the global structure of a spatial model of infectious disease in this paper we study an si model of infectious diseases that takes into account spatial inhomogeneities resulting in a system of reaction convection diffusion equations on a bounded domain the convection process is included to account for social interaction as modelled by the location of a focal point or den where the population will tend to aggregate we show that a vertical bifurcation of steady state solutions occurs in this model when birth rate is taken as the bifurcation parameter from which emanates a global secondary branch which then bifurcates at infinity subsequently we use singular perturbation techniques to give a description of the limiting spatial structure along this branch in large and small parameter limits finally the results are illustrated numerically on some biologically relevant cases

kalman filtering with intermittent observations on the boundedness of the expected error covariance this paper addresses the stability of a kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator we give a necessary condition and a sufficient condition with a trivial gap between them for the boundedness of the expected value of the estimation error covariance these conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order markov process hence we extend the class of systems for which these conditions are known in two directions namely by including degenerate systems and by considering network models more general than i i d and gilbert elliott we show that these conditions recover known results from the literature when evaluated for non degenerate systems under the assumption of i i d or gilbert elliott packet loss models

conditional cumulant of exposure method in logistic missing covariate regression summary we consider estimation in logistic regression where some covariate variables may be missing at random satten and kupper 1993 journal of the american statistical association88 200 208 proposed estimating odds ratio parameters using methods based on the probability of exposure by approximating a partial likelihood we extend their idea and propose a method that estimates the cumulant generating function of the missing covariate given observed covariates and surrogates in the controls our proposed method first estimates some lower order cumulants of the conditional distribution of the unobserved data and then solves a resulting estimating equation for the logistic regression parameter a simple version of the proposed method is to replace a missing covariate by the summation of its conditional mean and conditional variance given observed data in the controls we note that one important property of the proposed method is that when the validation is only on controls a class of inverse selection probability weighted semiparametric estimators cannot be applied because selection probabilities on cases are zeros the proposed estimator performs well unless the relative risk parameters are large even though it is technically inconsistent small sample simulations are conducted we illustrate the method by an example of real data analysis

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

kalman filtering with intermittent observations weak convergence to a stationary distribution the paper studies the asymptotic behavior of discrete time random riccati equations rre arising in kalman filtering when the arrival of the observations is described by a bernoulli independent and identically distributed i i d process we model the rre as an order preserving strongly sublinear random dynamical system rds under a sufficient condition stochastic boundedness and using a limit set dichotomy result for order preserving strongly sublinear rds we establish the asymptotic properties of the rre the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution whose support exhibits fractal behavior for stabilizable and detectable systems stochastic boundedness and hence weak convergence holds for any nonzero observation packet arrival probability and in particular we can establish weak convergence at operating arrival rates well below the critical probability for mean stability the resulting invariant measure in that situation does not possess a first moment we apply the weak feller property of the markov process governing the rre to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points which in general is not dense in the set of positive semi definite matrices we use the explicit characterization of the support of the invariant distribution and the almost sure a s ergodicity of the sample paths to easily compute statistics of the invariant distribution a one dimensional example illustrates that the support is a fractured subset of the non negative reals with self similarity properties

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

exploiting gene environment independence for analysis of case control studies an empirical bayes type shrinkage estimator to trade off between bias and efficiency summary standard prospective logistic regression analysis of case control data often leads to very imprecise estimates of gene environment interactions due to small numbers of cases or controls in cells of crossing genotype and exposure in contrast under the assumption of gene environment independence modern retrospective methods including the case only approach can estimate the interaction parameters much more precisely but they can be seriously biased when the underlying assumption of gene environment independence is violated in this article we propose a novel empirical bayes type shrinkage estimator to analyze case control data that can relax the gene environment independence assumption in a data adaptive fashion in the special case involving a binary gene and a binary exposure the method leads to an estimator of the interaction log odds ratio parameter in a simple closed form that corresponds to an weighted average of the standard case only and case control estimators we also describe a general approach for deriving the new shrinkage estimator and its variance within the retrospective maximum likelihood framework developed by chatterjee and carroll 2005 biometrika92 399 418 both simulated and real data examples suggest that the proposed estimator strikes a balance between bias and efficiency depending on the true nature of the gene environment association and the sample size for a given study

