inference with imputed conditional means abstract in this article we present analytic techniques for inference from a dataset in which missing values have been replaced by predictive means derived from an imputation model the derivations are based on asymptotic expansions of point estimators and their associated variance estimators and the resulting formulas can be thought of as first order approximations to standard multiple imputation procedures with an infinite number of imputations for the missing values our method where applicable may require substantially less computational effort than creating and managing a multiply imputed database moreover the resulting inferences can be more precise than those derived from multiple imputation because they do not rely on simulation our techniques use components of the standard complete data analysis along with two summary measures from the fitted imputation model if the imputation and analysis phases are carried out by the same person or organization then the method provides a quick assessm

equivalence between conditional and random effects likelihoods for pair matched case control studies two approaches dominate the analysis of highly stratified data sets use of conditional likelihood and random effects models conditioning is more traditional and has attractive robustness properties contemporary random effects approaches rely more on accurate assumptions but can be applied to a larger class of problems for pair matched studies with arbitrary numbers of categorical covariates we reconcile these two approaches showing that the conditional approach has an exact interpretation as a specific type of random effects model the random effects models that provide equivalence with conditioning naturally inherit all the attractive properties of that approach and we argue they are a pragmatic model choice we also discuss desirable characteristics of the random effects model that are entirely novel and that have foundational implications for example although our model is specified entirely within a full likelihood framework its assumed random effects distribution does not need a parametric f

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

inference for imputation estimators we derive an estimator of the asymptotic variance of both single and multiple imputation estimators we assume a parametric imputation model but allow for non and semiparametric analysis models our variance estimator in contrast to the estimator proposed by rubin 1987 is consistent even when the imputation and analysis models are misspecified and incompatible with one another

robustness of a multivariate normal approximation for imputation of incomplete binary data multiple imputation has become easier to perform with the advent of several software packages that provide imputations under a multivariate normal model but imputation of missing binary data remains an important practical problem here we explore three alternative methods for converting a multivariate normal imputed value into a binary imputed value 1 simple rounding of the imputed value to the nearer of 0 or 1 2 a bernoulli draw based on a coin flip where an imputed value between 0 and 1 is treated as the probability of drawing a 1 and 3 an adaptive rounding scheme where the cut off value for determining whether to round to 0 or 1 is based on a normal approximation to the binomial distribution making use of the marginal proportions of 0 s and 1 s on the variable we perform simulation studies on a data set of 206 802 respondents to the california healthy kids survey where the fully observed data on 198 262 individuals defines the population from which we repeatedly draw samples with missing data impute calculate statistics and confidence intervals and compare bias and coverage against the true values frequently we found satisfactory bias and coverage properties suggesting that approaches such as these that are based on statistical approximations are preferable in applied research to either avoiding settings where missing data occur or relying on complete case analyses considering both the occurrence and extent of deficits in coverage we found that adaptive rounding provided the best performance copyright 2006 john wiley sons ltd

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

bayesian analysis of case control studies a bayesian approach to the estimation of an odds ratio from case control data is considered the exact posterior density of the odds ratio and its moments are derived a log normal approximation to the density is shown to be adequate for practical purposes mechanisms for setting prior parameters are discussed and some examples are presented

multiple imputation of missing categorical and continuous values via bayesian mixture models with local dependence abstractwe present a nonparametric bayesian joint model for multivariate continuous and categorical variables with the intention of developing a flexible engine for multiple imputation of missing values the model fuses dirichlet process mixtures of multinomial distributions for categorical variables with dirichlet process mixtures of multivariate normal distributions for continuous variables we incorporate dependence between the continuous and categorical variables by 1 modeling the means of the normal distributions as component specific functions of the categorical variables and 2 forming distinct mixture components for the categorical and continuous data with probabilities that are linked via a hierarchical model this structure allows the model to capture complex dependencies between the categorical and continuous data with minimal tuning by the analyst we apply the model to impute missing values due to item nonresponse in an evaluation of the redesign of the survey of income and program partic

