asymptotic behavior for the navier stokes equations with nonzero external forces abstract we estimate the asymptotic behavior for the stokes solutions with external forces first we found that if there are external forces then the energy decays slowly even if the forces decay quickly then we also obtain the asymptotic behavior in the temporal spatial direction for weak solutions of the navier stokes equations we also provide a simple example of external forces which shows that the stokes solution does not decay quickly

bayesian isotonic regression and trend analysis in many applications the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor controlling for covariates in such cases interest often focuses on estimating the regression function while also assessing evidence of an association this article proposes a new framework for bayesian isotonic regression and order restricted inference approximating the regression function with a high dimensional piecewise linear model the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses accounting for flat regions and truncated normal densities to borrow information across the intervals and smooth the curve the prior is formulated as a latent autoregressive normal process this structure facilitates efficient posterior computation since the full conditional distributions of the parameters have simple conjugate forms point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single mcmc run generalizations to categorical outcomes and multiple predictors are described and the approach is applied to an epidemiology application

modeling for dynamic ordinal regression relationships an application to estimating maturity of rockfish in california abstractwe develop a bayesian nonparametric framework for modeling ordinal regression relationships which evolve in discrete time the motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age length and maturity the latter recorded on an ordinal scale the methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses this approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut off points relating the latent continuous and ordinal responses a novel dependent dirichlet process prior for time dependent mixing distributions extends the model to the dynamic setting the methodology is used for a detailed study of relationships between maturity age and length for chilipepper rockfish using data collected over 15 years along th

bayesian nonparametric inference for quantal response data the problem of nonparametric bayes estimation of a tolerance distribution based on quantal response data has been considered previously with a prior distribution based on the dirichlet process in the present article a broad class of priors is developed for this problem by allowing the hazard function of the tolerance distribution to be a realization of a nonnegative stochastic process with independent increments this class includes the dirichlet prior as a special case in addition priors over a space of absolutely continuous tolerance distributions which includes ifr dfr and u shaped failure rate distributions are constructed by taking the failure rate to be the superposition of two processes with independent increments posterior laplace transforms of the corresponding processes are obtained based on quantal response data with binomial sampling these posterior laplace transforms are then used to find bayes estimates and examples are given to illustrate the results

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

navier stokes flow in the weighted hardy space with applications to time decay problem abstract the asymptotic expansions of the navier stokes flow in r n and the rates of decay are studied with aid of weighted hardy spaces fujigaki and miyakawa 12 miyakawa 28 proved the nth order asymptotic expansion of the navier stokes flow if initial data decays like 1 x n 1 and if nth moment of initial data is finite in the present paper it is clarified that the moment condition for initial data is essential in order to obtain higher order asymptotic expansion of the flow and to consider the rapid time decay problem the second author 39 established the weighted estimates of the strong solutions in the weighted hardy spaces with small initial data which belongs to l n and a weighed hardy space firstly the refinement of the previous work 39 is achieved with alternative proof then the existence time of the solution in the weighted hardy spaces is characterized without any hardy norm as a result in two dimensional case the smallness condition on initial data is completely removed as an application the rapid time decay of the flow is investigated with aid of asymptotic expansions and of the symmetry conditions introduced by brandolese 3

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

a bayesian nonparametric approach to reliability abstract it is suggested that problems in a reliability context may be handled by a bayesian non parametric approach a stochastic process is defined whose sample paths may be assumed to be either increasing hazard rates or decreasing hazard rates by properly choosing the parameter functions of the process the posterior distribution of the hazard rates are derived for both exact and censored data bayes estimates of hazard rates c d f s densities and means are found under squared error type loss functions some simulation is done and estimates graphed to better understand the estimators finally estimates of the c d f from some data in a paper by kaplan and meier are constructed author