global secondary bifurcation in a non linear boundary value problem we consider a steady state non linear boundary value problem which arises in modelling the formation of vascular networks in response to tumour growth global bifurcation from both trivial and non trivial solution branches is considered with emphasis on the latter by investigating such secondary bifurcation it is shown that positive bounded solutions exist for all physically relevant values of a critical parameter a certain class of these solutions is discussed with respect to the application to tumour growth

empirical likelihood inference in nonlinear errors in covariables models with validation data in this article we study inference in parametric nonparametric errors in covariables regression models using an empirical likelihood approach based on validation data it is shown that the asymptotic behavior of the proposed estimator depends on the ratio of the sizes of the primary sample and the validation sample respectively unlike cases without measurement errors the limit distribution of the estimator is no longer tractable and cannot be used for constructing confidence regions monte carlo approximations are employed to simulate the limit distribution to increase the coverage accuracy of confidence regions two adjusted empirical likelihood estimators are recommended which in the limit have a standard chi squared distribution a simulation study is carried out to compare the proposed methods with other existing methods the new methods outperform the least squares method and one of them works better than simulation extrapolation simex estimation even when the restrictive model assumptions n

conditional and unconditional categorical regression models with missing covariates summary we consider methods for analyzing categorical regression models when some covariates 2 are completely observed but other covariates x are missing for some subjects when data on x are missing at random i e when the probability that x is observed does not depend on the value of x itself we present a likelihood approach for the observed data that allows the same nuisance parameters to be eliminated in a conditional analysis as when data are complete an example of a matched casecontrol study is used to demonstrate our approach

semiparametric bayesian analysis of matched case control studies with missing exposure this article considers bayesian analysis of matched case control problems when one of the covariates is partially missing within the likelihood context the standard approach to this problem is to posit a fully parametric model among the controls for the partially missing covariate as a function of the covariates in the model and the variables making up the strata sometimes the strata effects are ignored at this stage our approach differs not only in that it is bayesian but far more importantly in the manner in which it treats the strata effects we assume a dirichlet process prior with a normal base measure for the stratum effects and estimate all of the parameters in a bayesian framework three matched case control examples and a simulation study are considered to illustrate our methods and the computing scheme

technical communique robust state estimation for uncertain discrete time stochastic systems with missing measurements in this paper results of robust estimation of zhou 2010a are extended to state estimation with missing measurements a new procedure is derived which inherits the main properties of that of zhou 2010a in this extension a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult though introducing a monotonic function and using the so called squeeze rule this new robust estimator is proved to converge to a stable system numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of wang yang daniel and liu 2005

bayesian semiparametric modeling for matched case control studies with multiple disease states summary we present a bayesian approach to analyze matched case control data with multiple disease states the probability of disease development is described by a multinomial logistic regression model the exposure distribution depends on the disease state and could vary across strata in such a model the number of stratum effect parameters grows in direct proportion to the sample size leading to inconsistent mles for the parameters of interest even when one uses a retrospective conditional likelihood we adopt a semiparametric bayesian framework instead assuming a dirichlet process prior with a mixing normal distribution on the distribution of the stratum effects we also account for possible missingness in the exposure variable in our model the actual estimation is carried out through a markov chain monte carlo numerical integration scheme the proposed methodology is illustrated through simulation and an example of a matched study on low birth weight of newborns hosmer d a and lemeshow s 2000 applied logistic regression with two possible disease groups matched with a control group

brief paper consistency in least squares estimation in a previous paper the convenience of using martingale theory in the analysis of bayesian least squares estimation was demonstrated however certain restrictions had to be imposed on either the feedback structure or on the initial values for the estimation in the present paper these restrictions are removed and necessary and sufficient conditions for strong consistency in a bayesian sense are given for the gaussian white noise case without any assumptions on closed loop stability or on the feedback structure in the open loop case the poles are shown to be consistently estimated almost everywhere and in the closed loop case certain choices of control law are shown to assure consistency finally adaptive control laws are treated and implicit self tuning regulators are shown to converge to the desired control laws

a bayesian semiparametric model for case control studies with errors in variables summary we develop a model and a numerical estimation scheme for a bayesian approach to inference in case control studies with errors in covariables the model proposed in this paper is based on a nonparametric model for the unknown joint distribution for the missing data the observed covariates and the proxy this nonparametric distribution defines the measurement error component of the model which relates the missing covariates x with a proxy w the oxymoron nonparametric bayes refers to a class of flexible mixture distributions for the likelihood of disease given covariates we choose a logistic regression model by using a parametric disease model and nonparametric exposure model we obtain robust interpretable results quantifying the effect of exposure