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

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

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

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

the lin ni conjecture in negative geometries abstract we prove see theorem 1 1 that the lin ni conjecture for closed manifolds is false in dimensions n 4 5 when the scalar curvature is negative but that it holds true in the bounded energy setting when n 6 see theorem 1 2 as a corollary to theorem 1 1 we prove see theorem 2 2 that contrary to the 3 dimensional case the sup inf inequality does not hold in general with a sole control on the size of the potential for positive solutions of stationary critical schrodinger equations

small sample degrees of freedom with multiple imputation an appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete data inferences into a final inference the repeated imputation inference rubin 1987 this inference is based on a t distribution and is derived from a bayesian paradigm under the assumption that the complete data degrees of freedom com are infinite but the number of imputations m is finite when com is small and there is only a modest proportion of missing data the calculated repeated imputation degrees of freedom m for the t reference distribution can be much larger than com which is clearly inappropriate following the bayesian paradigm we derive an adjusted degrees of freedom m with the following three properties for fixed m and estimated fraction of missing information m monotonically increases in com m is always less than or equal to com and m equals m when com is infinite a small simulation study demonstrates the superior frequentist performance when using m rather than m

multiple imputation in cox regression when there are time varying effects of covariates in cox regression it is important to test the proportional hazards assumption and sometimes of interest in itself to study time varying effects tves of covariates tves can be investigated with log hazard ratios modelled as a function of time missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a complete case analysis two multiple imputation methods have been proposed for when the substantive model is a cox proportional hazards regression an approximate method imputing missing covariate values for the cox model in statistics in medicine 2009 by white and royston and a substantive model compatible method multiple imputation of covariates by fully conditional specification accommodating the substantive model in statistical methods in medical research 2015 by bartlett et al at present neither accommodates tves of covariates we extend them to do so for a general form for the tves and give specific details for tves modelled using restricted cubic splines simulation studies assess the performance of the methods under several underlying shapes for tves our proposed methods give approximately unbiased tve estimates for binary covariates with missing data but for continuous covariates the substantive model compatible method performs better the methods also give approximately correct type i errors in the test for proportional hazards when there is no tve and gain power to detect tves relative to complete case analysis ignoring tves at the imputation stage results in biased tve estimates incorrect type i errors and substantial loss of power in detecting tves we also propose a multivariable tve model selection algorithm the methods are illustrated using data from the rotterdam breast cancer study r code is provided

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

multiple imputation of missing blood pressure covariates in survival analysis this paper studies a non response problem in survival analysis where the occurrence of missing data in the risk factor is related to mortality in a study to determine the influence of blood pressure on survival in the very old 85 years blood pressure measurements are missing in about 12 5 per cent of the sample the available data suggest that the process that created the missing data depends jointly on survival and the unknown blood pressure thereby distorting the relation of interest multiple imputation is used to impute missing blood pressure and then analyse the data under a variety of non response models one special modelling problem is treated in detail the construction of a predictive model for drawing imputations if the number of variables is large risk estimates for these data appear robust to even large departures from the simplest non response model and are similar to those derived under deletion of the incomplete records

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

parametric fractional imputation for missing data analysis under a parametric model for missing data the em algorithm is a popular tool for flnding the maximum likelihood estimates mle of the parameters of the model imputation when carefully done can be used to facilitate the parameter estimation by applying the complete sample estimators to the imputed dataset the basic idea is to generate the imputed values from the conditional distribution of the missing data given the observed data multiple imputation is a bayesian approach to generate the imputed values from the conditional distribution in this article parametric fractional imputation is proposed as a parametric approach for generating imputed values using fractional weights the e step of the em algorithm can be approximated by the weighted mean of the imputed data likelihood where the fractional weights are computed from the current value of the parameter estimates some computational e ciency can be achieved using the idea of importance sampling in the monte carlo approximation of the conditional expectation the resulting estimator of the specifled parameters will be identical to the mle under missing data if the fractional weights are adjusted using a calibration step the proposed imputation method provides e cient parameter estimates for the model parameters specifled and also provides reasonable estimates for parameters that are not part of the imputation model for example domain means thus the proposed imputation method is a useful tool for general purpose data analysis variance estimation is covered and results from a limited simulation study are presented

multiple imputation for an incomplete covariate that is a ratio we are concerned with multiple imputation of the ratio of two variables which is to be used as a covariate in a regression analysis if the numerator and denominator are not missing simultaneously it seems sensible to make use of the observed variable in the imputation model one such strategy is to impute missing values for the numerator and denominator or the log transformed numerator and denominator and then calculate the ratio of interest we call this passive imputation alternatively missing ratio values might be imputed directly with or without the numerator and or the denominator in the imputation model we call this active imputation in two motivating datasets one involving body mass index as a covariate and the other involving the ratio of total to high density lipoprotein cholesterol we assess the sensitivity of results to the choice of imputation model and as an alternative explore fully bayesian joint models for the outcome and incomplete ratio fully bayesian approaches using winbugs were unusable in both datasets because of computational problems in our first dataset multiple imputation results are similar regardless of the imputation model in the second results are sensitive to the choice of imputation model sensitivity depends strongly on the coefficient of variation of the ratio s denominator a simulation study demonstrates that passive imputation without transformation is risky because it can lead to downward bias when the coefficient of variation of the ratio s denominator is larger than about 0 1 active imputation or passive imputation after log transformation is preferable 2013 the authors statistics in medicine published by john wiley sons ltd

