rigorous remarks about scaling laws in turbulent fluids a definition of scaling law for suitable families of measures is given and investigated first a number of necessary conditions are proved they imply the absence of scaling laws for 2d stochastic navier stokes equations and for the stochastic stokes linear problem in any dimension while they imply a lower bound on the mean vortex stretching in 3d second for the 3d stochastic navier stokes equations necessary and sufficient conditions for scaling laws to hold are given translating the problem into bounds for energy and enstrophy of high and low modes respectively unlike in the 2d case the validity or invalidity of such conditions in 3d remains open

generalized beta prior models on fraction defective in reliability test planning in many reliability analyses the probability of obtaining a defective unit in a production process should not be considered constant even though the process is stable and in control engineering experience or previous data of similar or related products may often be used in the proper selection of a prior model to describe the random fluctuations in the fraction defective a generalized beta family of priors several maximum entropy priors and other prior models are considered for this purpose in order to determine the acceptability of a product based on the lifelengths of some test units failure censored reliability sampling plans for location scale distributions using average producer and consumer risks are designed our procedure allows the practitioners to incorporate a restricted parameter space into the reliability analysis and it is reasonably insensitive to small disturbances in the prior information impartial priors are used to reflect prior neutrality between the producer and the consumer when a consensus on the elicited prior model is required nonetheless our approach also enables the producer and the consumer to assume their own prior distributions the use of substantial prior information can in many cases significantly reduce the amount of testing required however the main advantage of utilizing a prior model for the fraction defective is not necessarily reduced sample size but improved assessment of the true sampling risks an example involving shifted exponential lifetimes is considered to illustrate the results

discharge rates of medicare stroke patients to skilled nursing facilities bayesian logistic regression with unobserved heterogeneity abstract we determine factors both hospital specific and market area specific associated with hospitals propensities for discharging medicare stroke patients to skilled nursing facilities snf s in california and florida logistic regression is generalized to the case of a betabinomial hierarchical model in which covariate information is included in the hyperparameters of the second stage beta distribution it is found that the posterior mean of the proportion discharged to snf is approximately a weighted average i e shrinkage estimator of the logistic regression estimator and the observed rate we develop fully bayesian inference that takes into account uncertainty about the hyperparameters and we find that this also allows us to test for overdispersion in a natural way the number of observed zeros i e hospitals that sent no stroke patients to a snf is excessive compared to the number expected from a standard logistic regression model and is fit better by the hierarchical betabinomial mod

bayesian single and double variable sampling plans for the weibull distribution with censoring the sampling inspection problem is one of the main research topics in quality control in this paper we employ bayesian decision theory to study single and double variable sampling plans for the weibull distribution with type ii censoring a general loss function which includes the sampling cost the time consuming cost the salvage value and the after sales cost is proposed to determine the bayes risk and the corresponding optimal sampling plan explicit expressions for the bayes risks for both single and double sampling plans are derived respectively numerical examples are given to illustrate the effectiveness of the proposed method comparisons between single and double sampling plans are made and sensitivity analysis is performed

bayesian inference for small sample capture recapture data we consider data on the survival of a population of cephalorhynchus hectori hector s dolphins in a marine area of new zealand to estimate survival probabilities of animal populations a multiple capture recapture sampling scheme can be used in this paper we propose a practical methodology to derive approximations to posterior distributions based on laplace methods we show how to calculate bayes estimates and credible intervals in this setting

variables sampling inspection scheme for resubmitted lots based on the process capability index cpk abstract this paper attempts to develop a sampling inspection scheme by variables based on process performance index for product acceptance determination which examines the situation where resampling is permitted on lots not accepted on original inspection the equations for plan parameters the required sample size and the corresponding critical value are derived based on the exact sampling distribution rather than an approximation approach hence the decisions made are more accurate and reliable moreover the efficiency of the proposed variables resubmitted sampling plan is evaluated and compared with the existing variables single sampling plan for illustrative purpose an example is presented to demonstrate the use of the derived results for making a decision on product acceptance determination

