distributed detection in sensor networks with limited range multimodal sensors we consider a multiobject detection problem over a sensor network snet with limited range multimodal sensors the general problem complements the widely considered decentralized detection problem where all sensors observe the same object we develop a distributed detection approach based on recent development of the false discovery rate fdr and the associated benjamini hochberg bh procedure which rank orders scalar test statistics we first develop scalar test statistics for multidimensional data to handle multimodal sensor observations and establish its optimality in terms of the bh procedure we then propose a distributed algorithm for an idealized model to detect the sensors that are in the immediate vicinity of an object we show that the number of binary messages that need to be transmitted communication cost is upper bounded by the number of sensors that are in the vicinity of objects and is independent of the total number of sensors in the snet this brings forth an important principle for evaluating the performance of an snet namely the need for scalability of communications and performance with respect to the number of objects or events in an snet irrespective of the network size we then account for nonideal models by developing robust extensions to our developments under the idealized model the robustness properties ensure that both the error performance and communication cost degrade gracefully with interference

false discovery control in large scale spatial multiple testing summary the paper develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals we consider both pointwise and clusterwise spatial analyses and derive oracle procedures which optimally control the false discovery rate false discovery exceedance and false cluster rate a data driven finite approximation strategy is developed to mimic the oracle procedures on a continuous spatial domain our multiple testing procedures are asymptotically valid and can be effectively implemented using bayesian computational algorithms for analysis of large spatial data sets numerical results show that the procedures proposed lead to more accurate error control and better power performance than conventional methods we demonstrate our methods for analysing the time trends in tropospheric ozone in eastern usa

effects of statistical dependence on multiple testing under a hidden markov model the performance of multiple hypothesis testing is known to be affected by the statistical dependence among random variables involved the mechanisms responsible for this however are not well understood we study the effects of the dependence structure of a finite state hidden markov model hmm on the likelihood ratios critical for optimal multiple testing on the hidden states various convergence results are obtained for the likelihood ratios as the observations of the hmm form an increasing long chain analytic expansions of the first and second order derivatives are obtained for the case of binary states explicitly showing the effects of the parameters of the hmm on the likelihood ratios

power enhanced multiple decision functions controlling family wise error and false discovery rates improved procedures in terms of smaller missed discovery rates mdr for performing multiple hypotheses testing with weak and strong control of the family wise error rate fwer or the false discovery rate fdr are developed and studied the improvement over existing procedures such as the sidak procedure for fwer control and the benjamini hochberg bh procedure for fdr control is achieved by exploiting possible differences in the powers of the individual tests results signal the need to take into account the powers of the individual tests and to have multiple hypotheses decision functions which are not limited to simply using the individual p values as is the case for example with the sidak bonferroni or bh procedures they also enhance understanding of the role of the powers of individual tests or more precisely the receiver operating characteristic roc functions of decision processes in the search for better multiple hypotheses testing procedures a decision theoretic framework is utilized and through auxiliary randomizers the procedures could be used with discrete or mixed type data or with rank based nonparametric tests this is in contrast to existing p value based procedures whose theoretical validity is contingent on each of these p value statistics being stochastically equal to or greater than a standard uniform variable under the null hypothesis proposed procedures are relevant in the analysis of high dimensional large m small n data sets arising in the natural physical medical economic and social sciences whose generation and creation is accelerated by advances in high throughput technology notably but not limited to microarray technology

the cauchy problem for the hartree equations under random influences abstract in this paper the cauchy problem for the hartree equations under random influences is studied in the first part the randomization of the initial conditions introduced by n burq and n tzvetkov is used to show that the hartree equations admit strong solutions for data in h for some below the critical threshold s c in the second part the global well posedness and blow up results for the hartree equations with stochastic potential are considered

scattering for the focusing h1 2 critical hartree equation in energy space abstract we investigate the focusing nonlinear schrodinger equation nls of hartree type i t u u 2 d u 2 u in r 5 with initial data in energy space h 1 if m u 0 e u 0 m q e q u 0 2 u 0 2 q 2 q 2 then the solution with initial data u 0 is global and scatters here q is the ground state solution moreover we show that if m u 0 e u 0 m q e q but u 0 2 u 0 2 q 2 q 2 then the corresponding solution will blow up in finite time the argument of this work is based on the linear profile decomposition in the spirit of kenig merle