combining fractional polynomial model building with multiple imputation multivariable fractional polynomial mfp models are commonly used in medical research the datasets in which mfp models are applied often contain covariates with missing values to handle the missing values we describe methods for combining multiple imputation with mfp modelling considering in turn three issues first how to impute so that the imputation model does not favour certain fractional polynomial fp models over others second how to estimate the fp exponents in multiply imputed data and third how to choose between models of differing complexity two imputation methods are outlined for different settings for model selection methods based on wald type statistics and weighted likelihood ratio tests are proposed and evaluated in simulation studies the wald based method is very slightly better at estimating fp exponents type i error rates are very similar for both methods although slightly less well controlled than analysis of complete records however there is potential for substantial gains in power over the analysis of complete records we illustrate the two methods in a dataset from five trauma registries for which a prognostic model has previously been published contrasting the selected models with that obtained by analysing the complete records only 2015 the authors statistics in medicine published by john wiley sons ltd

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

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

handling missing data in matched case control studies using multiple imputation analysis of matched case control studies is often complicated by missing data on covariates analysis can be restricted to individuals with complete data but this is inefficient and may be biased multiple imputation mi is an efficient and flexible alternative we describe two mi approaches the first uses a model for the data on an individual and includes matching variables the second uses a model for the data on a whole matched set and avoids the need to model the matching variables within each approach we consider three methods full conditional specification fcs joint model mi using a normal model and joint model mi using a latent normal model we show that fcs mi is asymptotically equivalent to joint model mi using a restricted general location model that is compatible with the conditional logistic regression analysis model the normal and latent normal imputation models are not compatible with this analysis model all methods allow for multiple partially observed covariates non monotone missingness and multiple controls per case they can be easily applied in standard statistical software and valid variance estimates obtained using rubin s rules we compare the methods in a simulation study the approach of including the matching variables is most efficient within each approach the fcs mi method generally yields the least biased odds ratio estimates but normal or latent normal joint model mi is sometimes more efficient all methods have good confidence interval coverage data on colorectal cancer and fibre intake from the epic norfolk study are used to illustrate the methods in particular showing how efficiency is gained relative to just using individuals with complete data

large sample theory for parametric multiple imputation procedures we consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the proper imputation procedures proposed by rubin 1978 the asymptotic variance structure of the resulting estimators is provided this result is used to compare the relative efficiencies of different imputation procedures it also provides a basis to understand the behaviour of two monte carlo iterative estimators stochastic em celeux diebolt 1985 wei tanner 1990 and simulated em ruud 1991 we further develop properties of these estimators when they stop at iteration k with imputation size m an application to a mcasurement error problem is used to illustrate the results

minorization conditions and convergence rates for markov chain monte carlo abstract general methods are provided for analyzing the convergence of discrete time general state space markov chains such as those used in stochastic simulation algorithms including the gibbs sampler the methods provide rigorous a priori bounds on how long these simulations should be run to give satisfactory results results are applied to two models of the gibbs sampler a bivariate normal model and a hierarchical poisson model with gamma conditionals the methods use the notion of minorization conditions for markov chains

the homotopy perturbation method applied for solving complex valued differential equations with strong cubic nonlinearity abstract in this paper the homotopy perturbation method is adopted for solving a complex valued second order strongly nonlinear differential equation homotopy with an imbedding parameter p 0 1 is constructed the perturbation procedure with parameter p transforms the strongly nonlinear differential equation into a system of linear complex valued differential equations whose solutions give the approximate solution of the initial differential equation to illustrate the effectiveness and convenience of the suggested procedure a duffing equation with strong cubic nonlinearity is considered the periodic solution in the first approximation is obtained the solution is compared with the exact one and shows good agreement