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

a nonparametric bayesian modeling approach for cytogenetic dosimetry summary in cytogenetic dosimetry samples of cell cultures are exposed to a range of doses of a given agent in each sample at each dose level some measure of cell disability is recorded the objective is to develop models that explain cell response to dose such models can be used to predict response at unobserved doses more important such models can provide inference for unknown exposure doses given the observed responses typically cell disability is viewed as a poisson count but in the present work a more appropriate response is a categorical classification in the literature modeling in this case is very limited what exists is purely parametric we propose a fully bayesian nonparametric approach to this problem we offer comparison with a parametric model through a simulation study and the analysis of a real dataset modeling blood cultures exposed to radiation where classification is with regard to number of micronuclei per cell

a bayesian approach to robust binary nonparametric regression abstract this article presents a bayesian approach to binary nonparametric regression that assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions the article makes the following contributions first a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out and the estimates are made robust to outliers second the approach can handle a wide range of link functions third efficient state space based algorithms are used to carry out the computations fourth an extensive set of simulations is carried out which show that the bayesian estimator works well and compares favorably to two estimators that have recently been proposed and used in practice

weighted lq l1 estimate of the stokes flow in the half space abstract in this paper we derive the weighted l q l 1 estimate of the stokes solution u in the half space when 1 q we obtained that x r u l q c t 1 2 n 2 1 1 q x r x n a l 1 c t r 1 2 n 2 1 1 q x n a l 1 for 0 r n 1 1 1 q and x n r u l q c t 1 2 n 2 1 1 q x n r 1 a l 1 c t r 1 2 n 2 1 1 q x n a l 1 for 0 r n 1 1 q

order restricted tests for stratified comparisons of binomial proportions the data set presented relates a binomial response to ordered levels of an explanatory variable representing doses of a drug with data collected at several centers a study goal is to test independence of the response and the ordinal factor assuming under the alternative only that the binomial parameter is a monotonically increasing function of the ordinal predictor we present two likelihood ratio tests that are sensitive to order restricted alternatives simulating the exact distributions of the test statistics yields nearly exact p values we also discuss related analyses for comparing two groups on an ordinal response and we propose a test that is sensitive to a stochastic ordering alternative

linear bayes estimators of the potency curve in bioassay abstract the bayesian nonparametric approach to estimating the tolerance distribution in quantal bioassay has received some attention the computational difficulty in evaluating these bayes estimators has hindered their applications this paper explores the linear bayes approach to the bioassay problem these linear bayes estimators can be computed easily by using statistical software which has the capability of inverting a matrix let us state the quantal bioassay problem as follows the experimenter intends to test the potency of a stimulus by giving subjects injections of the stimulus at different levels namely he chooses l dosage levels t sub 1 t sub l and treats n sub 1 n sub l subjects at these levels respectively each subject possesses a fixed tolerance level if a stimulus exceeds a subject s tolerance level the subject responds positively if not there is no response therefore we observe the number of positive responses at each level these numbers are denoted by k sub 1 k sub l the potency curve f is the distribution of tolerance levels i e f is defined by the probability f t of getting a positive response to a dosage at level t for all t the objective of this article is to make inferences about the potency curve f keywords ferguson s dirichlet process

bayesian nonparametric estimation of continuous monotone functions with applications to dose response analysis in this article we consider monotone nonparametric regression in a bayesian framework the monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions and a general random probability measure is assumed as the prior for the mixing distribution we investigate the choice of the underlying parametric distribution function and find that the two sided power distribution function is well suited both from a computational and mathematical point of view the model is motivated by traditional nonlinear models for dose response analysis and provides possibilities to elicitate informative prior distributions on different aspects of the curve the method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose response analysis

existence and regularity of a class of weak solutions to the navier stokes equations abstract we construct a class of weak solutions to the navier stokes equations which have second order spatial derivatives and one order time derivatives of p power summability for 1 p 5 4 meanwhile we show that u l s 0 t w 2 r with 1 s 3 2 r 2 for 1 r 5 4 r can be relaxed not to exceed 3 2 if we consider only in the interior of in the end we extend the classical regularity theorem our results show that u is a regular solution if u l s 0 t l r with 1 s 3 2 r 1 for satisfying 1 3 with 1 s 1 r 5 6 for arbitrary domain in r 3 and 1 s 2 for r n with n 3 this result was previously obtained byh beirao da veiga chinese ann math ser b 16 1995 407 412

asymptotic behavior for the navier stokes equations in 2d exterior domains we show that the lp spatial temporal decay rates of solutions of incompressible flow in an 2d exterior domain when a domain has a boundary pressure term makes an obstacle since we do not have enough information on the pressure term near the boundary to overcome the difficulty we adopt the ideas in he xin c he z xin weighted estimates for nonstationary navier stokes equations in exterior domain methods appl anal 7 3 2000 443 458 and our previous results h o bae b j jin asymptotic behavior of stokes solutions in 2d exterior domains j math fluid mech in press h o bae b j jin temporal and spatial decay rates of navier stokes solutions in exterior domains submitted for publication for the spatial decay rate estimate we first extend temporal decay rate result of the navier stokes solutions for general lp space when the initial velocity is in l 2 lr 1 r q 1 r q

