nonparametric association analysis of bivariate competing risks data although nonparametric analyses of bivariate failure times under independent censoring have been widely studied nonparametric analyses of bivariate competing risks data have not yet been investigated such analyses are important in familial association studies where multiple interacting failure types may violate the independent censoring assumption we develop nonparametric estimators for the bivariate cause specific hazards function and the bivariate cumulative incidence function that are natural analogs of their univariate counterparts and make no assumptions about the dependence of the risks the estimators are shown to be uniformly consistent and to converge weakly to gaussian processes they provide the basis for novel time dependent association measures with the associated inferences yielding tests of cause specific independence in pairs the methodology performs well in simulations with realistic sample sizes its practical utility is illustrated in an analysis of dementia in the cache county st

nonparametric estimation of a multivariate distribution in the presence of censoring summary this paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right censored a distinction is made between what we term homogeneous and heterogeneous censoring it is shown how a multivariate empirical survivor function must be constructed in order to be considered a nonparametric maximum likelihood estimate of the underlying survivor function a closed form solution similar to the product limit estimate of kaplan and meier is possible with homogeneous censoring but an iterative method such as the em algorithm is required with heterogeneous censoring an example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables this anomaly is shown to disappear if

hazard based nonparametric survivor function estimation summary a representation is developed that expresses the bivariate survivor function as a function of the hazard function for truncated failure time variables this leads to a class of nonparametric survivor function estimators that avoid negative mass the transformation from hazard function to survivor function is weakly continuous and compact differentiable so that such properties as strong consistency weak convergence to a gaussian process and bootstrap applicability for a hazard function estimator are inherited by the corresponding survivor function estimator the set of point mass assignments for a survivor function estimator is readily obtained by using a simple matrix calculation on the set of hazard rate estimators special cases arise from a simple empirical hazard rate estimator and from an empirical hazard rate estimator following the redistribution of singly censored observations within strips the latter is shown to equal van der laan s repaired nonparametric maximum likelihood estimator for which a greenwood like variance estimator is given simulation studies are presented to compare the moderate sample performance of various nonparametric survivor function estimators

joint bayesian model selection and estimation of noisy sinusoids via reversible jump mcmc in this paper the problem of joint bayesian model selection and parameter estimation for sinusoids in white gaussian noise is addressed an original bayesian model is proposed that allows us to define a posterior distribution on the parameter space all bayesian inference is then based on this distribution unfortunately a direct evaluation of this distribution and of its features including posterior model probabilities requires evaluation of some complicated high dimensional integrals we develop an efficient stochastic algorithm based on reversible jump markov chain monte carlo methods to perform the bayesian computation a convergence result for this algorithm is established in simulation it appears that the performance of detection based on posterior model probabilities outperforms conventional detection schemes

rank tests for association with right censored data summary rank tests for association between a time variable and a continuous covariate and between two time variables are given in the presence of censoring in the first case these tests are related to the semiparametric tests of cox 1972 and prentice 1978 but differ in that the covariate is replaced by a score computed from its rank in the second case the test statistic is again a simple inner product which in the proportional hazards model reduces to the correlation between the two vectors of log rank scores the loss of efficiency arising from incorrect score functions is also explored when there is no censoring in this paper we consider a general model for association between pairs of observations in which either variable or both variables may be right censored the aim is to develop tests based on the generalized ranks of both variables which have maximal power at alternatives which are near to the null hypothesis of independence attention will be concentrated on two special cases of interest in survival analysis tests for association between a censored survival time and a possibly censored continuous covariate and tests for association between the times to different events beginning with cox 1972 the first situation has been studied extensively in a semiparametric set up in which information based on ranks is used for the time variable but exact values are used for the covariate procedures which use only the ranks of both variables have been developed by brown hollander korwar 1974 and more recently by o brien 1978 however neither of these procedures have been developed with a particular model in mind and one of the achievements of the present paper is to derive rank tests with good local power when a particular model such as the proportional hazards model holds in the case of a proportional hazards model with a continuous covariate the present development may be preferable to the semiparametric methods when the functional form of the relation ship between the hazard and the covariate is not known in advance or when errors or outliers may exist in the observed covariate values thus significance levels may be obtained which are not inflated by multiple regroupings or transformations of the covariate data although it would be expected that parametric model building with variables found to be associated with survival would often be carried out in further analyses

regularization theory and neural networks architectures we had previously shown that regularization principles lead to approximation schemes that are equivalent to networks with one layer of hidden units called regularization networks in particular s

em algorithms for gaussian mixtures with split and merge operation abstract in order to alleviate the problem of local convergence of the usual em algorithm a split and merge operation is introduced into the em algorithm for gaussian mixtures the split and merge equations are first presented theoretically these equations show that the merge operation is a well posed problem whereas the split operation is an ill posed problem because it is the inverse procedure of the merge two methods for solving this ill posed problem are developed through the singular value decomposition and the cholesky decomposition accordingly a new modified em algorithm is constructed our experiments demonstrate that this algorithm is efficient for unsupervised color image segmentation