semiparametric bayes multiple testing applications to tumor data in national toxicology program ntp studies investigators want to assess whether a test agent is carcinogenic overall and specific to certain tumor types while estimating the dose response profiles because there are potentially correlations among the tumors a joint inference is preferred to separate univariate analyses for each tumor type in this regard we propose a random effect logistic model with a matrix of coefficients representing log odds ratios for the adjacent dose groups for tumors at different sites we propose appropriate nonparametric priors for these coefficients to characterize the correlations and to allow borrowing of information across different dose groups and tumor types global and local hypotheses can be easily evaluated by summarizing the output of a single monte carlo markov chain mcmc two multiple testing procedures are applied for testing local hypotheses based on the posterior probabilities of local alternatives simulation studies are conducted and an ntp tumor data set is analyzed illustrating the proposed approach

optimal rates of convergence for estimating the null density and proportion of nonnull effects in large scale multiple testing an important estimation problem that is closely related to large scale multiple testing is that of estimating the null density and the proportion of nonnull effects a few estimators have been introduced in the literature however several important problems including the evaluation of the minimax rate of convergence and the construction of rate optimal estimators remain open in this paper we consider optimal estimation of the null density and the proportion of nonnull effects both minimax lower and upper bounds are derived the lower bound is established by a two point testing argument where at the core is the novel construction of two least favorable marginal densities f 1 and f 2 the density f 1 is heavy tailed both in the spatial and frequency domains and f 2 is a perturbation of f 1 such that the characteristic functions associated with f 1 and f 2 match each other in low frequencies the minimax upper bound is obtained by constructing estimators which rely on the empirical characteristic function and fourier analysis the estimator is shown to be minimax rate optimal compared to existing methods in the literature the proposed procedure not only provides more precise estimates of the null density and the proportion of the nonnull effects but also yields more accurate results when used inside some multiple testing procedures which aim at controlling the false discovery rate fdr the procedure is easy to implement and numerical results are given

hybrid dirichlet mixture models for functional data summary in functional data analysis curves or surfaces are observed up to measurement error at a finite set of locations for say a sample of n individuals often the curves are homogeneous except perhaps for individual specific regions that provide heterogeneous behaviour e g damaged areas of irregular shape on an otherwise smooth surface motivated by applications with functional data of this nature we propose a bayesian mixture model with the aim of dimension reduction by representing the sample of n curves through a smaller set of canonical curves we propose a novel prior on the space of probability measures for a random curve which extends the popular dirichlet priors by allowing local clustering non homogeneous portions of a curve can be allocated to different clusters and the n individual curves can be represented as recombinations hybrids of a few canonical curves more precisely the prior proposed envisions a conceptual hidden factor with k levels that acts locally on each curve we discuss several models incorporating this prior and illustrate its performance with simulated and real data sets we examine theoretical properties of the proposed finite hybrid dirichlet mixtures specifically their behaviour as the number of the mixture components goes to 1 and their connection with dirichlet process mixtures

a bayesian discovery procedure we discuss a bayesian discovery procedure for multiple comparison problems we show that under a coherent decision theoretic framework a loss function combining true positive and false positive counts leads to a decision rule based on a threshold of the posterior probability of the alternative under a semi parametric model for the data we show that the bayes rule can be approximated by the optimal discovery procedure odp recently introduced by storey 2007a improving the approximation leads us to a bayesian discovery procedure bdp which exploits the multiple shrinkage in clusters implied by the assumed nonparametric model we compare the bdp and the odp estimates in a simple simulation study and in an assessment of differential gene expression based on microarray data from tumor samples we extend the setting of the odp by discussing modifications of the loss function that lead to different single thresholding statistics finally we provide an application of the previous arguments to dependent spatial data

geometric optics and long range scattering for one dimensional nonlinear schrodinger equations with the methods of geometric optics used in 2 we provide a new proof of some results of 10 to construct modified wave operators for the one dimensional cubic schrodinger equation we improve the rate of convergence of the nonlinear solution towards the simplified evolution and get better control of the loss of regularity in sobolev spaces in particular using the results of 9 we deduce the existence of a modified scattering operator with small data in some sobolev spaces we show that in terms of geometric optics this gives rise to a random phase shift at a caustic