bayesian nonparametric inference on the dose level with specified response rate the richness of nonparametric bayesian models has attracted many different applications its application in dose finding studies has been hindered due to lack of methodologies on the nonparametric bayesian inference on percentiles the primary interest in dose finding studies focuses inference on the unknown toxicity or efficacy dose level corresponding to a prespecified rate this paper shows how this problem may generally be handled by deriving inference on percentiles of a distribution following a dirichlet process prior in particular theoretical results are derived to obtain the nonparametric bayesian inference of the unknown dose level this is followed by a description of the numerical implementation of that theory the method also allows efficient estimation of the entire potency curve finally the usefulness of the approach is demonstrated via an experimental data example

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

a bayesian analysis of quantal bioassay experiments incorporating historical controls via bayes factors this paper addresses model based bayesian inference in the analysis of data arising from bioassay experiments in such experiments increasing doses of a chemical substance are given to treatment groups usually rats or mice for a fixed period of time usually 2 years the goal of such an experiment is to determine whether an increased dosage of the chemical is associated with increased probability of an adverse effect usually presence of adenoma or carcinoma the data consists of dosage survival time and the occurrence of the adverse event for each unit in the study to determine whether such relationship exists this paper proposes using bayes factors to compare two probit models the model that assumes increasing dose effects and the model that assumes no dose effect these models account for the survival time of each unit through a poly k type correction in order to increase statistical power the proposed approach allows the incorporation of information from control groups from previous studies the proposed method is able to handle data with very few occurrences of the adverse event the proposed method is compared with a variation of the peddada test via simulation and is shown to have higher power we demonstrate the method by applying it to the two bioassay experiment datasets previously analyzed by other authors copyright 2017 john wiley sons ltd

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

an anova model for dependent random measures we consider dependent nonparametric models for related random probability distributions for example the random distributions might be indexed by a categorical covariate indicating the treatment levels in a clinical trial and might represent random effects distributions under the respective treatment combinations we propose a model that describes dependence across random distributions in an analysis of variance anova type fashion we define a probability model in such a way that marginally each random measure follows a dirichlet process dp and use the dependent dirichlet process to define the desired dependence across the related random measures the resulting probability model can alternatively be described as a mixture of anova models with a dp prior on the unknown mixing measure the main features of the proposed approach are ease of interpretation and computational simplicity because the model follows the standard anovastructure interpretation and inference parallels conventions for anova mode

posterior distribution of a dirichlet process from quantal response data the posterior distribution of a dirichlet process from n quantal responses at r dosage levels has been recognized by antoniak as a mixture of dirichlet processes the purpose of this paper is to develop a systematic procedure for computing finite dimensional distributions of such mixtures which can be equivalently expressed as multivariate beta distributions with random parameter vectors it is shown that the sequence of random parameter vectors of the updated beta posteriors from observations at increasing dosage levels evolves in a manner which is described by r separate markov chains this description is then used to derive the asymptotic posterior distribution the weak limits of the relevant markov chains are shown to be solutions of certain stochastic differential equations and the random parameter vector of the posterior beta distribution is shown to be asymptotically normal the mean vector and covariance matrix of which are given by recursion formulas

optimal designs for dose finding studies with an active control summary dose finding studies often compare several doses of a new compound with a marketed standard treatment as an active control in the past however research has focused mostly on experimental designs for placebo controlled dose finding studies to the best of our knowledge optimal designs for dose finding studies with an active control have not been considered so far as the statistical analysis for an active controlled dose finding study can be formulated in terms of a mixture of two regression models the related design problem is different from what has been investigated before in the literature we present a rigorous approach to the problem of determining optimal designs for estimating the smallest dose achieving the same treatment effect as the active control we determine explicitly the locally optimal designs for a broad class of models employed in such studies we also discuss robust design strategies and determine related bayesian and standardized minimax optimal designs we illustrate the results by investigating alternative designs for a clinical trial which has recently appeared in a consulting project of one of the authors

probits of mixtures the tolerances of individuals insects parasites in a population have a frequency or probability distribution called a tolerance distribution many tolerance distributions in bioassay studies can be the result of a rather heterogeneous population of individuals and can often be modelled as a mixture of a number of standard unimodal distributions a probit analysis can be generalized to the case where the tolerance distribution is a mixture of location and scale parameter distributions in this article the existence and determination of the maximum likelihood estimates are investigated an expectation maximization em algorithm for probits of mixtures is developed and it is shown that by application of the em algorithm the problem of probits of mixtures can be separated into a series of probits of individual component tolerance distributions