asymptotic behavior of recursive state estimations with intermittent measurements convergence rate and stationary distribution approximation are investigated in this paper for both the covariance matrix of the kalman filter and the pseudo covariance matrix of a robust recursive state estimator developed by us when the measurement dropping process is described by a markov chain and an associated plant is both controllable and observable it is proved that if the dropping probability is less than 1 these two matrices converge exponentially to a stationary distribution independent of its initial values moreover when they are initialized with the stabilizing solution of an associated algebraic riccati equation both of them are shown to converge to an ergodic process based on these results two approximations are derived for their stationary probability distributions as well as a bound of approximation errors it has been made clear that rather than the delta function suggested by kar and moura a series of delta functions give a more accurate approximation and replacement of these estimators update gain by a constant matrix usually deteriorates their steady estimation accuracy a numerical example is provided to illustrate the obtained theoretical results

maximum likelihood inference on a mixed conditionally and marginally specified regression model for genetic epidemiologic studies with two phase sampling summary two phase stratified sampling designs can reduce the cost of genetic epidemiologic studies by limiting expensive ascertainments of genetic and environmental exposure to an efficiently selected subsample phase ii of the main study phase i family history and some covariate information which may be cheaply gathered for all subjects at phase i can be used for sampling of informative subjects at phase ii we develop alternative maximum likelihood methods for analysis of data from such studies by using a novel regression model that permits the estimation of marginal risk parameters that are associated with the genetic and environmental covariates of interest while simultaneously characterizing the conditional risk of the disease associated with family history after adjusting for the other covariates the methods and appropriate asymptotic theories are developed with and without an assumption of gene environment independence allowing the distribution of the environmental factors to remain non parametric the performance of the alternative methods and of sampling strategies is studied by using simulated data involving rare and common genetic variants an application of the methods proposed is illustrated by using a case control study of colorectal adenoma embedded within the prostate lung colorectal and ovarian cancer screening trial

moderate deviations of a random riccati equation the paper characterizes the invariant filtering measures resulting from kalman filtering with intermittent observations in which the observation arrival is modeled as a bernoulli process with packet arrival probability our prior work showed that for 0 the sequence of random conditional error covariance matrices converges weakly to a unique invariant distribution this paper shows that as approaches one the family 0 satisfies a moderate deviations principle with good rate function i 1 as 1 the family converges weakly to the dirac measure p concentrated on the fixed point of the associated discrete time riccati operator 2 the probability of a rare event an event bounded away from p under decays to zero as a power law of 1 as 1 and 3 the best power law decay exponent is obtained by solving a deterministic variational problem involving the rate function i for specific scenarios the paper develops computationally tractable methods that lead to efficient estimates of rare event probabilities under

inferences about exposure disease associations using probability of exposure information unconditional and conditional likelihood methods are proposed for modeling odds and odds ratios relating a binary disease variable and an exposure variable that is only known probabilistically e g via measurement of a surrogate exposure variable while adjusting appropriately for a vector of covariables assuming nondifferential errors a probabilistic structure is developed that permits analysis of the marginal relation between disease and the surrogate while maintaining important properties of the marginal relation between disease and true exposure in particular analyses conditioned on marginal totals in surrogate disease tables remove the same nuisance parameters as are removed in a conditional analysis of true exposure disease tables in addition a relation between the probability of exposure poe in the disease and disease free groups is derived permitting the use of information about exposure from populations with structure different from the study population examples are presented illustr