a recursive local polynomial approximation method using dirichlet clouds and radial basis functions we present a recursive function approximation technique that does not require the storage of the arrival data stream our work is motivated by algorithms in stochastic optimization which require approximating functions in a recursive setting such as a stochastic approximation algorithm the unique collection of these features in this technique is essential for nonlinear modeling of large data sets where the storage of the data becomes prohibitively expensive and in circumstances where our knowledge about a given query point increases as new information arrives the algorithm presented here employs radial basis functions rbfs to provide locally adaptive parametric models such as linear models the local models are updated using recursive least squares and only store the statistical representative of the local approximations the resulting scheme is very fast and memory efficient without compromising accuracy in comparison to methods well accepted as the standard and some advanced techniques used for fu

bayesian information criteria and smoothing parameter selection in radial basis function networks summary by extending schwarz s 1978 basic idea we derive a bayesian information criterion which enables us to evaluate models estimated by the maximum penalised likelihood method or the method of regularisation the proposed criterion is applied to the choice of smoothing parameters and the number of basis functions in radial basis function net work models monte carlo experiments were conducted to examine the performance of the nonlinear modelling strategy of estimating the weight parameters by regularisation and then determining the adjusted parameters by the bayesian information criterion the simulation results show that our modelling procedure performs well in various situations

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

a sequential learning scheme for function approximation using minimal radial basis function neural networks this article presents a sequential learning algorithm for function approximation and time series prediction using a minimal radial basis function neural network rbfnn the algorithm combines the growth criterion of the resource allocating network ran of platt 1991 with a pruning strategy based on the relative contribution of each hidden unit to the overall network output the resulting network leads toward a minimal topology for the rbfnn the performance of the algorithm is compared with ran and the enhanced ran algorithm of kadirkamanathan and niranjan 1993 for the following benchmark problems 1 hearta from the benchmark problems database proben1 2 hermite polynomial and 3 mackey glass chaotic time series for these problems the proposed algorithm is shown to realize rbfnns with far fewer hidden neurons with better or same accuracy

a lil type result for the product limit estimator let x1 x2 xn be i i d r v s with p x u f u and y1 y2 yn be i i d p y u g u where both f and g are unknown continuous survival functions for i 1 2 n set i 1 if xi yi and 0 if xi yi and zi min itxi yi one way to estimate f from the observations zi i i l n is by means of the product limit p l estimator fn kaplan meier 1958 6

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

large sample behaviour of the product limit estimator on the whole line weak convergence results are proved for the product limit estimator on the whole line applications are given to confidence band construction estimation of mean lifetime and to the theory of q functions the results are obtained using stochastic calculus and in probability linear bounds for empirical processes

bayesian wavelet networks for nonparametric regression radial wavelet networks have been proposed previously as a method for nonparametric regression we analyze their performance within a bayesian framework we derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model this process bypasses the need to test or select a finite number of networks during the modeling process predictions are formed by mixing over many models of varying dimension and parameterization we show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series

a model selection rule for sinusoids in white gaussian noise the model selection problem for sinusoidal signals has often been addressed by employing the akaike 1974 information criterion aic and the minimum description length principle mdl the popularity of these criteria partly stems from the intrinsically simple means by which they can be implemented they can however produce misleading results if they are not carefully used the aic and mdl have a common form in that they comprise two terms a data term and a penalty term the data term quantifies the residuals of the model and the penalty term reflects the desideratum of parsimony while the data terms of the aic and mdl are identical the penalty terms are different in most of the literature the aic and mdl penalties are however both obtained by apportioning an equal weight to each additional unknown parameter be it phase amplitude or frequency by contrast we demonstrate that the penalties associated with the amplitude and phase parameters should be weighted differently than the penalty attached to the frequencies following the bayesian methodology we derive a model selection criterion for sinusoidal signals in gaussian noise which also contains the log likelihood and the penalty terms the simulation results disclose remarkable improvement in our selection rule over the commonly used mdl and aic

radial basis function network training using a nonsymmetric partition of the input space and particle swarm optimization this paper presents a novel algorithm for training radial basis function rbf networks in order to produce models with increased accuracy and parsimony the proposed methodology is based on a nonsymmetric variant of the fuzzy means fm algorithm which has the ability to determine the number and locations of the hidden node rbf centers whereas the synaptic weights are calculated using linear regression taking advantage of the short computational times required by the fm algorithm we wrap a particle swarm optimization pso based engine around it designed to optimize the fuzzy partition the result is an integrated framework for fully determining all the parameters of an rbf network the proposed approach is evaluated through its application on 12 real world and synthetic benchmark datasets and is also compared with other neural network training techniques the results show that the rbf network models produced by the pso based nonsymmetric fm algorithm outperform the models produced by the other techniques exhibiting higher prediction accuracies in shorter computational times accompanied by simpler network structures