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

bayesian dose finding in phase i ii clinical trials using toxicity and efficacy odds ratios a bayesian adaptive design is proposed for dose finding in phase i ii clinical trials to incorporate the bivariate outcomes toxicity and efficacy of a new treatment without specifying any parametric functional form for the drug dose response curve we jointly model the bivariate binary data to account for the correlation between toxicity and efficacy after observing all the responses of each cohort of patients the dosage for the next cohort is escalated deescalated or unchanged according to the proposed odds ratio criteria constructed from the posterior toxicity and efficacy probabilities a novel class of prior distributions is proposed through logit transformations which implicitly imposes a monotonic constraint on dose toxicity probabilities and correlates the probabilities of the bivariate outcomes we conduct simulation studies to evaluate the operating characteristics of the proposed method under various scenarios the new bayesian design based on the toxicity efficacy odds ratio trade offs exhibits good properties and treats most patients at the desirable dose levels the method is illustrated with a real trial design for a breast medical oncology study

markov chain monte carlo in approximate dirichlet and beta two parameter process hierarchical models summary we present some easy to construct random probability measures which approximate the dirichlet process and an extension which we will call the beta two parameter process the nature of these constructions makes it simple to implement markov chain monte carlo algorithms for fitting nonparametric hierarchical models and mixtures of nonparametric hierarchical models for the dirichlet process we consider a truncation approximation as well as a weak limit approximation based on a mixture of dirichlet processes the same type of truncation approximation can also be applied to the beta two parameter process both methods lead to posteriors which can be fitted using markov chain monte carlo algorithms that take advantage of blocked coordinate updates these algorithms promote rapid mixing of the markov chain and can be readily applied to normal mean mixture models and to density estimation problems we prefer the truncation approximations since a simple device for monitoring the adequacy of the approximation can be easily computed from the output of the gibbs sampler furthermore for the dirichlet process the truncation approximation offers an exponentially higher degree of accuracy over the weak limit approximation for the same computational effort we also find that a certain beta two parameter process may be suitable for finite mixture modelling because the distinct number of sampled values from this process tends to match closely the number of components of the underlying mixture distribution

bayesian inference for semiparametric binary regression abstract we propose a regression model for binary response data that places no structural restrictions on the link function except monotonicity and known location and scale predictors enter linearly we demonstrate bayesian inference calculations in this model by modifying the dirichlet process we obtain a natural prior measure over this semiparametric model and we use polya sequence theory to formulate this measure in terms of a finite number of unobserved variables we design a markov chain monte carlo algorithm for posterior simulation and apply the methodology to data on radiotherapy treatments for cancer

bayesian nonparametric inference for effective doses in a quantal response experiment ramsey 1972 biometrics 28 841 858 developed a prior distribution for a single response curve arising from an indirect biological assay based upon quantal responses this paper presents the derivation of the exact prior and posterior distributions of an effective dose which follow from ramsey s prior since the posterior distribution of an effective dose is numerically difficult to compute in a large experiment methods for approximating this distribution are given numerical examples are presented to show the accuracy of the approximate methods finally the usefulness of the present results in assessing ramsey s prior is illustrated

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

bifurcations in elastic plastic materials abstract when strain softening elastic plastic materials are loaded into the plastic regime they often exhibit deformations that are localized into small regions at some point in the loading process this intense localized deformation limits the formability of materials and will often quickly lead to failure with continued loading localized deformation is often associated with satisfaction of the classical discontinuous bifurcation criterion here we propose that the loss of strong ellipticity criterion should be used in place of the classical discontinuous bifurcation criterion as a necessary condition for localization the application of the strong ellipticity criterion implies that a bifurcation mode associated with loss of positive definiteness of the symmetric part of the acoustic tensor must be identified rather than a mode associated with the first zero eigenvalue of the acoustic tensor itself the eigensystem for the symmetric part of the tangent modulus tensor is obtained for several different plasticity models this eigensystem provides information about deformation modes associated with both diffuse and discontinuous bifurcations material properties boundary conditions and body geometry are all shown to affect the diffuse and localized deformation modes that are generated numerous experimental observations of necking and localization in metal specimens subject to various boundary conditions are explained with the proposed approach