nonlinear scattering with nonlocal interaction we consider the scattering problem for the hartree type equation in n withn 2 i frac partial u partial t frac 1 2 delta u v u 2 u where v x sum limits j 1 2 lambda j x gamma j lambda 1 lambda 2 ne 0 0 lambda j in mathbb r gamma j 0 and denotes the convolution in n we prove the existence of wave operators inh0 k l2 n x k l2 n for any positive integerk under the assumption 1 1 2 2 this is an optimal result in the sense that the existence of wave operators breaks down if min 1 2 1 the case where 1 1 2 2 is also treated according to the sign of 2

universal dynamics for the defocusing logarithmic schrodinger equation we consider the nonlinear schrodinger equation with a logarithmic nonlinearity in a dispersive regime we show that the presence of the nonlinearity affects the large time behavior of the solution the dispersion is faster than usual by a logarithmic factor in time and the positive sobolev norms of the solution grow logarithmically in time moreover after rescaling in space by the dispersion rate the modulus of the solution converges to a universal gaussian profile these properties are suggested by explicit computations in the case of gaussian initial data and remain when an extra power like nonlinearity is present in the equation one of the key steps of the proof consists in using the madelung transform to reduce the equation to a variant of the isothermal compressible euler equation whose large time behavior turns out to be governed by a parabolic equation involving a fokker planck operator

combining multiple biomarker models in logistic regression in medical research there is great interest in developing methods for combining biomarkers we argue that selection of markers should also be considered in the process traditional model variable selection procedures ignore the underlying uncertainty after model selection in this work we propose a novel model combining algorithm for classification in biomarker studies it works by considering weighted combinations of various logistic regression models five different weighting schemes are considered in the article the weights and algorithm are justified using decision theory and risk bound results simulation studies are performed to assess the finite sample properties of the proposed model combining method it is illustrated with an application to data from an immunohistochemical study in prostate cancer

a perturbation technique that works even when the non linearity is not small abstract we extend the lindstedt poincare small non linearity based perturbation scheme to strongly non linear systems the extended technique starts from a physically non existent neighboring linear system this system is created by adding an optimal linear spring term to the system side of each linear differential equation starting at the zeroth level and balancing that term by adding an equal one to the forcing side one level down unlike the ritz method which also works for strongly non linear systems results can be obtained beyond the first level without resorting to numerical techniques thus the extended method keeps the intuition guiding straightforwardness of the perturbation method while giving accurate beyond first level hand derivable numerical results examples are presented for free vibrations with cubic and antisymmetric quadratic non linearities and for harmonic solutions of the undamped duffing equation the forms of the solutions allow the regions of validity of the expansions to be estimated an internal method of estimating accuracy of the perturbation solutions is developed and checked with the free vibration examples the exact solutions of which are available this internal method is then used to estimate the accuracy of the new solutions to the duffing equation these new duffing equation solutions give accurate results in all regions where stable harmonic solutions are known to exist in particular they give accurate results at and near the vertical tangent to the resonance curve a region where hayashi s amplitude expansion based perturbation solution necessarily breaks down

piecewise linearized methods for oscillators with fractional power nonlinearities a piecewise linearization method based on the taylor series expansion of nonlinear ordinary differential equation with respect to time displacement and velocity is developed for the study of one degree of freedom nonlinear oscillators with smooth and fractional power nonlinearities the method provides smooth solutions and explicit nonstandard finite difference expressions for the displacement and velocity and is exact for constant coefficients linear ordinary differential equations with linear time dependent forcings the method is applied to ten oscillators with fractional power nonlinearities and its results are compared with those of harmonic balance techniques ritz procedure and numerical solutions based on nonstandard finite difference methods in terms of displacement velocity energy and angular frequency when available it is shown that the linearization method presented here provides slightly more less accurate results than those of nonstandard methods for fractional powers greater smaller than one and both techniques are more accurate than those that freeze the nonlinearities at the previous time step or linearize the nonlinear terms with respect to only the displacement or the velocity for the examples and time steps considered in this paper the linearization method has been found to be more accurate than the harmonic balance and ritz procedures

global well posedness and scattering for the energy critical defocusing hartree equation for radial data abstract we consider the defocusing h 1 critical hartree equation for the radial data in all dimensions n 5 we show the global well posedness and scattering results in the energy space the new ingredient in this paper is that we first take advantage of the term i x a i 1 2 u 2 1 x d x d t in the localized morawetz identity to rule out the possibility of energy concentration instead of the classical morawetz estimate dependent of the nonlinearity

estimating the null distribution to adjust observed confidence levels for genome scale screening summary in a novel approach to the multiple testing problem efron 2004 journal of the american statistical association 99 96 104 2007a journal of the american statistical association 102 93 103 2007b annals of statistics 35 1351 1377 formulated estimators of the distribution of test statistics or nominal p values under a null distribution suitable for modeling the data of thousands of unaffected genes nonassociated single nucleotide polymorphisms or other biological features estimators of the null distribution can improve not only the empirical bayes procedure for which it was originally intended but also many other multiple comparison procedures such estimators in some cases improve the proposed multiple comparison procedure mcp based on a recent non bayesian framework of minimizing expected loss with respect to a confidence posterior a probability distribution of confidence levels the flexibility of that mcp is illustrated with a nonadditive loss function designed for genomic screening rather than for validation the merit of estimating the null distribution is examined from the vantage point of the confidence posterior mcp cpmcp in a generic simulation study of genome scale multiple testing conditioning the observed confidence level on the estimated null distribution as an approximate ancillary statistic markedly improved conditional inference specifically simulating gene expression data however indicates that estimation of the null distribution tends to exacerbate the conservative bias that results from modeling heavy tailed data distributions with the normal family to enable researchers to determine whether to rely on a particular estimated null distribution for inference or decision making an information theoretic score is provided as the sum of the degree of ancillarity and the degree of inferential relevance the score reflects the balance conditioning would strike between the two conflicting terms the cpmcp and other methods introduced are applied to gene expression microarray data

optimal screening and discovery of sparse signals with applications to multistage high throughput studies summary a common feature in large scale scientific studies is that signals are sparse and it is desirable to narrow down significantly the focus to a much smaller subset in a sequential manner we consider two related data screening problems one is to find the smallest subset such that it virtually contains all signals and another is to find the largest subset such that it essentially contains only signals these screening problems are closely connected to but distinct from the more conventional signal detection or multiple testing problems we develop phase transition diagrams to characterize the fundamental limits in simultaneous inference and derive data driven screening procedures which control the error rates with near optimality properties applications in the context of multistage high throughput studies are discussed

sequential design for microarray experiments a critical aspect in the design of microarray studies is the determination of the sample size necessary to declare genes differentially expressed across different experimental conditions in this article we propose a sequential approach where the decision to stop the experiment depends on the accumulated microarray data the study could stop whenever sufficient data have been accumulated to identify gene expression changes across several experimental conditions the gene expression response is modeled by a robust linear regression model we then construct a sequential confidence interval for the intercept of this model which represents the median gene expression at a given experimental condition we derive the stopping rule of the experiment for both continuous and discrete sequential approaches and give the asymptotic properties of the stopping variable we demonstrate the desirable properties of our sequential approach both theoretically and numerically in our application to a study of hormone responsive breast cancer cell lines we estimated the stopping variable for the sample size determination to be smaller than the actual sample size available to conduct the experiment this means that we can obtain an accurate assessment of differential gene expression without compromising the cost and size of the study altogether we anticipate that this approach could have an important contribution to microarray studies by improving the usual experimental designs and methods of analysis

semiparametric bayesian local functional models for diffusion tensor tract statistics we propose a semiparametric bayesian local functional model bfm for the analysis of multiple diffusion properties e g fractional anisotropy along white matter fiber bundles with a set of covariates of interest such as age and gender bfm accounts for heterogeneity in the shape of the fiber bundle diffusion properties among subjects while allowing the impact of the covariates to vary across subjects a nonparametric bayesian lpp2 prior facilitates global and local borrowings of information among subjects while an infinite factor model flexibly represents low dimensional structure local hypothesis testing and credible bands are developed to identify fiber segments along which multiple diffusion properties are significantly associated with covariates of interest while controlling for multiple comparisons moreover bfm naturally group subjects into more homogeneous clusters posterior computation proceeds via an efficient markov chain monte carlo algorithm a simulation study is performed to evaluate the finite sample performance of bfm we apply bfm to investigate the development of white matter diffusivities along the splenium of the corpus callosum tract and the right internal capsule tract in a clinical study of neurodevelopment in new born infants

tail posterior probability for inference in pairwise and multiclass gene expression data we consider the problem of identifying differentially expressed genes in microarray data in a bayesian framework with a noninformative prior distribution on the parameter quantifying differential expression we introduce a new rule tail posterior probability based on the posterior distribution of the standardized difference to identify genes differentially expressed between two conditions and we derive a frequentist estimator of the false discovery rate associated with this rule we compare it to other bayesian rules in the considered settings we show how the tail posterior probability can be extended to testing a compound null hypothesis against a class of specific alternatives in multiclass data