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

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

linearized perturbation method for stochastic analysis of a rill erosion model the linearization and correction method lcm proposed by he is a simple and effective perturbation technique to solve nonlinear equations to analyze the random properties of rill erosion model a new stochastic perturbation technique called linearized perturbation method is developed by combining the traditional stochastic perturbation method with the lcm comparisons between the numerical results obtained by the linearized perturbation method and those obtained by monte carlo method indicated an excellent agreement however the calculation efficiency of the linearized perturbation method is higher

bayesian analysis of case control studies with categorical covariates in a case control study the appropriate likelihood is the retrospective likelihood i e the likelihood of exposure given disease for the classical frequentist analysis the prospective likelihood i e the likelihood of disease given exposure and the retrospective likelihood produce the same odds ratio estimators for exposure and so logistic regression may be used for both the bayesian analysis is not so simple but the bayesian framework for case control studies offers flexible possibilities for the hierarchical modelling that is needed in many contexts we review the bayesian approaches to the analysis of case control studies developed so far show how to extend these approaches to the situation of a study with any number of categorical or discretised continuous exposure variables and identifying suitable priors we then show how the resulting models may be fitted using markov chain monte carlo methods and provide an illustration based on genotype data

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

multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

sign changing bubble towers for asymptotically critical elliptic equations on riemannian manifolds given a smooth compact riemannian n manifold m g we consider the equation gu hu u 2 2 eu where h is a c1 function on m the exponent 2 2n n 2 is the critical sobolev exponent and e is a small positive real parameter such that e 0 we prove the existence of blowing up families of sign changing solutions which develop bubble towers at some point where the function h is greater than the yamabe potential n 24 n 1 scalg

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

positive clusters for smooth perturbations of a critical elliptic equation in dimensions four and five abstract we construct clustering positive solutions for a perturbed critical elliptic equation on a closed manifold of dimension n 4 5 such a construction is already available in the literature in dimensions n 6 see for instance 10 14 30 32 36 and not possible in dimension 3 by 25 this also provides new patterns for the lin ni 26 problem on closed manifolds and completes results by brezis and li 8 about this problem

modeling unobserved sources of heterogeneity in animal abundance using a dirichlet process prior in surveys of natural populations of animals a sampling protocol is often spatially replicated to collect a representative sample of the population in these surveys differences in abundance of animals among sample locations may induce spatial heterogeneity in the counts associated with a particular sampling protocol for some species the sources of heterogeneity in abundance may be unknown or unmeasurable leading one to specify the variation in abundance among sample locations stochastically however choosing a parametric model for the distribution of unmeasured heterogeneity is potentially subject to error and can have profound effects on predictions of abundance at unsampled locations in this article we develop an alternative approach wherein a dirichlet process prior is assumed for the distribution of latent abundances this approach allows for uncertainty in model specification and for natural clustering in the distribution of abundances in a data adaptive way we apply this approach in an analysis of counts based on removal samples of an endangered fish species the okaloosa darter results of our data analysis and simulation studies suggest that our implementation of the dirichlet process prior has several attractive features not shared by conventional fully parametric alternatives

maximum likelihood estimation for mixed continuous and categorical data with missing values summary maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented the general location model of olkin tate 1961 and extensions introduced by krzanowski 1980 1982 form the basis for our methods maximum likelihood estimation with incomplete data is achieved by an application of the em algorithm dempster laird rubin 1977 special cases of the algorithm include orchard woodbury s 1972 algorithm for incomplete normal samples fuchs s 1982 algorithms for log linear modelling of partially classified contingency tables and day s 1969 algorithm for multivariate normal mixtures applications include a imputation of missing values b logistic regression and discriminant analysis with missing predictors and unclassified observations c linear regression with missing continuous and categorical predictors and d parametric cluster analysis with incomplete data methods are illustrated using data from the st louis risk research project some key word8 cluster analysis discriminant analysis em algorithm incomplete data linear regression logistic regression log linear model mixture model

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

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

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

the effect of linear perturbations on the yamabe problem in conformal geometry the compactness conjecture asserts that the set of yamabe metrics on a smooth compact aspherical riemannian manifold left m g right is compact established in the locally conformally flat case by schoen lecture notes in mathematics vol 1365 pp 120 154 springer berlin 1989 surveys pure application and mathematics 52 longman science technology pp 311 320 harlow 1991 and for n le 24 by khuri marques schoen j differ geom 81 1 143 196 2009 it has revealed to be generally false for n ge 25 as shown by brendle j am math soc 21 4 951 979 2008 and brendle marques j differ geom 81 2 225 250 2009 a stronger version of it the compactness under perturbations of the yamabe equation is addressed here with respect to the linear geometric potential frac n 2 4 n 1 mathrm scal g mathrm scal g being the scalar curvature of left m g right we show that a priori l infty bounds fail for linear perturbations on all manifolds with n ge 4 as well as a priori gradient l 2 bounds fail for non locally conformally flat manifolds with n ge 6 and for locally conformally flat manifolds with n ge 7 in several situations the results are optimal our proof combines a finite dimensional reduction and the construction of a suitable ansatz for the solutions generated by a family of varying metrics in the conformal class of g