decohesive carrying capacity of a disk under tension and in plane torsion abstract an elastic perfectly plastic circular disk with rigid circular inclusion of the radius a subjected to simultaneous uniform radial tension and in plane torsion is considered external radius of the disk is assumed to be infinitely large just to simplify the boundary conditions limit load carrying capacity of such a disk cannot be reached it is preceded by decohesive carrying capacity dcc defined by infinitely large radial strains e r they attain their upper bound for r a then the shearing strains r at r a increase infinitely as well in contradistinction to the limit carrying capacity the decohesive carrying capacity depends essentially on poisson s ratio v interaction curves corresponding to dcc are shown in the plane of external loadings a comparison with the condition of discontinuous bifurcation under uniform stresses and strains is given and full agreement is found though in the case under consideration the state of stress is evidently non uniform diagrams of stress and strain distribution at the moment of decohesion are also presented

space time asymptotics of the two dimensional navier stokes flow in the whole plane abstract we consider the space time behavior of the two dimensional navier stokes flow introducing some qualitative structure of initial data we succeed to derive the first order asymptotic expansion of the navier stokes flow without moment condition on initial data in l 1 r 2 l 2 r 2 moreover we characterize the necessary and sufficient condition for the rapid energy decay u t 2 o t 1 as t motivated by miyakawa schonbek 21 by weighted estimated in hardy spaces we discuss the possibility of the second order asymptotic expansion of the navier stokes flow assuming the first order moment condition on initial data moreover observing that the navier stokes flow u t lies in the hardy space h 1 r 2 for t 0 we consider the asymptotic expansions in terms of hardy norm finally we consider the rapid time decay u t 2 o t 3 2 as t with cyclic symmetry introduced by brandolese 2

bayesian nonparametric inference for random distributions and related functions in recent years bayesian nonparametric inference both theoretical and computational has witnessed considerable advances however these advances have not received a full critical and comparative analysis of their scope impact and limitations in statistical modelling many aspects of the theory and methods remain a mystery to practitioners and many open guestions remain in this paper we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the bayesian nonparametric and or semiparametric framework

a bayesian approach to the analysis of quantal bioassay studies using nonparametric mixture models we develop a bayesian nonparametric mixture modeling framework for quantal bioassay settings the approach is built upon modeling dose dependent response distributions we adopt a structured nonparametric prior mixture model which induces a monotonicity restriction for the dose response curve particular emphasis is placed on the key risk assessment goal of calibration for the dose level that corresponds to a specified response the proposed methodology yields flexible inference for the dose response relationship as well as for other inferential objectives as illustrated with two data sets from the literature

decay rate of solutions of navier stokes equations in 3 dimensional half space abstract in this article we derive the l 2 spatial decay rate of a weak solution of the incompressible flow in the half space when the half space or some other fluid region with boundary is concerned pressure estimate is main obstacle since we do not have enough information of the pressure on the boundary in this paper we give an idea which does not require any pressure information on the boundary and we hope that our idea could be applied to other problems such as exterior domain problem

bayesian spatial monotonic multiple regression we consider monotonic multiple regression for contiguous regions the regression functions vary regionally and may exhibit spatial structure we develop bayesian nonparametric methodology that permits estimation of both continuous and discontinuous functional shapes using marked point process and reversible jump markov chain monte carlo techniques spatial dependence is incorporated by a flexible prior distribution which is tuned using cross validation and bayesian optimization we derive the mean and variance of the prior induced by the marked point process approach asymptotic results show consistency of the estimated functions posterior realizations enable variable selection the detection of discontinuities and prediction in simulations and in an application to a norwegian insurance data set our methodology shows better performance than existing approaches

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

bayesian inference on order constrained parameters in generalized linear models summary in biomedical studies there is often interest in assessing the association between one or more ordered categorical predictors and an outcome variable adjusting for covariates for a k level predictor one typically uses either a k 1 degree of freedom df test or a single df trend test which requires scores for the different levels of the predictor in the absence of knowledge of a parametric form for the response function one can incorporate monotonicity constraints to improve the efficiency of tests of association this article proposes a general bayesian approach for inference on order constrained parameters in generalized linear models instead of choosing a prior distribution with support on the constrained space which can result in major computational difficulties we propose to map draws from an unconstrained posterior density using an isotonic regression transformation this approach allows flat regions over which increases in the level of a predictor have no effect bayes factors for assessing ordered trends can be computed based on the output from a gibbs sampling algorithm results from a simulation study are presented and the approach is applied to data from a time to pregnancy study