wavelet based sequential monte carlo blind receivers in fading channels with unknown channel statistics recently an adaptive bayesian receiver for blind detection in flat fading channels was developed by the present authors based on the sequential monte carlo methodology that work is built on a parametric modeling of the fading process in the form of a state space model and assumes the knowledge of the second order statistics of the fading channel in this paper we develop a nonparametric approach to the problem of blind detection in fading channels without assuming any knowledge of the channel statistics the basic idea is to decompose the fading process using a wavelet basis and to use the sequential monte carlo technique to track both the wavelet coefficients and the transmitted symbols a novel resampling based wavelet shrinkage technique is proposed to dynamically choose the number of wavelet coefficients to best fit the fading process under such a framework blind detectors for both flat fading channels and frequency selective fading channels are developed simulation results are provided to demonstrate the excellent performance of the proposed blind adaptive receivers

towards a black box algorithm for nonlinear function approximation over high dimensional domains we propose an algorithm for constructing nonlinear models from high dimensional scattered data the algorithm progresses iteratively adding a new function at each step to refine the model the placement of the functions is driven by a statistical hypothesis test that reveals geometric structure when it fails at each step the added function is fit to data contained in a spatio temporally defined local region to determine the parameters particularly the scale of the local model unlike currently available techniques for nonlinear function fitting over scattered data the proposed method requires no ad hoc parameters thus the number of basis functions required for an accurate fit is determined automatically by the algorithm we illustrate the approach using several illustrative problems including modeling data on manifolds and the prediction of financial time series the algorithm is presented in the context of radial basis functions but in principle can be employed with other methods for function approximation such as multilayer perceptrons

robust full bayesian learning for radial basis networks we propose a hierarchical full bayesian model for radial basis networks this model treats the model dimension number of neurons model parameters regularization parameters and noise parameters as unknown random variables we develop a reversible jump markov chain monte carlo mcmc method to perform the bayesian computation we find that the results obtained using this method are not only better than the ones reported previously but also appear to be robust with respect to the prior specification in addition we propose a novel and computationally efficient reversible jump mcmc simulated annealing algorithm to optimize neural networks this algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function it performs a global search in the joint space of the parameters and number of parameters thereby surmounting the problem of local minima to a large extent we show that by calibrating the full hierarchical bayesian prior we can obtain the classical akaike information criterion bayesian information criterion and minimum description length model selection criteria within a penalized likelihood framework finally we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible jump mcmc simulated annealing method

a non parametric maximum likelihood estimator for bivariate interval censored data we derive a non parametric maximum likelihood estimator for bivariate interval censored data using standard techniques for constrained convex optimization our approach extends those taken for univariate interval censored data we illustrate the estimator with bivariate data from an aids study

estimation of a bivariate distribution function under random censorship summary estimators are proposed of the underlying distribution function of independent bivariate random vectors which are subject to random right censorship in each coordinate the estimators satisfy the monotonicity requirements of a distribution function are uniformly strongly consistent at a rate equal to that of the empirical distribution function and are fairly simple to compute

the latent class twin method the twin method refers to the use of data from same sex identical and fraternal twins to estimate the genetic and environmental contributions to a trait or outcome the standard twin method is the variance component twin method that estimates heritability the fraction of variance attributed to additive genetic inheritance the latent class twin method estimates two quantities that are easier to interpret than heritability the genetic prevalence which is the fraction of persons in the genetic susceptibility latent class and the heritability fraction which is the fraction of persons in the genetic susceptibility latent class with the trait or outcome we extend the latent class twin method in three important ways first we incorporate an additive genetic model to broaden the sensitivity analysis beyond the original autosomal dominant and recessive genetic models second we specify a separate survival model to simplify computations and improve convergence third we show how to easily adjust for covariates by extending the method of propensity scores from a treatment difference to zygosity applying the latent class twin method to data on breast cancer among nordic twins we estimated a genetic prevalence of 1 a result with important implications for breast cancer prevention research

sequential monte carlo methods to train neural network models we discuss a novel strategy for training neural networks using sequential monte carlo algorithms and propose a new hybrid gradient descent sampling importance resampling algorithm hysir in terms of computational time and accuracy the hybrid sir is a clear improvement over conventional sequential monte carlo techniques the new algorithm may be viewed as a global optimization strategy that allows us to learn the probability distributions of the network weights and outputs in a sequential framework it is well suited to applications involving on line nonlinear and nongaussian signal processing we show how the new algorithm outperforms extended kalman filter training on several problems in particular we address the problem of pricing option contracts traded in financial markets in this context we are able to estimate the one step ahead probability density functions of the options prices

modification of the greenwood formula for correlated response times life table methodology for interval censored survival times is used to estimate marginal survival probabilities from data consisting of independent cohorts of correlated responses we restrict our attention to situations where response times within cohorts are exchangeable and the marginal survival distributions are the same for all individuals within any cohort a modification of the greenwood formula is derived for estimating variances and covariances of the estimates of the marginal survival probabilities simulation results show that this formula provides accurate adjustments for within cohort correlations in finite samples comparisons with a nonparametric maximum likelihood estimator indicate negligible loss in efficiency from using simple life table estimators of marginal survival probabilities that ignore the within cohort correlations data from an angioplasty study where more than one procedure is performed on some patients are used to illustrate this methodology