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

long range scattering for nonlinear schrodinger equations in one space dimension we consider the scattering problem for the nonlinear schrodinger equation in 1 1 dimensions open image in new window where x r 0 r p 3 we show that modified wave operators for exist on a dense set of a neighborhood of zero in the lebesgue spacel2 r or in the sobolev spaceh1 r the modified wave operators are introduced in order to control the long range nonlinearity u 2u

a computational algebraic investigation of the decomposition method for time dependent problems the convergence of the decomposition method as applied to time dependent problems governed by the heat or wave equations is investigated numerically using computational algebraic techniques

long range scattering and modified wave operators for some hartree type equations iii gevrey spaces and low dimensions abstract we study the theory of scattering for a class of hartree type equations with long range interactions in arbitrary space dimension n 1 including the case of hartree equations with time dependent potential v t x t x with 0 1 and 0 n this includes the case of potential v x x and can be extended to the limiting case of nonlinear schrodinger equations with cubic nonlinearity t n u 2 u using gevrey spaces of asymptotic states and solutions we prove the existence of modified local wave operators at infinity with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators thereby extending the results of previous papers which covered the range 0 1 but only 0 n 2 and were therefore restricted to space dimension n 3

global well posedness and scattering for the defocusing hartree equation in r3 abstract we consider the defocusing h 1 2 subcritical hartree equation i t u u x u 2 u 2 3 in r 3 we prove its global well posedness and scattering property in h s r 3 for s 7 2 2 when 5 2 s 3 2 2 1 when 5 2 this improves the previous work of miao xu and zhao 2009 18 a new ingredient used here is that we apply some bilinear strichartz estimates

an artificial parameter decomposition method for nonlinear oscillators applications to oscillators with odd nonlinearities abstract a method for obtaining series solutions of nonlinear second order ordinary differential equations based on the introduction of an artificial parameter is presented and shown to be identical to the well known adomian s decomposition technique the method is formulated in both integral and differential forms for the determination of the limit cycle of oscillators with odd nonlinearities two differential forms and one integral form of the artificial parameter method are presented these versions are based on introducing a linear stiffness term with an unknown frequency and the use of either the original independent variable or a new independent variable that depends linearly on the unknown frequency of the oscillator the three formulations provide identical results and their application to eight oscillators with odd nonlinearities shows that the artificial parameter technique presented in this paper predicts the same frequency of oscillation as the harmonic balance and iterative techniques as well as modified linstedt poincare methods however the method presented here is based on the introduction of an artificial parameter and does not require the presence of small perturbation parameters in the ordinary differential equation it is also shown that two and three level iterative methods yield the same frequency of oscillation as the artificial parameter technique presented in this paper provided that the initial iterate of the former coincides with the leading order solution of the latter and only one iteration of iterative techniques and only the second approximation of the artificial parameter method are determined

long range scattering for the maxwell schrodinger system in the lorenz gauge without any restriction on the size of data abstract this paper concerns the scattering theory for the maxwell schrodinger ms system in the lorenz gauge or more precisely the existence of the modified wave operators for this system in r 3 1 space time we construct solutions to the ms system which behave as free maxwell and schrodinger waves with prescribed asymptotic states when t without any restriction on the size thereof since this system belongs to the borderline between the short range case and the long range case we need modification of phase for the schrodinger function

asymptotics for large time of solutions to the nonlinear schrodinger and hartree equations we study the asymptotic behavior in time of solutions to the cauchy problems for the nonlinear schrodinger equation with a critical power nonlinearity and the hartree equation we prove the existence of modified scattering states and the sharp time decay estimate in the uniform norm of solutions to the cauchy problem with small initial data this estimate is very important for the proof of the existence of modified scattering states to the nonlinear schrodinger equations with a critical nonlinearity and the hartree equation in order to derive the desired estimates we introduce a certain phase function since the previous methods based solely on a priori estimates of the operator x it acting on the solution without specifying any phase function do not work for the critical case under consideration the well known nonexistence of the usual l 2 scattering states shows that our result is sharp