upper and lower bounds of temporal and spatial decays for the navier stokes equations we obtain the lower bounds of the temporal spatial decays for weak solutions of the navier stokes equations c0 1 t 5 2i4 1 2 i 2u t l2 c1 1 t 5 2i4 for i 1 2 the upper bound parts are estimated in several papers for example bae and jin submitted and he and xin proc roy soc edinburg section a 131 3 2001 597 by the interpolation arguments we also have c0 1 t 54 2 1 x 2 2u t l2 c1 1 t 54 2 for 0 2

properties of discontinuous bifurcation solutions in elasto plasticity explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic plastic materials are presented it then follows that the classical value of the critical hardening modulus derived by rice 1976 proc 14th iutam congr delft the netherlands pp 207 220 north holland amsterdam is in fact the only possible one furthermore from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non associated volumetric flow rules while the devialoric portion is associated the considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening the result obtained by rudnicki and rice 1975 j mech phys solids 23 371 394 for a drucker pruger material appear as a special case other criteria that are investigated arc those of coulomb and rankine less

dose response curve estimation a semiparametric mixture approach summary in the estimation of a dose response curve parametric models are straightforward and efficient but subject to model misspecifications nonparametric methods are robust but less efficient as a compromise we propose a semiparametric approach that combines the advantages of parametric and nonparametric curve estimates in a mixture form our estimator takes a weighted average of the parametric and nonparametric curve estimates in which a higher weight is assigned to the estimate with a better model fit when the parametric model assumption holds the semiparametric curve estimate converges to the parametric estimate and thus achieves high efficiency when the parametric model is misspecified the semiparametric estimate converges to the nonparametric estimate and remains consistent we also consider an adaptive weighting scheme to allow the weight to vary according to the local fit of the models we conduct extensive simulation studies to investigate the performance of the proposed methods and illustrate them with two real examples

bayesian monotone regression using gaussian process projection shape constrained regression analysis has applications in dose response modelling environmental risk assessment disease screening and many other areas incorporating the shape constraints can improve estimation efficiency and avoid implausible results we propose a novel method focusing on monotone curve and surface estimation which uses gaussian process projections our inference is based on projecting posterior samples from the gaussian process we develop theory on continuity of the projection and rates of contraction our approach leads to simple computation with good performance in finite samples the proposed projection method can also be applied to other constrained function estimation problems including those in multivariate settings

bayesian semiparametric isotonic regression for count data this article proposes a semiparametric bayesian approach for inference on an unknown isotonic regression function f x characterizing the relationship between a continuous predictor x and a count response variable y adjusting for covariates z a dirichlet process mixture of poisson distributions is used to avoid parametric assumptions on the conditional distribution of y given x and z then to also avoid parametric assumptions on f x a novel prior formulation is proposed that enforces the nondecreasing constraint and assigns positive prior probability to the null hypothesis of no association through the use of carefully tailored hyperprior distributions we allow for borrowing of information across different regions of x in estimating f x and in assessing hypotheses about local increases in the function due to conjugacy properties posterior computation is straightforward using a markov chain monte carlo algorithm the methods are illustrated using data from an epidemiologic study of sleep pr

nonparametric bayesian bioassay including ordered polytomous response abstract previous attempts at implementing fully bayesian nonparametric bioassay have enjoyed limited success due to computational difficulties we show here how this problem may be generally handled using a sampling based approach to develop desired marginal posterior distributions and their features a useful extension is presented which treats the case of ordered polytomous response illustrative examples are provided

stability enhancement by boundary control in 2 d channel flow in this paper we stabilize the parabolic equilibrium profile in a two dimensional 2 d channel flow using actuators and sensors only at the wall the control of channel flow was previously considered by speyer and coworkers and bewley and coworkers who derived feedback laws based on linear optimal control and implemented by wall normal actuation with an objective to achieve global lyapunov stabilization we arrive at a feedback law using tangential actuation using teamed pairs of synthetic jets or rotating disks and only local measurements of wall shear stress allowing to embed the feedback in microelectromechanical systems mems hardware without need for wiring this feedback is shown to guarantee global stability in at least h sup 2 norm which by sobolev s embedding theorem implies continuity in space and time of both the flow field and the control as well as their convergence to the desired steady state the theoretical results are limited to low values of reynolds number however we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher