decay of solutions of nonlinear wave equations in three space dimensions abstract given a solution of the cauchy problem for nonlinear wave equations of the type 2 u t 2 u f u 0 in three space dimensions the asymptotic behaviour in time is considered it is shown that for nonlinearities which behave like powers u 1 u uniform decay holds with a certain rate depending on if 5 1 2 1 2 13 and moreover scattering states exist if is not too small this improves former results of w a strauss j funct anal 2 1968 409 457

a note on the null condition for quadratic nonlinear klein gordon systems in two space dimensions we consider the cauchy problem for quadratic nonlinear klein gordon systems in two space dimensions with masses satisfying the resonance relation under the null condition in the sense of j m delort d fang and r xue j funct anal 211 2004 no 2 288 323 we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted sobolev space our proof is based on an algebraic characterization of nonlinearities satisfying the null condition 2012 wiley periodicals inc

nonlinear scattering theory at low energy abstract we study the scattering theory of a conservative nonlinear one parameter group of operators on a hilbert space x relative to a group of linear unitary operators under certain hypotheses the scattering operator carries a neighborhood of 0 in x into x the theory is designed to apply to the semilinear schrodinger and klein gordon equations

wave operators and analytic solutions for systems of non linear klein gordon equations and of non linear schrodinger equations we consider in a 1 3 space time arbitrary finite systems of nonlinear klein gordon equations respectively schrodinger equations with an arbitrary local and analytic non linearity in the unknown and its first and second order space time respectively first order space derivatives having no constant or linear terms no restriction is given on the frequency sign of the initial data in the case of non linear klein gordon equations all masses are supposed to be different from zero

on global small amplitude solutions to systems of cubic nonlinear klein gordon equations with different mass terms in one space dimension abstract we consider the cauchy problem for systems of cubic nonlinear klein gordon equations with different mass terms in one space dimension we prove some result concerning the global existence of small amplitude solutions and their asymptotic behavior as a consequence we see that the condition for small data global existence is actually influenced by the difference of masses in some cases

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

multiple hypothesis testing by clustering treatment effects multiple hypothesis testing and clustering have been the subject of extensive research in high dimensional inference yet these problems usually have been treated separately by defining true clusters in terms of shared parameter values we could improve the sensitivity of individual tests because more data bearing on the same parameter values are available we develop and evaluate a hybrid methodology that uses clustering information to increase testing sensitivity and accommodates uncertainty in the true clustering to investigate the potential efficacy of the hybrid approach we first study a stylized example in which each object is evaluated with a standard z score but different objects are connected by shared parameter values we show that there is increased testing power when the clustering is estimated sufficiently well we next develop a model based analysis using a conjugate dirichlet process mixture model the method is general but for specificity we focus attention on microarray gene expressi

normal forms and quadratic nonlinear klein gordon equations on construit une transformation qui change l equation a non linearite cubique que l on sait resoudre a 3 1 dimensions on demontre que la solution du probleme original a le meme comportement asymptotique que l equation de klein gordon non lineaire

small data blow up for semilinear klein gordon equations energy heuristics predict global existence from small data for semi linear klein gordon systems when the nonlinearity has order p 1 2 n we complement these heuristics and previous rigorous existence results by demonstrating blow up from small data for p 1 2 n

a bilinear estimate and its application to a quadratic nonlinear klein gordon equation in two space dimensions abstract we study the existence of the wave operators for the nonlinear klein gordon equation with quadratic nonlinearity in two space dimensions t 2 1 u u 2 t x r r 2 we prove existence of wave operators in lower order sobolev spaces by using estimates of bilinear operators associated with klein gordon equation

semiparametric bayesian inference for phage display data we discuss inference for a human phage display experiment with three stages the data are tripeptide counts by tissue and stage the primary aim of the experiment is to identify ligands that bind with high affinity to a given tissue we formalize the research question as inference about the monotonicity of mean counts over stages the inference goal is then to identify a list of peptide tissue pairs with significant increase over stages we use a semi parametric dirichlet process mixture of poisson model the posterior distribution under this model allows the desired inference about the monotonicity of mean counts however the desired inference summary as a list of peptide tissue pairs with significant increase involves a massive multiplicity problem we consider two alternative approaches to address this multiplicity issue first we propose an approach based on the control of the posterior expected false discovery rate we notice that the implied solution ignores the relative size of the increase this motivates a second approach based on a utility function that includes explicit weights for the size of the increase