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

nonparametric regression using bayesian variable selection abstract this paper estimates an additive model semiparametrically while automatically selecting the significant independent variables and the appropriate power transformation of the dependent variable the nonlinear variables are modeled as regression splines with significant knots selected from a large number of candidate knots the estimation is made robust by modeling the errors as a mixture of normals a bayesian approach is used to select the significant knots the power transformation and to identify outliers using the gibbs sampler to carry out the computation empirical evidence is given that the sampler works well on both simulated and real examples and that in the univariate case it compares favorably with a kernel weighted local linear smoother the variable selection algorithm in the paper is substantially faster than previous bayesian variable selection algorithms

a practical bayesian framework for backpropagation networks a quantitative and practical bayesian framework is described for learning of mappings in feedforward networks the framework makes possible 1 objective comparisons between solutions using alternative network architectures 2 objective stopping rules for network pruning or growing procedures 3 objective choice of magnitude and type of weight decay terms or additive regularizers for penalizing large weights etc 4 a measure of the effective number of well determined parameters in a model 5 quantified estimates of the error bars on network parameters and on network output and 6 objective comparisons with alternative learning and interpolation models such as splines and radial basis functions the bayesian evidence automatically embodies occam s razor penalizing overflexible and overcomplex models the bayesian approach helps detect poor underlying assumptions in learning models for learning models well matched to a problem a good correlation between generalization ability and the bayesian evidence is obtained

a bayesian framework to identify principal intravoxel diffusion profiles based on diffusion weighted mr imaging in this paper we introduce a new method to characterize the intravoxel anisotropy based on diffusion weighted imaging dwi the proposed solution under a fully bayesian formalism deals with the problem of joint bayesian model selection and parameter estimation to reconstruct the principal diffusion profiles or primary fiber orientations in a voxel we develop an efficient stochastic algorithm based on the reversible jump markov chain monte carlo rjmcmc method in order to perform the bayesian computation rjmcmc is a good choice for this problem because of its ability to jump between models of different dimensionality this methodology provides posterior estimates of the parameters of interest fiber orientation diffusivities etc unconditional of the model assumed it also gives an empirical posterior distribution of the number of primary nerve fiber orientations given the dwi data different probability maps can be assessed using this methodology 1 the intravoxel fiber orientation map or orientational distribution function that gives the probability of finding a fiber in a particular spatial orientation 2 a three dimensional map of the probability of finding a particular number of fibers in each voxel 3 a three dimensional maxpro maximum probability map that provides the most probable number of fibers for each voxel in order to study the performance and reliability of the presented approach we tested it on synthetic data an ex vivo phantom of intersecting capillaries and dwi data from a human subject

the rate of strong uniform consistency for the product limit estimator the maximal deviation of the product limit estimate from the estimated distribution function is investigated as a consequence of a functional law of the iterated logarithm the log log law is proved for this deviation on appropriate half lines with the precise constants this result implies that the log log law need not hold in general for the maximal deviation on the whole line then a general asymptotic order of magnitude is determined for the latter deviation this order depends on the joint behaviour of the censoring and censored distributions in a well defined way corresponding to specific joint behaviours several limsup results are deduced as consequence including all the previously known log log type laws in improved form the results are also extended to the variable censoring model

an inverse problem involving the titchmarsh weyl m function let m denote the titchmarsh weyl m function associated with the differential equation with neumann boundary condition at 0 in the case q c m 0 e for some integer m and e 0 we prove the following result theorem 2 1 if for some integer 3 we know that im l 2 m 0 0 on the ray e i then q v 0 0 for all v in the set 0 1 m for which 2 mod

estimates of marginal survival for dependent competing risks based on an assumed copula summary when time to death and time to censoring are associated one may be appreciably misled when the marginal survival functions are estimated using the product limit estimators which assume independent censoring if no assumption about the relationship between the two times is made the marginal survival functions are not identifiable a natural function that defines the association between the two random variables is the copula we show that if this function is known then the competing risks data are sufficient to identify the marginal survival functions and construct a suitable estimator this estimator is consistent and reduces to the kaplan meier estimator when death and censoring times are independent this statistic can be used to provide bounds on the marginal survival functions based on a range of possible associations between the competing risks

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

self consistent nonparametric maximum likelihood estimator of the bivariate survivor function summary as usually formulated the nonparametric likelihood for the bivariate survivor function is overparameterized resulting in uniqueness problems for the corresponding nonparametric maximum likelihood estimator here the estimation problem is redefined to include parameters for marginal hazard rates and for double failure hazard rates only at informative uncensored failure time grid points where there is pertinent empirical information double failure hazard rates at other grid points in the risk region are specified rather than estimated with this approach the nonparametric maximum likelihood estimator is unique and can be calculated using a two step procedure the first step involves setting aside all doubly censored observations that are interior to the risk region the nonparametric maximum likelihood estimator from the remaining data turns out to be the dabrowska 1988 estimator the omitted doubly censored observations are included in the procedure in the second stage using self consistency resulting in a noniterative nonparametric maximum likelihood estimator for the bivariate survivor function simulation evaluation and asymptotic distributional results are provided moderate sample size efficiency for the survivor function nonparametric maximum likelihood estimator is similar to that for the dabrowska estimator as applied to the entire dataset while some useful efficiency improvement arises for the corresponding distribution function estimator presumably due to the avoidance of negative mass assignments

regression modeling of semicompeting risks data semicompeting risks data are often encountered in clinical trials with intermediate endpoints subject to dependent censoring from informative dropout unlike with competing risks data dropout may not be dependently censored by the intermediate event there has recently been increased attention to these data in particular inferences about the marginal distribution of the intermediate event without covariates in this article we incorporate covariates and formulate their effects on the survival function of the intermediate event via a functional regression model to accommodate informative censoring a time dependent copula model is proposed in the observable region of the data which is more flexible than standard parametric copula models for the dependence between the events the model permits estimation of the marginal distribution under weaker assumptions than in previous work on competing risks data new nonparametric estimators for the marginal and dependence models are derived from nonlinear estimating equations and are shown to be uniformly consistent and to converge weakly to gaussian processes graphical model checking techniques are presented for the assumed models nonparametric tests are developed accordingly as are inferences for parametric submodels for the time varying covariate effects and copula parameters a novel time varying sensitivity analysis is developed using the estimation procedures simulations and an aids data analysis demonstrate the practical utility of the methodology

nonparametric bivariate estimation with randomly censored data summary the estimation of a bivariate distribution function with randomly censored data is considered it is assumed that the censoring occurs independently of the lifetimes and that deaths and losses which occur simultaneously can be separated two estimators are developed a reduced sample estimator and a self consistent one it is shown that the latter estimator satisfies a nonparametric likelihood function and is unique up to the final uncensored values in any dimension it jumps at the points of double deaths in both dimensions some key word8 censored data kaplan meier estimator life table product limit estimator survival estimation

a sequential monte carlo method for motif discovery we propose a sequential monte carlo smc based motif discovery algorithm that can efficiently detect motifs in datasets containing a large number of sequences the statistical distribution of the motifs is modeled by an underlying position weight matrix pwm and both the pwm and the positions of the motifs within the sequences are estimated by the smc algorithm the proposed smc motif discovery technique can locate motifs under a number of scenarios including the single block model two block model with unknown gap length motifs of unknown lengths motifs with unknown abundance and sequences with multiple unique motifs the accuracy of the smc motif discovery algorithm is shown to be superior to that of the existing methods based on mcmc or em algorithms furthermore it is shown that the proposed method can be used to improve the results of existing motif discovery algorithms by using their results as the priors for the smc algorithm

a note on nonparametric estimators of the bivariate survival function under univariate censoring summary a simple nonparametric estimator is proposed for the underlying bivariate distribution of paired failure times in the presence of univariate right censoring the estimator is shown to be a particular path dependent estimator which is a generalisation of an estimator proposed by campbell foldes 1982 under univariate censoring this path dependent estimator has the smallest variance among all path dependent estimators which includes the estimator proposed by lin ying 1993

asymptotic map criteria for model selection the two most popular model selection rules in signal processing literature have been akaike s 1974 criterion aic and rissanen s 1978 principle of minimum description length mdl these rules are similar in form in that they both consist of data and penalty terms their data terms are identical but the penalties are different mdl being more stringent toward overparameterization aic penalizes for each additional model parameter with an equal incremental amount of penalty regardless of the parameter s role in the model in most of the literature on model selection mdl appears in a form that also suggests equal penalty for every unknown parameter this mdl criterion we refer to as naive mdl in this paper we show that identical penalization for every parameter is not appropriate and that the penalty has to depend on the model structure and type of model parameters the approach to showing this is bayesian and it relies on large sample theory we derive maximum a posteriori map rules for several different families of competing models and obtain forms that are similar to aic and naive mdl for some families however we find that the derived penalties are different in those cases our extensive simulations show that the map rule outperforms aic and naive mdl

a frailty model for informative censoring to account for the correlation between failure and censoring we propose a new frailty model for clustered data in this model the risk to be censored is affected by the risk of failure this model allows flexibility in the direction and degree of dependence between failure and censoring it includes the traditional frailty model as a special case it allows censoring by some causes to be analyzed as informative while treating censoring by other causes as noninformative it can also analyze data for competing risks to fit the model the em algorithm is used with markov chain monte carlo simulations in the e steps simulation studies and analysis of data for kidney disease patients are provided consequences of incorrectly assuming noninformative censoring are investigated