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

on a robust version of the integral representation formula of nonlinear filtering the paper is concerned with completing unfinished business on a robust representation formula for the conditional expectation operator of nonlinear filtering such a formula robust in the sense that its dependence on the process of observations is continuous was stated in 2 without proof the main purpose of this paper is to repair this deficiency

missing exposure data in stereotype regression model application to matched case control study with disease subclassification with advances in modern medicine and clinical diagnosis case control data with characterization of finer subtypes of cases are often available in matched case control studies missingness in exposure values often leads to deletion of entire stratum and thus entails a significant loss in information when subtypes of cases are treated as categorical outcomes the data are further stratified and deletion of observations becomes even more expensive in terms of precision of the category specific odds ratio parameters especially using the multinomial logit model the stereotype regression model for categorical responses lies intermediate between the proportional odds and the multinomial or baseline category logit model the use of this class of models has been limited as the structure of the model implies certain inferential challenges with nonidentifiability and nonlinearity in the parameters we illustrate how to handle missing data in matched case control studies with finer disease subclassification within the cases under a stereotype regression model we present both monte carlo based full bayesian approach and expectation conditional maximization algorithm for the estimation of model parameters in the presence of a completely general missingness mechanism we illustrate our methods by using data from an ongoing matched case control study of colorectal cancer simulation results are presented under various missing data mechanisms and departures from modeling assumptions

conditional regression analysis of the exposure disease odds ratio using known probability of exposure values conditional inference methods are proposed for the odds ratio between binary exposure and disease variables when only the probability of exposure is known for each study subject we develop a conditional likelihood approach that removes nuisance parameters and permits inferences to be made about important parameters in log odds ratio regression models we also discuss a heuristic procedure based on estimating the unknown number of truly exposed individuals this procedure provides a simple framework for interpreting our likelihood based statistics and leads to a mantel haenszel type estimator and a goodness of fit test as an example of the use of this methodology we present an analysis of some genetic data of swift et al 1976 cancer research 36 209 215

prospective analysis of logistic case control studies abstract in a classical case control study prentice and pyke proposed to ignore the study design and instead base estimation and inference on a random sampling i e prospective formulation we generalize this prospective formulation of case control studies to include multiplicative models stratification missing data measurement error robustness and other examples the resulting estimators which ignore the case control study aspect and instead are based on a random sampling formulation are typically consistent for nonintercept parameters and are asymptotically normally distributed we derive the resulting asymptotic covariance matrix of the parameter estimates the covariance matrix obtained by ignoring the case control sampling scheme and using prospective formulas instead is shown to be at worst asymptotically conservative and asymptotically correct in a variety of problems a simple sufficient condition guaranteeing the latter is obtained

semiparametric inference in matched case control studies with missing covariate data summary we consider the problem of matched studies with a binary outcome that are analysed using conditional logistic regression and for which data on some covariates are missing for some study participants methods for this problem involve either modelling the distribution of missing covariates or modelling the probability of data being missing for this second approach the previously proposed method did not make use of data for those persons with missing covariate data except in the model for the missingness we propose a new class of estimators that use outcome and available covariate data for all study participants and show that a particular member of this class always has better efficiency than the previously proposed estimator we illustrate the efficiency gains that are possible with our approach using simulated data

a framework for state space estimation with uncertain models develops a framework for state space estimation when the parameters of the underlying linear model are subject to uncertainties compared with existing robust filters the proposed filters perform regularization rather than deregularization it is shown that under certain stabilizability and detectability conditions the steady state filters are stable and that for quadratically stable models the filters guarantee a bounded error variance moreover the resulting filter structures are similar to various time and measurement update prediction and information forms of the kalman filter albeit ones that operate on corrected parameters rather than on the given nominal parameters simulation results and comparisons with spl hscr sub spl infin guaranteed cost and set valued state estimation filters are provided

a semiparametric mixture approach to case control studies with errors in covariables abstract methods are devised for estimating the parameters of a prospective logistic model in a case control study with dichotomous response d that depends on a covariate x for a portion of the sample both the gold standard x and a surrogate covariate w are available however for the greater portion of the data only the surrogate covariate w is available by using a mixture model the relationship between the true covariate and the response can be modeled appropriately for both types of data the likelihood depends on the marginal distribution of x and the measurement error density w x d the latter is modeled parametrically based on the validation sample the marginal distribution of the true covariate is modeled using a nonparametric mixture distribution in this way we can improve the efficiency and reduce the bias of the parameter estimates the results also apply when there is no validation data provided the error distribution is known or estimated from an independent data source many of the