nonlinear small data scattering for the wave and klein gordon equation on etudie l operateur diffusion qui appartient a la paire d equations u tt au f u 0 et u tt au 0 a represente l operateur j 1 n 2 x j 2 m 2 m r et f u u 1 u ou r 1

the global cauchy problem for the nls and nlkg with small rough data abstract by using the unit cube decomposition to the frequency spaces we study the cauchy problem for the nonlinear schrodinger equation and the nonlinear klein gordon equation some global well posedness results are obtained for the small cauchy data in some modulation spaces m p 1 s

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

sharp threshold of global existence and blow up of the combined nonlinear klein gordon equation abstract in this paper we show the global well posedness and blow up result of the solutions with the energy below the threshold for the combined nonlinear klein gordon equation u t t u u u p 1 u u q 1 u d 3 in the energy space h 1 r d l 2 r d where 1 4 d q p 1 4 d 2 we give a threshold of blow up and global well posedness using a modified variational approach in the spirit of ibrahim et al 2011 7

temps d existence pour l equation de klein gordon semi lineaire a donnees petites periodiques we study lower bounds for the maximal time of existence t of a smooth solution to a semi linear klein gordon equation u u f u u with periodic cauchy data of small size if f vanishes at order r at 0 we prove that t c 2 if r 2 t c r 1 log r 3 if r 3 we construct examples showing the optimality of these results for convenient values of r

introduction to scattering for radial 3d nlkg below energy norm abstract we prove scattering for some radial 3d semilinear klein gordon equations with rough data first we prove strichartz type estimates in mixed norm spaces then by using these decays we establish some local bounds by combining these results to a morawetz type estimate and a radial sobolev inequality we control the variation of an almost conserved quantity on arbitrary large intervals once we have showed that this quantity is controlled we prove that some of these local bounds can be upgraded to global bounds this is enough to establish scattering all the estimates involved require a delicate analysis due to the nature of the nonlinearity and the lack of scaling

false discovery control for random fields this article extends false discovery rates to random fields for which there are uncountably many hypothesis tests we develop a method for finding regions in the field s domain where there is a significant signal while controlling either the proportion of area or the proportion of clusters in which false rejections occur the method produces confidence envelopes for the proportion of false discoveries as a function of the rejection threshold from the confidence envelopes we derive threshold procedures to control either the mean or the specified tail probabilities of the false discovery proportion an essential ingredient of this construnction is a new algorithm to compute a confidence superset for the set of all true null locations we demonstrate our method with applications to scan statistics and functional neuroimaging

modified scattering for the critical nonlinear schrodinger equation abstract we consider the nonlinear schrodinger equation i u t u u 2 n u in all dimensions n 1 where c and 0 we construct a class of initial values for which the corresponding solution is global and decays as t like t n 2 if 0 and like t log t n 2 if 0 moreover we give an asymptotic expansion of those solutions as t we construct solutions that do not vanish so as to avoid any issue related to the lack of regularity of the nonlinearity at u 0 to study the asymptotic behavior we apply the pseudo conformal transformation and estimate the solutions by allowing a certain growth of the sobolev norms which depends on the order of regularity through a cascade of exponents

analyticity of the scattering operator for the nonlinear klein gordon equation with cubic nonlinearity the wave and scattering operators for the equation left square m 2 right varphi lambda varphi 2 0 withm 0 and 0 on four dimensional minkowski space are analytic on the space of finite energy cauchy data i e l21 r3 l2 r3

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

remark on the scattering operator for the cubic nonlinear dirac equation in three space dimensions abstract this paper is concerned with the scattering operator s for the three dimensional dirac equation with a cubic nonlinearity it follows from known results that s is well defined on a neighborhood of 0 in the sobolev space h r 3 c 4 for any 1 in the present paper we prove that for any m n and s max m there exists some neighborhood u of 0 in the weighted sobolev space h s m r 3 c 4 such that s u h s m r 3 c 4

the nested dirichlet process in multicenter studies subjects in different centers may have different outcome distributions this article is motivated by the problem of nonparametric modeling of these distributions borrowing information across centers while also allowing centers to be clustered starting with a stick breaking representation of the dirichlet process dp we replace the random atoms with random probability measures drawn from a dp this results in a nested dp prior which can be placed on the collection of distributions for the different centers with centers drawn from the same dp component automatically clustered together theoretical properties are discussed and an efficient markov chain monte carlo algorithm is developed for computation the methods are illustrated using a simulation study and an application to quality of care in u s hospitals

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

long time decay for 2d klein gordon equation abstract we obtain a dispersive long time decay in weighted energy norms for solutions of the 2d klein gordon equations the decay extends the results obtained by jensen kato and murata for the equations of schrodinger s type by the spectral approach for the proof we modify the approach to make it applicable to relativistic equations

an inequality for correlations in unidimensional monotone latent variable models for binary variables it is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations the negative logarithm of the correlations satisfies the triangle inequality this inequality is not implied by the condition that the correlations are nonnegative the criterion that coefficient h exceeds 0 30 or manifest monotonicity the inequality implies both a lower bound and an upper bound for each correlation between two items based on the correlations of those two items with every possible third item it is discussed how this can be used in mokken s a theory and procedure of scale analysis mouton the hague 1971 scale analysis

on asymptotic stability in 3d of kinks for the model we add to a kink which is a 1 dimensional structure two transversal directions we then check its asymptotic stability with respect to compactly supported perturbations in 3d and a time evolution under a nonlinear wave equation nlw the problem is inspired by work by jack xin on asymptotic stability in dimension larger than 1 of fronts for reaction diffusion equations the proof involves a separation of variables the transversal variables are treated as in work on nonlinear klein gordon equation nlkg originating from klainerman and from shatah in a particular elaboration due to delort et al the longitudinal variable is treated by means of a result by weder on dispersion for schrodinger operators in id

posterior probability maps and spms this technical note describes the construction of posterior probability maps that enable conditional or bayesian inferences about regionally specific effects in neuroimaging posterior probability maps are images of the probability or confidence that an activation exceeds some specified threshold given the data posterior probability maps ppms represent a complementary alternative to statistical parametric maps spms that are used to make classical inferences however a key problem in bayesian inference is the specification of appropriate priors this problem can be finessed using empirical bayes in which prior variances are estimated from the data under some simple assumptions about their form empirical bayes requires a hierarchical observation model in which higher levels can be regarded as providing prior constraints on lower levels in neuroimaging observations of the same effect over voxels provide a natural two level hierarchy that enables an empirical bayesian approach in this note we present a brief motivation and the operational details of a simple empirical bayesian method for computing posterior probability maps we then compare bayesian and classical inference through the equivalent ppms and spms testing for the same effect in the same data

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

the time periodic solution for a 2d dissipative klein gordon equation abstract in this paper we study a 2d dissipative klein gordon equation with periodic boundary condition the existence and uniqueness of a time periodic solution is proved by the galerkin method and leray schauder fixed point theorem

empirical bayes analysis of a microarray experiment microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels a typical microarray experiment can produce millions of data points raising serious problems of data reduction and simultaneous inference we consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes a simple nonparametric empirical bayes model is introduced which is used to guide the efficient reduction of the data to a single summary statistic per gene and also to make simultaneous inferences concerning which genes were affected by the radiation although our focus is on one specific experiment the proposed methods can be applied quite generally the empirical bayes inferences are closely related to the frequentist false discovery rate fdr criterion

on space time means and everywhere defined scattering operators for nonlinear klein gordon equations on demontre l existence d operateurs de diffusion definis partout pour certaines equations de klein gordon non lineaires