a return to the hardy littlewood integral inequality this paper is concerned with the extension and generalization of a classic integral inequality first considered by hardy and littlewood in 1932 the integral inequality is big int b a p f 2 q f 2 big 2 leqslant k int b a w f 2 int b a w w 1 pf qf 2 f in delta where k is a positive number the coefficients p q and w are real valued and w 0 on the interval a b infty a b leqslant infty and p 1 q w in l loc a b delta is the maximal linear manifold of functions f for which the two integrals on the right hand side are both finite the hardy littlewood inequality is the special case a 0 b infty p w 1 and q 0 on 0 infty here k 4 and all the cases of equality can be identified in this paper the results of everitt in 1971 connecting the above inequality with the titchmarsh weyl m coefficient of the associated differential equation py qy lambda wy on a b are restated in an improved form and are shown to hold under the above minimal conditions on the coefficients p q and w it is proved that the best possible value for the number k satisfies 1 k leqslant infty and that within these bounds all values of k can be realized in the course of establishing these results new information of independent interest is obtained about the behaviour of the m coefficient near the real axis examples are given to exhibit the wide range of possibilities for the integral inequality recent results on the asymptotic form of the m coefficient and on the transformation theory of the associated differential equation are shown to have applications for the general properties of the inequality all recent contributions to this general integral inequality are listed in the references and their content is surveyed during the course of the paper

calibration and empirical bayes variable selection for the problem of variable selection for the normal linear model selection criteria such as aic c p bic and ric have fixed dimensionality penalties such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical bayes formulation based on this calibration we propose empirical bayes selection criteria that use hyperparameter estimates instead of fixed choices for obtaining these estimates both marginal and conditional maximum likelihood methods are considered as opposed to traditional fixed penalty criteria these empirical bayes criteria have dimensionality penalties that depend on the data their performance is seen to approximate adaptively the performance of the best fixed penalty criterion across a variety of orthogonal and nonorthogonal set ups including wavelet regression empirical bayes shrinkage estimators of the selected coefficients are also proposed

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

bivariate estimation with right truncated data abstract bivariate estimation with survival data has received considerable attention recently however most of the work has focused on random censoring models another common feature of survival data random truncation is considered in this study truncated data may arise if the time origin of the events under study precedes the observation period in a random right truncation model one observes the iid samples of y t only if y t where y is the variable of interest and t is an independent variable that prevents the complete observation of y suppose that y x is a bivariate vector of random variables where y is subject to right truncation in this study the bivariate reverse hazard vector is introduced and a nonparametric estimator is suggested an estimator for the bivariate survival function is also proposed weak convergence and strong consistency of this estimator are established via a representation by iid variables an expression for the limiting covariance function is provided and a

a weibull model for dependent censoring a bivariate weibull model is proposed for censored survival data when there may be dependence between the survival and censoring random variables the model is based on marginal transformations of the pickands class of bivariate exponential distributions assuming the model to hold the joint distribution of survival and censoring times is shown to be identifiable and the maximum likelihood estimator of the parameters is shown to be consistent

local polynomial regression with correlated errors in random design and unknown correlation structure summaryautomated or data driven bandwidth selection methods tend to break down in the presence of correlated errors while this problem has previously been studied in the fixed design setting for kernel regression the results were applicable only when there is knowledge about the correlation structure this article generalizes these results to the random design setting and addresses the problem in situations where no prior knowledge about the correlation structure is available we establish the asymptotic optimality of our proposed bandwidth selection criterion based on kernels k satisfying k 0 0

kaplan meier estimate on the plane estimation of the bivariate survival function from censored data is considered the product integral representation of univariate survival functions is generalized to the bivariate case and used to determine identifiability of the survival function of the partially observed data a bivariate analogue of the kaplan meier estimate is introduced and its almost sure consistency is studied extensions to the general multivariate case are sketched

a model for informative censoring abstract in the usual model for censored survival analysis observations are of the form x min t c where t and c are nonnegative random variables representing lifetime and censoring time respectively under the usual assumption of independence of t and c the kaplan meier estimator kme is the appropriate estimator of s t pr t t the kme can lead to substantial overestimates of survival probabilities if the event of censoring indicates an unfavorable prognosis for future survival we consider an alternative model in which censoring only occurs in a subpopulation defined by the frailty distribution a self consistent estimator of the survival function appropriate to the model is obtained

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

nonparametric estimation of the bivariate survival function with an application to vertically transmitted aids summary in this paper we propose a nonparametric estimator of the bivariate survival function when the two durations are subject to right censoring we consider the situation where the duration variables are successive and are always observed in a particular order and the censoring mechanism bears on their sum rather than on each separately thus if they are correlated the second duration is right censored by a dependent variable a nonparametric maximum likelihood estimator is derived that takes the dependent censoring into account we also derive the asymptotic variance of the estimator and show how it can be estimated the methods are applied on a vertically acquired mother to child transmission aids data set the first duration corresponds to the hiv incubation period and the second to the period of aids

nonparametric association analysis of exchangeable clustered competing risks data summary the work is motivated by the cache county study of aging a population based study in utah in which sibship associations in dementia onset are of interest complications arise because only a fraction of the population ever develops dementia with the majority dying without dementia the application of standard dependence analyses for independently right censored data may not be appropriate with such multivariate competing risks data where death may violate the independent censoring assumption nonparametric estimators of the bivariate cumulative hazard function and the bivariate cumulative incidence function are adapted from the simple nonexchangeable bivariate setup to exchangeable clustered data as needed with the large sibships in the cache county study time dependent association measures are evaluated using these estimators large sample inferences are studied rigorously using empirical process techniques the practical utility of the methodology is demonstrated with realistic samples both via simulations and via an application to the cache county study where dementia onset clustering among siblings varies strongly by age