fitting stratified proportional odds models by amalgamating conditional likelihoods classical methods for fitting a varying intercept logistic regression model to stratified data are based on the conditional likelihood principle to eliminate the stratum specific nuisance parameters when the outcome variable has multiple ordered categories a natural choice for the outcome model is a stratified proportional odds or cumulative logit model however classical conditioning techniques do not apply to the general k category cumulative logit model k 2 with varying stratum specific intercepts as there is no reduction due to sufficiency the nuisance parameters remain in the conditional likelihood we propose a methodology to fit stratified proportional odds model by amalgamating conditional likelihoods obtained from all possible binary collapsings of the ordinal scale the method allows for categorical and continuous covariates in a general regression framework we provide a robust sandwich estimate of the variance of the proposed estimator for binary exposures we show equivalence of our approach to the estimators already proposed in the literature the proposed recipe can be implemented very easily in standard software we illustrate the methods via three real data examples related to biomedical research simulation results comparing the proposed method with a random effects model on the stratification parameters are also furnished

finite sample properties of multiple imputation estimators finite sample properties of multiple imputation estimators under the linear regression model are studied the exact bias of the multiple imputation variance estimator is presented a method of reducing the bias is presented and simulation is used to make comparisons we also show that the suggested method can be used for a general class of linear estimators

ellipsoidally symmetric extensions of the general location model for mixed categorical and continuous data summary the general location model olkin tate 1961 krzanowski 1980 1982 little schluchter 1985 has categorical variables marginally distributed as a multinomial and continuous variables conditionally normally distributed with different means across cells defined by the categorical variables but a common covariance matrix across cells two extensions of the general location model are obtained the first replaces the common covariance matrix with different but proportional covariance matrices where the proportionality constants are to be estimated the second replaces the multivariate normal distributions of the first extension with multivariate t distributions where the degrees of freedom can also vary across cells and are to be estimated the t distribution is just one example of more general ellipsoidally symmetric distributions that can be used in place of the normal these extensions can provide more accurate fits to real data and can be viewed as tools for robust inference moreover the models can be very useful for multiple imputation of ignorable missing values maximum likelihood estimation using the aecm algorithm meng van dyk 1997 is presented as is a monotone data gibbs sampling scheme for drawing parameters and missing values from their posterior distributions to illustrate the techniques a numerical example is presented

logistic regression for two stage case control data summary samples of diseased cases and nondiseased controls are drawn at random from the population at risk after classification according to the exposure of interest subsamples of cases and controls are selected for purposes of covariable ascertainment a modification of the usual logistic regression analysis yields consistent estimates of covariable adjusted relative risks and their standard errors by balancing the numbers of exposed and nonexposed for whom covariable inforniation is ascertained within case and control samples some efficiency may be gained over the usual single stage design particularly when the exposure is rare and the relative risks associated with the covariables are large the procedure may be useful also when covariable information is missing for a large part of the sample

on a conjecture of lin ni for a semilinear neumann problem let q be a bounded domain in rn n 3 and a 0 we consider au au u n 2 n 2 in q2 u 0 in q au av 0 on i2 and show that for a sufficiently small the minimal energy solutions are only constants

partially collapsed gibbs samplers theory and methods ever increasing computational power along with ever more sophisticated statistical computing techniques is making it possible to fit ever more complex statistical models among the more computationally intensive methods the gibbs sampler is popular because of its simplicity and power to effectively generate samples from a high dimensional probability distribution despite its simple implementation and description however the gibbs sampler is criticized for its sometimes slow convergence especially when it is used to fit highly structured complex models here we present partially collapsed gibbs sampling strategies that improve the convergence by capitalizing on a set of functionally incompatible conditional distributions such incompatibility generally is avoided in the construction of a gibbs sampler because the resulting convergence properties are not well understood we introduce three basic tools marginalization permutation and trimming that allow us to transform a gibbs sampler into a part

on the stationary distribution of iterative imputations iterative imputation in which variables are imputed one at a time each given a model predicting from all the others is a popular technique that can be convenient and exible as it replaces a potentially dicult multivariate modeling problem with relatively simple univariate regressions in this paper we begin to characterize the stationary distributions of iterative imputations and their statistical properties more precisely when the conditional models are compatible dened in the text we give a set of sucient conditions under which the imputation distribution converges in total variation to the posterior distribution of a bayesian model when the conditional models are incompatible but are valid we show that the combined imputation estimator is consistent