wave operators to a quadratic nonlinear klein gordon equation in two space dimensions abstract we study asymptotics around the final states of solutions to the nonlinear klein gordon equations with quadratic nonlinearities in two space dimensions t 2 m 2 u u 2 t x r r 2 where c we prove that if the final states u 1 h q q 1 4 4 q r 2 h 5 2 1 r 2 h 1 2 r 2 u 2 h q q 1 3 4 q r 2 h 3 2 1 r 2 h 1 1 r 2 and u 1 h 1 2 u 2 h 1 1 is sufficiently small where 4 q then there exists a unique global solution u c t l 2 r 2 to the nonlinear klein gordon equations such that u t tends as t in the l 2 sense to the solution u 0 t u 1 cos i m t i m 1 u 2 sin i m t of the free klein gordon equation

the unit condition and global existence for a class of nonlinear klein gordon equations abstract global existence for a special class of nonlinear klein gordon equations in two space dimensions is proved in particular it is shown that for small initial data the equation tt u u u u 2 has a global solution

scattering operator for nonlinear klein gordon equations in higher space dimensions abstract we prove the existence of the scattering operator in the neighborhood of the origin in the weighted sobolev space h 1 with max 3 2 1 2 n for the nonlinear klein gordon equation with a power nonlinearity u t t u u u 1 u t x r r n where 1 4 n 2 1 4 n for n 3 c

a quadratic nonlinear schrodinger equation in one space dimension abstract in this paper we study the cauchy problem for the quadratic derivative nonlinear schrodinger equation iu t u xx u x 2 t x r 2 u 0 x u 0 x r we suppose that the initial data are small in the weighted sobolev space h 3 1 r then we prove that there exist global in time small solutions to the cauchy problem we study the large time behavior of solutions and construct the modified asymptotics for large time values

bayesian inference for the common location parameter of several shifted exponential populations abstract consider k random samples which are independently drawn from k shifted exponential distributions with respective scale parameters 1 2 k and common location parameter on the basis of the given samples and in a bayesian framework we address the problem of point and interval estimation of the location parameter under the conjugate priors which are usually proper priors moreover we also address the problem of testing the equality of the location parameters we propose bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior the noninformative prior is usually improper which yields a calibration problem that makes the bayes factor to be defined up to a multiplicative constant so we propose the default bayesian hypothesis testing procedures based on the fractional bayes factor and the intrinsic bayes factors under the reference priors our proposed bayesian procedures are compared and contrasted via a comparison study a simulation study and a real world data analysis to the existing classical exact procedures proposed by tippett tippett s method tippett 1931 fisher fisher s method fisher 1932 stouffer inverse normal method stouffer et al 1949 and george logit method george 1977 and to the generalized variable procedures proposed by tsui and weerahandi generalized p value method tsui and weerahandi 1989

bayesian multiple comparisons using dirichlet process priors abstract we consider the problem of multiple comparisons from a bayesian viewpoint the family of dirichlet process priors is applied in the form of baseline prior likelihood combinations to obtain posterior probabilities for various hypotheses of equality among population means the baseline prior likelihood combinations considered here are beta binomial and normal inverted gamma with equal variances on treatment means the prior probabilities of the hypotheses depend directly on the concentration parameter of the dirichlet process prior finding posterior distributions is analytically intractable we use gibbs sampling the posterior probabilities of hypotheses of interest are easily obtained as a by product in evaluating the marginal posterior distributions of the parameters the proposed procedure is compared to duncan s multiple range test and shown to be more powerful under certain alternative hypotheses

the cauchy problem for non linear klein gordon equations we consider in n 1 n 2 the non linear klein gordon equation we prove for such an equation that there is a neighbourhood of zero in a hilbert space of initial conditions for which the cauchy problem has global solutions and on which there is asymptotic completeness the inverse of the wave operator linearizes the non linear equation if moreover the equation is manifestly poincare covariant then the non linear representation of the poincare lie algebra associated with the non linear klein gordon equation is integrated to a non linear representation of the poincare group on an invariant neighbourhood of zero in the hilbert space this representation is linearized by the inverse of the wave operator the hilbert space is in both cases the closure of the space of the differentiable vectors for the linear representation of the poincare group associated with the klein gordon equation with respect to a norm defined by the representation of the enveloping algebra

quadratic nonlinear klein gordon equation in one dimension we study the initial value problem for the quadratic nonlinear klein gordon equation vtt v vxx v2 t r x r with initial conditions v 0 x v0 x vt 0 x v1 x x r where v0 and v1 are real valued functions r using the method of normal forms of shatah normal forms and quadratic nonlinear klein gordon equations commun pure appl math 38 685 696 1985 we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous work of j m delort existence globale et comportement asymptotique pour l equation de klein gordon quasi lineaire a donnees petites en dimension 1 ann sci ec normale super 34 4 1 61 2001