a general version of the hardy littlewood polya everitt help inequality the inequality 0 1 below is naturally associated with the equation pu qu u by assuming that one end point of the interval a b is regular and the other limit point for this equation everitt characterized the best constant k in tems of spectral properties of the equation this paper sketches a theory for more general inequalities 0 2 0 3 similarly related to the equation su tu here s and t are ordinary symmetric differential expressions a characterization of the best constants in 0 2 0 3 is given which generalises that of everitt for the case when s is of order 1 and t is multiplication by a positive function all possible inequalities are given together with the best constants and cases of equality furthermore an example is given of a valid inequality 0 1 on an interval with both end points regular for the corresponding differential equation this contradicts a conjecture by everitt and evans finally the general theory for the left definite inequality 0 3 is specialised to the case when s is a sturm liouville expression a family of examples is given for which the best constants can be explicitly calculated

a simple nonparametric estimator of the bivariate survival function under univariate censoring summary in the presence of univariate censoring the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at risk probability to the survival function of the censoring time the use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve the estimator is strongly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function numerical studies demonstrate that both the survival curve estimator and its covariance function estimator perform markedly well for practical sample sizes applications to the correlation problem and to the interval estimation of the difference in median survival times are also studied

comparing two failure time distributions in the presence of dependent censoring summary in a randomised clinical trial to compare two groups of patients suppose that the time to disease occurrence the major response variable may be subject to dependent censoring by death or selective patient withdrawal while the patients who have reached the disease endpoint are followed for their secondary endpoints or survival information to adjust for the dependent censoring in assessing the group difference in disease occurrence we assume that on a logarithmic scale the times to disease occurrence and dependent censoring for the two groups satisfy a bivariate location shift model with a completely unspecified underlying distribution rank based procedures are constructed for making inferences about the location shift parameter model checking techniques are also developed numerical studies show that the proposed methods are appropriate for practical use an illustration with data taken from a recent aids clinical trial is provided

density estimation with bivariate censored data abstract in this article we construct a kernel estimate of the probability density function from bivariate data that have been randomly censored we study the large sample properties of the proposed estimator using a strong approximation result we establish consistency and asymptotic normality and give a convenient representation of the kernel density estimator simulation studies show that the proposed procedure gives a good estimate of the true density function even when the sample size is moderate we discuss various issues about implementation of the estimator including bandwidth selection and boundary effects the procedure can be generalized to higher dimensional variables in a straightforward manner

a generalized kaplan meier estimator in the theory of competing risks the nonparametric kaplan meier estimator plays an important role in this paper a bivariate nonparametric estimator for the competing risk problem is given which for the special case of independent causes gives the kaplan meier estimator this paper also introduces a matrix w through which dependent models for the competing problem can be studied these results also indicate the special case on the matrix w for which the bounds to the survival function given by peterson 4 can be obtained

on inequalities for powers of linear operators and for quadratic forms let h be a hilbert space in which a symmetric operator s with a dense domain d s is given and let s have a finite deficiency index r s this paper contains a necessary and sufficient condition for validity of the following inequalities of kolmogorov type and a method for calculating the best possible constants c n m s moreover let be a symmetric bilinear functional with a dense domain d such that d s d and f g sf g for all f d s g d a necessary and sufficient condition for validity of the inequality as well as a method for calculating the best possible constant k are obtained then an analogous approach is worked out in order to obtain the best possible additive inequalities of the form the paper is concluded by establishing the best possible constants in the inequalities where t is an arbitrary dissipative operator the theorems are extensions of the results of ju i ljubic w n everitt and t kato

regression analysis of grouped survival data informative censoring and double sampling to analyze grouped survival data subject to informative censoring we propose the following two part model a logistic regression model for the hazard for failure given covariates and a logistic regression model for the hazard for informative censoring given time of failure and covariates we fit the model to survival data arising from a double sampling design in a full follow up ff sample subjects are followed after censoring and in a partial follow up pf sample subjects are not followed after censoring we illustrate the methodology using data from a study of wound infection in which patients in the pf sample are censored by release from the hospital whereas patients in the ff sample are followed after hospital release we discuss identifiability when there is only a pf sample we also consider how the allocation between the pf and ff samples affects the precision of estimates

a two stage dimension reduction method for transformed responses and its applications researchers in the biological sciences nowadays often encounter the curse of dimensionality to tackle this sufficient dimension reduction aims to estimate the central subspace in which all the necessary information supplied by the covariates regarding the response of interest is contained subsequent statistical analysis can then be made in a lower dimensional space while preserving relevant information many studies are concerned with the transformed response rather than the original one but they may have different central subspaces when estimating the central subspace of the transformed response direct methods will be inefficient in this article we propose a more efficient two stage estimator of the central subspace of a transformed response this approach is extended to censored responses and is applied to combining multiple biomarkers simulation studies and data examples support the superiority of the procedure copyright 2012 oxford university press