on kalman filtering for conditionally gaussian systems with random matrices abstract we consider linear stochastic systems with additive white gaussian noise with the added generality that the system matrices are random and adapted to the observation process the main result of this paper is that in order for the standard kalman filter to generate the conditional mean and conditional covariance of the conditionally gaussian distributed state it is sufficient for the random matrices to be finite with probability one at each time instant this generalizes the best previous results available to date to our knowledge which require the more stringent hypothesis that the entries of the random matrices should possess finite second moments at each time instant a significant application of the results of this paper is to the problem of recursive identification of the unknown parameters of a controlled linear stochastic system in such problems the observation matrix is typically generated by complicated nonlinear feedback as for example in adaptive control and the finiteness of the second moments is difficult if not impossible to establish while the finiteness with probability one has been established in many applications

semiparametric regression splines in matched case control studies nous developpons des methodes semi parametriques pour des etudes cas temoin apparies en utilisant les splines de regression trois methodes sont developpees un schema approximatif de validation croisee pour estimer le parametre de lissage inherent aux splines de regression et egalement des methodes monte carlo de type em mcem et bayesienne pour ajuster le modele de spline de regression nous comparons l approche approximative de validation croisee les approches mcem et bayesienne par simulation et nous montrons qu elles apparaissent approximativement de meme efficacite la methode approximative par validation croisee semblant la plus interessante sur le plan des calculs un exemple d epidemiologie equine ayant motive ce travail est utilise pour expliciter nos approches

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

estimation in choice based sampling with measurement error and bootstrap analysis in this paper we discuss the estimation of a logit binary response model the sampling is choice based and is done in two stages we investigate a likelihood based estimator which reduces to the usual logistic estimator when there is no measurement error and which takes into account the constraints imposed by the structure of the problem estimated standard errors obtained by formulae for prospective analysis are asymptotically correct a robust estimation procedures is proposed and an asymptotic covariance matrix obtained several bootstrap methods are applied to this retrospective problem numerical results are presented to illustrate useful properties of the methods

on a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage in this note we consider the following problem suppose a set of sensors is jointly trying to estimate a process one sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors what is the sensor schedule that results in the minimum error covariance we describe a stochastic sensor selection strategy that is easy to implement and is computationally tractable the problem described above comes up in many domains out of which we discuss two in the sensor selection problem there are multiple sensors that cannot operate simultaneously e g sonars in the same frequency band thus measurements need to be scheduled in the sensor coverage problem a geographical area needs to be covered by mobile sensors each with limited range thus from every position the sensors obtain a different view point of the area and the sensors need to optimize their trajectories the algorithm is applied to these problems and illustrated through simple examples

likelihood methods for missing covariate data in highly stratified studies summary the paper considers canonical link generalized linear models with stratum specific nuisance intercepts and missing covariate data this family includes the conditional logistic regression model existing methods for this problem each of which uses a conditioning argu ment to eliminate the nuisance intercept model either the missing covariate data or the missingness process the paper compares these methods under a common likelihood framework the semiparametric efficient estimator is identified and a new estimator which reduces dependence on the model for the missing covariate is proposed a simulation study compares the methods with respect to efficiency and robustness to model misspecification

case control studies with errors in covariates we devise methods for estimating the parameters of a prospective logistic model with dichotomous response d and arbitrary covariates x from case control data when these covariates are measured with error we suppose that some fraction of the cases and controls provide only the error prone covariate measurements w the incomplete or reduced data whereas some of the cases and controls provide measurements on x and w the complete data we assume a measurement error density with a finite set of parameters namely fw xd w x d and nondifferential error is treated as a special case of this model fw x w x our algorithm estimates both the logistic parameters and from a pseudolikelihood because empirical distribution functions are used in place of needed distributions in the pseudolikelihoods the required asymptotic theory is more elaborate than for pseudolikelihoods based on substitution for a finite number of nuisance parameters we also examine computationally simpler methods under t

robustness and risk sensitive filtering this paper gives a precise meaning to the robustness of risk sensitive filters for problems in which one is uncertain as to the exact value of the probability model it is shown that risk sensitive estimators including filters enjoy an error bound which is the sum of two terms the first of which coincides with an upper bound on the error that one would obtain if one knew exactly the underlying probability model while the second term is a measure of the distance between the true and design probability models the paper includes a discussion of several approaches to estimation including h sub spl infin filtering