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

inviscid limit for the damped boussinesq equation abstract in this paper we consider the limit behavior of solutions to the cauchy problem for damped boussinesq equation in the regime of small viscosity in r n it is shown that the strong solutions of damped boussinesq equation converge to a strong solution of boussinesq equation in any time interval 0 t the key idea is that we only take into account the effect of dispersion and overlook the effect of dissipation in the damped boussinesq equation which is a kind of new view we analyze the dispersion by the techniques of high low frequency decomposition and littlewood paley dyadic decomposition stationary phase estimate and some properties of bessel function

the optimal discovery procedure a new approach to simultaneous significance testing summary the neyman pearson lemma provides a simple procedure for optimally testing a single hypothesis when the null and alternative distributions are known this result has played a major role in the development of significance testing strategies that are used in practice most of the work extending single testing strategies to multiple tests has focused on formulating and estimating new types of significance measures such as the false discovery rate these methods tend to be based on p values that are calculated from each test individually ignoring information from the other tests i show here that one can improve the overall performance of multiple significance tests by borrowing information across all the tests when assessing the relative significance of each one rather than calculating p values for each test individually the optimal discovery procedure is introduced which shows how to maximize the number of expected true positive results for each fixed number of expected false positive results the optimality that is achieved by this procedure is shown to be closely related to optimality in terms of the false discovery rate the optimal discovery procedure motivates a new approach to testing multiple hypotheses especially when the tests are related as a simple example a new simultaneous procedure for testing several normal means is defined this is surprisingly demonstrated to outperform the optimal single test procedure showing that a method which is optimal for single tests may no longer be optimal for multiple tests connections to other concepts in statistics are discussed including stein s paradox shrinkage estimation and the bayesian approach to hypothesis testing

nonlinear scattering theory for a class of wave equations in hs abstract for the semi linear higher order wave equation and the nonlinear higher order schrodinger equation we show that the scattering operators map a band in h s into h s if the nonlinearities have sub critical powers in h s the smoothness of the scattering operators and the uniform boundedness of strong solutions for the defocusing nls equation are also shown provided that the nonlinearities have subcritical growth in h 1 moreover the spatial decaying behavior of solutions in energy space for the defocusing nls equation are obtained

a system of quadratic nonlinear klein gordon equations in 2d abstract we consider the system of quadratic nonlinear klein gordon equations t 2 v 1 v 1 m 1 2 v 1 v 1 v 2 t 2 v 2 v 2 m 2 2 v 2 v 1 2 in two space dimensions under the mass condition such that 2 m 1 m 2 we construct the scattering operator in an almost natural weighted sobolev class h 1 1 or the scattering problem in lower order sobolev class h 4 3 1 h 1 where 0 is small

smoothing properties and retarded estimates for some dispersive evolution equations smoothing properties in the form of space time integrability properties play an important role in the study of dispersive evolution equations a number of them follow from a combination of general arguments and specific estimates we present a general formulation which makes the separation between the two types of ingredients as clear as possible and we illustrate it with the examples of the schrodinger equation of the wave equation and of a class of 1 1 dimensional equations related to the benjamin ono equation of special interest for the cauchy problem are retarded estimates expressed in terms of those properties we derive a number of such estimates associated with the last example and we mention briefly an application of those estimates to the cauchy problem for the generalized benjamin ono equation