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

applications of a parametric model for informative censoring in this article we explore the use of a parametric model for analyzing survival data which is defined to allow sensitivity analysis for the presence of informative censoring the dependence between the failure and the censoring processes is expressed through a parameter delta and a general bias function b t theta we calculate the expectation of the potential bias due to informative censoring which is an overall measure of how misleading our results might be if censoring is actually nonignorable bounds are also calculated for quantities of interest e g parameter of the distribution of the failure process which do not depend on the choice of the bias function for fixed delta an application that relates to systematic lupus erythematosus data illustrates how additional information can result in reducing the uncertainty on estimates of the location parameter sensitivity analysis on a relative risk parameter is also explored

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

the theil sen estimator with doubly censored data and applications to astronomy abstract the theil sen estimator of the slope parameter in simple linear regression is extended to data with both the response and the covariate subject to censoring based on inverting a suitable version of kendall s statistic this estimator requires weak assumptions and is simple to compute and a simple estimate of its asymptotic variance is obtained a second extension of the theil sen estimator based on a direct estimation of the median of pairwise slopes is given these estimators are compared numerically with versions of schmitt s estimator and applied to two data sets from the recent astronomical literature

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

nonparametric estimation of a bivariate survival function in the presence of censoring a new family of estimators of a bivariate survival function based on censored vectors is obtained from a decomposition of the bivariate survival function these estimators are uniformly consistent under bivariate censoring and are self consistent under univariate censoring

bayesian model choice asymptotics and exact calculations abstract model determination is a fundamental data analytic task here we consider the problem of choosing amongst a finite with loss of generality we assume two set of models after briefly reviewing classical and bayesian model choice strategies we present a general predictive density which includes all proposed bayesian approaches we are aware of using laplace approximations we can conveniently assess and compare asymptotic behavior of these approaches concern regarding the accuracy of these approximation for small to moderate sample sizes encourages the use of monte carlo techniques to carry out exact calculations a data set fit with nested non linear models enables comparison between proposals and between exact and asymptotic values

cardinal interpolation a bayesian probability density for an interpolating function is developed and its desirable properties and practical potential are demonstrated this density has an often needed but previously unachieved property here called cardinal interpolation which ensures extrapolation to the density of the least squares linear model in particular the mean of the cardinal interpolation density is a smooth function that intersects given x y points and which extrapolates to their least squares line and the variance of this density is a smooth function that is zero at the point x values that increases with distance from the nearest point x value and that extrapolates to the well known quadratic variance function for the least squares line the new cardinal interpolation density is developed for gaussian radial basis interpolators using fully bayesian methods that optimize interpolator smoothness this optimization determines the basis function widths and yields an interpolating density that is non gaussian except for large magnitude x and which is therefore not the outcome of a gaussian process further new development shows that the salient property of extrapolation to the density of the least squares linear model can be achieved for more general approximating not just interpolating functions

bayesian radial basis functions of variable dimension a bayesian framework for the analysis of radial basis functions rbf is proposed that accommodates uncertainty in the dimension of the model a distribution is defined over the space of all rbf models of a given basis function and posterior densities are computed using reversible jump markov chain monte carlo samplers green 1995 this alleviates the need to select the architecture during the modeling process the resulting networks are shown to adjust their size to the complexity of the data

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f

accurate uncertainty quantification using inaccurate computational models this paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non gaussian uncertainties it combines state of the art techniques in advanced monte carlo sampling with bayesian formulations the key departure from existing works is the use of inexpensive approximate computational models in a rigorous manner such models can readily be derived by coarsening the discretization size in the solution of the governing pdes increasing the time step when integration of odes is performed using fewer iterations if a nonlinear solver is employed or making use of lower order models it is shown that even in cases where the inaccurate models provide very poor approximations of the high fidelity response statistics of the latter can be quantified accurately with significant reductions in the computational effort multiple approximate models can be used and rigorous confidence bounds of the estimates produced are provided at all stages

strong uniform consistency for nonparametric survival curve estimators from randomly censored data let p x t f t p y t g t and p z t h t h t f t g t an important problem of survival analysis is the estimation of the distribution function f recently the properties of two types of estimators were investigated one of them is the product limit p l estimator of kaplan and meier 8 the other is the nonparametric bayesian estimator introduced by v susarla and j van ryzin 11 in an earlier paper 13 b b winter and the authors proved the uniform consistency of the p l in a second joint paper 6 there was proved the uniform consistency of the p l with rate of o log n l12 nll4 the results of the above two papers were proved without any continuity conditions on f and g in case of arbitrary f and discrete g having finitely many jump points the uniform consistency of the p l with rate factor 0 log nl t was proved in 5 in 10 susarla and van rjzin proved for the bayesian estimator the pointwise consistency with rate factor o log n and the pointwise mean square consistency with rate factor