonlinear aeroelastic behavior of an airfoil in this paper we present an expert system to perform steady state response predictions we consider an aeroelastic model simulating a two degree of freedom airfoil oscillating in pitch and plunge with a freeplay nonlinearity in the pitch degree of freedom in the proposed data driven methodology a freeplay is first confirmed and then the locations of the switching points are determined a state space formulation is constructed to model the piece wise linear system the parameters of the system are estimated using the kalman filter and the expectation maximization algorithm the attractive feature of the present approach is its ability to accurately predict the steady state behavior of the nonlinear aeroelastic system with freeplay using only a limited amount of transient input data to demonstrate the effectiveness of the proposed methodology we present applications to freeplay aeroelastic data arising from wind tunnel experiments and numerical simulations

convergence theorems for generalized alternating minimization procedures the em algorithm is widely used to develop iterative parameter estimation procedures for statistical models in cases where these procedures strictly follow the em formulation the convergence properties of the estimation procedures are well understood in some instances there are practical reasons to develop procedures that do not strictly fall within the em framework we study em variants in which the e step is not performed exactly either to obtain improved rates of convergence or due to approximations needed to compute statistics under a model family over which e steps cannot be realized since these variants are not em procedures the standard g em convergence results do not apply to them we present an information geometric framework for describing such algorithms and analyzing their convergence properties we apply this framework to analyze the convergence properties of incremental em and variational em for incremental em we discuss conditions under these algorithms converge in likelihood for variational em we show how the e step approximation prevents convergence to local maxima in likelihood

sparse kalman filtering approaches to realized covariance estimation from high frequency financial data estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns market microstructure noise and jumps one technique for addressing both asynchronous returns and market microstructure is the kalman expectation maximization kem algorithm however the kem approach assumes log normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix in this paper we extend the kem algorithm to price models that include jumps we propose a sparse kalman filtering approach to this problem in particular we develop a kalman expectation conditional maximization algorithm to determine the unknown covariance as well as detecting the jumps in order to promote a sparse estimate of the jumps we consider both laplace and the spike and slab jump priors numerical results using simulated data show that each of these approaches provide for improved covariance estimation relative to the kem method in a variety of settings where jumps occur

a bilinear estimate with applications to the kdv equation u x 0 u0 x where u0 h r our principal aim here is to lower the best index s for which one has local well posedness in h r i e existence uniqueness persistence and continuous dependence on the data for a finite time interval whose size depends on u0 hs equation in 1 1 was derived by korteweg and de vries 21 as a model for long wave propagating in a channel a large amount of work has been devoted to the existence problem for the ivp 1 1 for instance see 9 10 the inverse scattering method applies to this problem and under appropriate decay assumptions on the data several existence results have been established see 5 6 14 28 33 another approach inherited from hyperbolic problems relies on the energy estimates and in particular shows that 1 1 is locally well posed in h r for s 3 2 see 2 3 12 29 30 31 using these results and conservation laws global in time well posedness in h r s 2 was established see 3 12 30 also global in time weak solutions in the energy space h r were constructed in 34 in 13 and 22 a local smoothing effect for solutions of 1 1 was discovered this combined with the conservation laws was used in 13 and 22 to construct global in time weak solutions with data in h r and even in l r in 16 we introduced oscillatory integral techniques to establish local well posedness of 1 1 in h r s 3 4 and hence global in time well posedness in h r s 1 in 16 we showed how to obtain the above mentioned result by picard iteration in an appropriate function space in 4 j bourgain introduced new function spaces adapted to the linear operator t 3 x for which there are good bilinear estimates for the nonlinear term x u 2 using these spaces bourgain was able to establish local well posedness of 1 1 in h r l r and hence by a conservation

diversity combining for ds ss systems with time varying correlated fading branches diversity combining of multiple time varying and correlated fading branches is investigated for direct sequence spread spectrum systems the correlated branches are modeled and estimated jointly as a vector autoregressive var process the joint estimation is shown to provide performance gain over separate estimation of the fading branches the parameter matrices of the var model are estimated via the method of expectation maximization em with two algorithms the first algorithm using results from kalman smoothing provides a closed form solution to the maximization problem in the iterative em procedure however the iterative em kalman algorithm operates repeatedly on a batch of training data and results in large storage requirements and long processing delays to overcome these disadvantages a new algorithm with only forward time recursions is proposed that approximates the iterative em solution and efficiently adapts to slowly changing doppler spreads as a result the new algorithm significantly reduces memory and training sequence requirements through computer simulations a near ideal bit error rate performance is found for both algorithms and the efficacy of the new adaptive algorithm for channels with changing doppler spreads is demonstrated