consistency of bayes estimators of a binary regression function when do nonparametric bayesian procedures overfit to shed light on this question we consider a binary regression problem in detail and establish frequentist consistency for a certain class of bayes procedures based on hierarchical priors called uniform mixture priors these are defined as follows let v be any probability distribution on the nonnegative integers to sample a function f from the prior v first sample m from v and then sample f uniformly from the set of step functions from 0 1 into 0 1 that have exactly m jumps i e sample all m jump locations and m 1 function values independently and uniformly the main result states that if a data stream is generated according to any fixed measurable binary regression function f o 1 2 then frequentist consistency obtains that is for any v with infinite support the posterior of v concentrates on any l1 neighborhood of f 0 solution of an associated large deviations problem is central to the consistency proof

bayesian nonparametric variable selection as an exploratory tool for discovering differentially expressed genes high throughput scientific studies involving no clear a priori hypothesis are common for example a large scale genomic study of a disease may examine thousands of genes without hypothesizing that any specific gene is responsible for the disease in these studies the objective is to explore a large number of possible factors e g genes in order to identify a small number that will be considered in follow up studies that tend to be more thorough and on smaller scales a simple hierarchical linear regression model with random coefficients is assumed for case control data that correspond to each gene the specific model used will be seen to be related to a standard bayesian variable selection model relatively large regression coefficients correspond to potential differences in responses for cases versus controls and thus to genes that might matter for large scale studies and using a dirichlet process mixture model for the regression coefficients we are able to find clusters of regression effects of genes with increasing potential effect or relevance in relation to the outcome of interest one cluster will always correspond to genes whose coefficients are in a neighborhood that is relatively close to zero and will be deemed least relevant other clusters will correspond to increasing magnitudes of the random latent regression coefficients using simulated data we demonstrate that our approach could be quite effective in finding relevant genes compared with several alternative methods we apply our model to two large scale studies the first study involves transcriptome analysis of infection by human cytomegalovirus the second study s objective is to identify differentially expressed genes between two types of leukemia copyright 2012 john wiley sons ltd

final state problem for the cubic nonlinear klein gordon equation we study the final state problem for the nonlinear klein gordon equation utt u uxx u3 t r x r where r we prove the existence of solutions in the neighborhood of the approximate solutions 2 re u t w t where u t is the free evolution group defined by u t f 1e it f x 1 x2 f and f 1 are the direct and inverse fourier transformations respectively and w t x f 1 u e 3 2 i 2 u 2log t with a given final data u is a real valued function and 3 i u l is small

on scattering and everywhere defined scattering operators for nonlinear klein gordon equations asymptotic properties of solutions of the nonlinear klein gordon equation t2u u m2u f u 0 nlkg u 0 tu 0 are investigated which are inherited from the corresponding solutions v of the linear klein gordon equation t2v v m2v 0v 0 tv 0 kg in particular the finiteness of time integrals in lq over r of certain sobolevnorms in space of the solution is proved to be such a hereditary property together with a device by w a strauss and a weak decay result for the kg due to r s strichartz this is used to prove that under suitable restrictions on the nonlinearity the scattering operator for the nlkg is defined on all of l21 l2 for n 3

analyticity of scattering for the ϕ 4 theory we consider scattering for the equation m2 3 0 on four dimensional minkowski space form 0 one to one and onto wave operatorsw h h are known to exist for all 0 whereh denotes the hilbert space of finite energy cauchy data we prove that the maps u w u and u w 1 u are continuous from 0 h toh and extend to real analytic functions from an open neighborhood of 0 h 0 h to the hilbert spaceh 1 of cauchy data with poincare invariant norm form 0 wave operatorsw are known to exist as diffeomorphisms ofh for all 0 where hereh denotes the hilbert space of finite einstein energy cauchy data in this case we prove that the maps u w u and u w 1 u extend to real analytic functions from a neighborhood of 0 h h toh

bayesian nonparametric spatial modeling with dirichlet process mixing customary modeling for continuous point referenced data assumes a gaussian process that is often taken to be stationary when such models are fitted within a bayesian framework the unknown parameters of the process are assumed to be random so a random gaussian process results here we propose a novel spatial dirichlet process mixture model to produce a random spatial process that is neither gaussian nor stationary we first develop a spatial dirichlet process model for spatial data and discuss its properties because of familiar limitations associated with direct use of dirichlet process models we introduce mixing by convolving this process with a pure error process we then examine properties of models created through such dirichlet process mixing in the bayesian framework we implement posterior inference using gibbs sampling spatial prediction raises interesting questions but these can be handled finally we illustrate the approach using simulated data as well as a dataset involving precipitati