long range scattering for non linear schrodinger and hartree equations in space dimension n 2 we consider the scattering problem for the non linear schrodinger nls equation with a power interaction with critical powerp 1 2 n in space dimensionsn 2 and 3 and for the hartree equation with potential x 1 in space dimensionn 2 we prove the existence of modified wave operators in thel2 sense on a dense set of small and sufficiently regular asymptotic states

optimal sample size for multiple testing the case of gene expression microarrays we consider the choice of an optimal sample size for multiple comparison problems the motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression however the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests we discuss two decision problems in the context of this setup the sample size selection and the decision about the multiple comparisons we adopt a decision theoretic approach using loss functions that combine the competing goals of discovering as many differentially expressed genes as possible while keeping the number of false discoveries manageable for consistency we use the same loss function for both decisions the decision rule that emerges for the multiple comparison problem takes the exact form of the rules proposed in the recent literature to control the posterior expected falsediscovery rate for the sample size selection we combine the expe

shrunken p values for assessing differential expression with applications to genomic data analysis in many scientific problems involving high throughput technology inference must be made involving several hundreds or thousands of hypotheses recent attention has focused on how to address the multiple testing issue much focus has been devoted toward the use of the false discovery rate in this article we consider an alternative estimation procedure titled shrunken p values for assessing differential expression spade the estimators are motivated by risk considerations from decision theory and lead to a completely new method for adjustment in the multiple testing problem in addition the decision theoretic framework can be used to derive a decision rule for controlling the number of false positive results some theoretical results are outlined the proposed methodology is illustrated using simulation studies and with application to data from a prostate cancer gene expression profiling study

investigation of the properties of the period for the nonlinear oscillator x 1 x 2 x 0 abstract the mathematical properties of a nonlinear oscillator having the square of the angular frequency depend quadratically on the velocity is presented the major conclusion is that the exact period t a is well defined for all values of the amplitude where the initial conditions are taken to be x 0 a and x 0 0 an approximate expression is derived for t a

solutions of nonlinear oscillators with fractional powers by an iteration procedure a modified iteration procedure is applied to nonlinear oscillations with fractional powers with the procedure the excellent approximate frequencies and the corresponding periodic solutions can be easily obtained

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

bayesian semiparametric multiple shrinkage high dimensional and highly correlated data leading to non or weakly identified effects are commonplace maximum likelihood will typically fail in such situations and a variety of shrinkage methods have been proposed standard techniques such as ridge regression or the lasso shrink estimates toward zero with some approaches allowing coefficients to be selected out of the model by achieving a value of zero when substantive information is available estimates can be shrunk to nonnull values however such information may not be available we propose a bayesian semiparametric approach that allows shrinkage to multiple locations coefficients are given a mixture of heavy tailed double exponential priors with location and scale parameters assigned dirichlet process hyperpriors to allow groups of coefficients to be shrunk toward the same possibly nonzero mean our approach favors sparse but flexible structure by shrinking toward a small number of random locations the methods are illustrated using a study of genetic polymorphisms and parkinson s disease

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

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

functional car models for large spatially correlated functional datasets abstractwe develop a functional conditional autoregressive car model for spatially correlated data for which functions are collected on areal units of a lattice our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure in both the space and functional domains we show theoretically that our construction leads to a car model at each functional location with spatial covariance parameters varying and borrowing strength across the functional domain using basis transformation strategies the nonseparable spatial functional model is computationally scalable to enormous functional datasets generalizable to different basis functions and can be used on functions defined on higher dimensional domains such as images through simulation studies we demonstrate that accounting for the spatial correlation in our modeling leads to improved functional regression performance applied to a high throughput spatiall

a new perturbative approach to nonlinear problems a recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the lagrangian such as 4 by 2 1 and then treating as a small parameter it is shown here that the same approach gives excellent results when applied to difficult nonlinear differential equations such as the lane emden thomas fermi blasius and duffing equations

on fourier time splitting methods for nonlinear schrodinger equations in the semi classical limit ii analytic regularity we consider the time discretization based on lie trotter splitting for the nonlinear schrodinger equation in the semi classical limit with initial data under the form of wkb states we show that both the exact and the numerical solutions keep a wkb structure on a time interval independent of the planck constant we prove error estimates which show that the quadratic observables can be computed with a time step independent of the planck constant the functional framework is based on time dependent analytic spaces in order to overcome a previously encountered loss of regularity phenomenon