effects of exposure misclassification on regression analyses of epidemiologic follow up study data in epidemiologic studies subjects are often misclassified as to their level of exposure ignoring this misclassification error in the analysis introduces bias in the estimates of certain parameters and invalidates many hypothesis tests for situations in which there is misclassification of exposure in a follow up study with categorical data we have developed a model that permits consideration of any number of exposure categories and any number of multiple category covariates when used with logistic and poisson regression procedures this model helps assess the potential for bias when misclassification is ignored when reliable ancillary information is available the model can be used to correct for misclassification bias in the estimates produced by these regression procedures

efficient designs of gene environment interaction studies implications of hardy weinberg equilibrium and gene environment independence it is important to investigate whether genetic susceptible variants exercise the same effects in populations that are differentially exposed to environmental risk factors here we assess the power of four two phase case control design strategies for assessing multiplicative gene environment g e interactions or for assessing genetic or environmental effects in the presence of g e interactions with a di allelic snp and a binary e we obtained closed form maximum likelihood estimates of both main effect and interaction odds ratio parameters under the constraints of g e independence and hardy weinberg equilibrium and used the wald statistic for all tests we concluded that i for testing g e interactions or genetic effects in the presence of g e interactions when data for e is fully available it is preferable to ascertain data for g in a subsample of cases with similar numbers of exposed and unexposed and a random subsample of controls and ii for testing g e interactions or environmental effects in the presence of g e interactions when data for g is fully available it is preferable to ascertain data for e in a subsample of cases that has similar numbers for each genotype and a random subsample of controls in addition supplementing external control data to an existing casecontrol sample leads to improved power for assessing effects of g or e in the presence of g e interactions

distributed kalman filtering over massive data sets analysis through large deviations of random riccati equations this paper studies the convergence of the estimation error process and the characterization of the corresponding invariant measure in distributed kalman filtering for potentially unstable and large linear dynamic systems a gossip network protocol termed modified gossip interactive kalman filtering m gikf is proposed where sensors exchange their filtered states estimates and error covariances and propagate their observations via intersensor communications of rate is defined as the averaged number of intersensor message passages per signal evolution epoch the filtered states are interpreted as stochastic particles swapped through local interaction this paper shows that the conditional estimation error covariance sequence at each sensor under m gikf evolves as a random riccati equation rre with markov modulated switching by formulating the rre as a random dynamical system it is shown that the network achieves weak consensus i e the conditional estimation error covariance at a randomly selected sensor converges weakly in distribution to a unique invariant measure further it is proved that as this invariant measure satisfies the large deviation ld upper and lower bounds implying that this measure converges exponentially fast in probability to the dirac measure p where p is the stable error covariance of the centralized kalman filtering setup the ld results answer a fundamental question on how to quantify the rate at which the distributed scheme approaches the centralized performance as the intersensor communication rate increases

on kalman filtering for detectable systems with intermittent observations we consider the problem of kalman filtering when observations are available according to a bernoulli process it is known that there exists a critical probability pc such that if measurements are available with probability greater than pc then the expected prediction covariance is bounded for all initial conditions otherwise it is unbounded for some initial conditions we show that when the system observation matrix restricted to the observable subspace is invertible the known lower bound on pc is in fact the exact critical probability this result is based on a novel decomposition of positive semidefinite matrices

a bayesian approach to prospective binary outcome studies with misclassification in a binary risk factor misclassification in a binary exposure variable within an unmatched prospective study may lead to a biased estimate of the disease exposure relationship it usually gives falsely small credible intervals because uncertainty in the recorded exposure is not taken into account when there are several other perfectly measured covariates interrelationships may introduce further potential for bias bayesian methods are proposed for analysing binary outcome studies in which an exposure variable is sometimes misclassified but its correct values have been validated for a random subsample of the subjects this bayesian approach can model relationships between explanatory variables and between exploratory variables and the probabilities of misclassification three logistic regressions are used to relate disease to true exposure misclassified exposure to true exposure and true exposure to other covariates credible intervals may be used to make decisions about whether certain parameters are unnecessary and hence whether the model can be reduced in complexity in the disease exposure model for parameters representing coefficients related to perfectly measured covariates the precision of posterior estimates is only slightly lower than would be found from data with no misclassification for the risk factor which has misclassification the estimates of model coefficients obtained are much less biased than those with misclassification ignored

a global branch of solutions to a semilinear equation on an unbounded interval keywords semilinear second order differential equation bifurcation asymptotic bifurcation neumann problem global branch reference ana article 1985 001view record in web of science record created on 2008 12 10 modified on 2016 08 08