loss function approaches to predict a spatial quantile and its exceedance region in the analysis of spatial data it is common to predict a spatial exceedance and its associated exceedance region this is scientifically important because unusual events tend to strongly affect the environment we use classes of loss functions based on image metrics e g baddeley s loss function to predict the spatial exceedance region we then propose a joint loss to predict a spatial quantile and its exceedance region the optimal predictor is obtained by minimizing the posterior expected loss given the process parameters which we achieve by simulated annealing various predictors are compared through simulation this methodology is applied to a spatial data set of temperature change over the americas

analysis of fmri time series revisited abstract this paper presents a general approach to the analysis of functional mri time series from one or more subjects the approach is predicated on an extension of the general linear model that allows for correlations between error terms due to physiological noise or correlations that ensue after temporal smoothing this extension uses the effective degrees of freedom associated with the error term the effective degrees of freedom are a simple function of the number of scans and the temporal autocorrelation function a specific form for the latter can be assumed if the data are smoothed in time to accentuate hemodynamic responses with a neural basis this assumption leads to an expedient implementation of a flexible statistical framework the importance of this small extension is that in contradistinction to our previous approach any parametric statistical analysis can be implemented we demonstrate this point using a multiple regression analysis that tests for effects of interest activations due to word generation while taking explicit account of some obvious confounds

inference for the reliability function based on progressively type ii censored data from the pareto model the generalized variable approach abstract the problem of hypothesis testing and interval estimation based on the generalized variable method for the reliability function of pareto distribution using progressively type ii censored data with fixed removals are considered the confidence limits and testing procedures have to be numerically obtained however the required computations are simple and straightforward there are no exact or approximate testing procedures and confidence intervals for reliability parameter of a pareto distribution based on the progressively type ii right censored data with random or fixed removals available in the literature in addition generalized coverage probabilities generalized size of the test and adjusted and unadjusted generalized powers of the test are also discussed comparison of the reliability function under the classical paradigm and the generalized paradigm is done citing an illustrative example and an example based on the simulated data to demonstrate the advantages and merits of the proposed generalized variable method over the classical method

on the classical solutions of two dimensional inviscid rotating shallow water system abstract we prove global existence and asymptotic behavior of classical solutions for two dimensional inviscid rotating shallow water system with small initial data subject to the zero relative vorticity condition one of the key steps is a reformulation of the problem into a symmetric quasilinear klein gordon system with quadratic nonlinearity for which the global existence of classical solutions is then proved with combination of the vector field approach and the normal form method we also probe the case of general initial data and reveal a lower bound for the lifespan that is almost inversely proportional to the size of the initial relative vorticity

global existence of small amplitude solutions to nonlinear klein gordon equations in four space time dimensions consider the following class of nonlinear wave equations square text u u text text f u u u n k g where t 2 1 2 2 2 3 2 is the d alembertian of the 4 dimensional minkowski space time and f a smooth function of u u t x and its first and second partial derivates vanishing together with its first derivatives at u u u 0 in other words f is at least quadratic in u u u in a neighborhood of the trivial solution u 0 we subject u to the pure initial value problem text u mkern 1mu varepsilon text f x u t varepsilon g x at t 0 i v p with f g c 0 3 and e 0 a small parameter

weighted energy decay for 3d klein gordon equation abstract we obtain a dispersive long time decay in weighted energy norms for solutions of the 3d klein gordon equation with generic potential the decay extends the results obtained by jensen and kato for the 3d schrodinger equation for the proof we modify the spectral approach of jensen and kato to make it applicable to relativistic equations

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

almost global existence for hamiltonian semilinear klein gordon equations with small cauchy data on zoll manifolds this paper is devoted to the proof of almost global existence results for klein gordon equations on zoll manifolds e g spheres of arbitrary dimension with hamiltonian nonlinearities when the cauchy data are smooth and small the proof relies on birkhoff normal form methods and on the specific distribution of eigenvalues of the laplacian perturbed by a potential on zoll manifolds 2007 wiley periodicals inc

on the pitman yor process with spike and slab base measure summaryfor the most popular discrete nonparametric models beyond the dirichlet process the prior guess at the shape of the data generating distribution also known as the base measure is assumed to be diffuse such a specification greatly simplifies the derivation of analytical results allowing for a straightforward implementation of bayesian nonparametric inferential procedures however in several applied problems the available prior information leads naturally to the incorporation of an atom into the base measure and then the dirichlet process is essentially the only tractable choice for the prior in this paper we fill this gap by considering the pitman yor process with an atom in its base measure we derive computable expressions for the distribution of the induced random partitions and for the predictive distributions these findings allow us to devise an effective generalized polya urn gibbs sampler applications to density estimation clustering and curve estimation with both simulated and real data serve as an illustration of our results and allow comparisons with existing methodology in particular we tackle a functional data analysis problem concerning basal body temperature curves

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

generalized confidence intervals abstract the definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances under certain conditions the extended definition is shown to preserve a repeated sampling property that a practitioner expects from exact confidence intervals the proposed procedure is also applied to the problem of constructing confidence intervals for the difference in two exponential means and for variance components in mixed models a repeated sampling property of generalized p values is also given with this characterization one can carry out fixed level tests of parameters of continuous distributions on the basis of generalized p values finally pratt s paradox is revisited and a procedure that resolves the paradox is given

global existence of small solutions for quadratic quasilinear klein gordon systems in two space dimensions consider a quasi linear system of two klein gordon equations with masses m1 m2 we prove that when m1a2m2 and m2a2m1 such a system has global solutions for small smooth compactly supported cauchy data this extends a result proved by sunagawa j differential equations 192 2 2003 308 in the semi linear case moreover we show that global existence holds true also when m1 2m2 and a convenient null condition is satisfied by the nonlinearities

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

small analytic solutions to the hartree equation we consider the cauchy problem for the hartree equation in space dimension d 3 we assume that the interaction potential v belongs to the weak ld 2 space we prove that if the initial data is sufficiently small in the l2 sense and either or its fourier transform f satisfies a real analytic condition then the solution u t is also real analytic for any t 0 we also prove that if and v satisfy some strong condition then u t can be extended to an entire function on cd for any t 0 a part of our method is applicable to the final value problem we remark that no l2 smallness condition is imposed on first and higher order partial derivatives of and f

the scattering problem for the three dimensional cubic nonlinear klein gordon equation with rapidly decreasing input data abstract the scattering problem for the three dimensional cubic nonlinear klein gordon equation is studied it has been shown that the scattering operator s is well defined on a neighborhood in the critical space h 1 2 r 3 h 1 2 r 3 of 0 we prove that if functions f and g are in the schwartz space s r 3 and small in the sense of the critical space then the corresponding output data f g s f g also belongs to s r 3 s r 3 furthermore we give sufficient conditions for f g such that all order partial derivatives of f and g decay more rapidly than a same exponential function

global existence of small solutions to nonlinear evolution equations abstract we study the global existence and asymptotic behaviour of small solutions of a large class of nonlinear partial differential equations if the nonlinear terms are of high degree the solutions will be asymptotic to solutions of the linear equation

neumann problem for the nonlinear klein gordon equation abstract the neumann initial boundary value problem for the nonlinear klein gordon equation 0 1 v t t v v x x v 3 t x r r v 0 x v 0 x v t 0 x v 1 x x r x v t 0 h t t r for real v 0 x v 1 x and h t is considered we prove the global well posedness for the initial boundary value problem 0 1 and we present a sharp time decay estimate of the solution in the uniform norm also we study the asymptotic behavior of the solution to 0 1 we show that the cubic nonlinearity in the neumann initial boundary value problem 0 1 is scattering critical

hs global well posedness for semilinear wave equations abstract we consider the cauchy problem for semilinear wave equations in r n with n 3 making use of bourgain s method in conjunction with the endpoint strichartz estimates of keel and tao we establish the hs global well posedness with s