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

large sample joint posterior approximations when full conditionals are approximately normal modern bayesian statistical methods such as gibbs and metropolis hastings sampling were developed to liberate statisticians from the necessity of making large sample assumptions and to facilitate the numerical approximation of problems that had previously been analytically intractable counter to this trend we develop a method for constructing asymptotic joint posterior approximations based on models with k blocks of parameters and where the corresponding properly normalized full conditionals are themselves asymptotically normal we illustrate these techniques by applying them to particular linear and generalized linear mixed models glmms we also consider the relevance of different parameterizations with regard to our asymptotics recent work has indicated that gibbs samplers based on so called centering parameterizations result in better convergence properties for the resulting markov chains our results for the one way random effects model shed some light on this issue for this example we also

bounds on kolmogorov spectra for the navier stokes equations let u x t be a possibly weak solution of the navier stokes equations on all of r 3 or on the torus r 3 z 3 denoting the fourier transform by u fu the energy spectrum of u t is the spherical integral

random effects weibull regression model for occupational lifetime abstract with great interest we read the recent publication of sohn et al sohn s y chang i s moon t h 2007 random effects weibull regression model for occupational lifetime european journal of operational research 179 124 131 on a weibull regression model with random effects for modelling occupational lifetime we congratulate sohn and colleagues on their comprehensive and clearly written paper nevertheless we would like to comment on two points the first regarding the moments of the underlying weibull distribution the second regarding the relations of sohn s model to the class of frailty models

computing optimal confidence sets for pareto models under progressive censoring this paper presents two families of joint confidence sets for the pareto shape and precision parameters based on progressively censored data which include the existing regions in the literature as particular cases and derives explicit expressions for the corresponding areas upon using fiducial arguments an exact and quick computational method is then proposed in order to find the smallest area pareto region which depends on the minimal sufficient statistic with a specified confidence level shortest length confidence intervals for the pareto parameters are also provided the reduction in area of the minimal joint confidence region with respect to the existing sets is substantial in most situations and impressive in some cases for illustrative and comparative purposes two practical studies concerning device lifetimes and business failures are considered applications of the smallest confidence sets include uses in hypothesis testing and estimation in particular it is possible to construct confidence intervals for functions of the pareto parameters as well as pointwise and simultaneous confidence bands for the pareto reliability function

laplace approximations for posterior expectations when the mode occurs at the boundary of the parameter space abstract this article gives asymptotic expansions for posterior expectations when the mode is on the boundary of the parameter space the idea based on the divergence theorem is to reduce the high dimensional integrals over the parameters space to surface integrals over the boundary of the parameter space and then apply the usual interior mode laplace method to the latter integrals it is shown that these approximations have second order accuracy the method is illustrated with applications to a two sample binomial problem and a random eflects model

estimation of cancer mortality rates a bayesian analysis of small frequencies a bayesian method is presented for estimating mortality rates of specific diseases when the frequency of deaths over a specified time period is assumed to have a poisson distribution with mean proportional to the population size the estimators use information from related populations each having its own rate which is assumed distributed according to a common prior distribution about which some information is available the method is illustrated using data from an epidemiological study on the geographic variation of cancer mortality in missouri comparisons are also made with a simpler empirical bayes method excerpt

critical strong feller regularity for markov solutions to the navier stokes equations abstract the main purpose of this paper is to show that markov solutions to the 3d navier stokes equations driven by gaussian noise have the strong feller property up to the critical topology given by the domain of the stokes operator to the power one fourth

existence of densities for the 3d navier stokes equations driven by gaussian noise we prove three results on the existence of densities for the laws of finite dimensional functionals of the solutions of the stochastic navier stokes equations in dimension 3 in particular under very mild assumptions on the noise we prove that finite dimensional projections of the solutions have densities with respect to the lebesgue measure which have some smoothness when measured in a besov space this is proved thanks to a new argument inspired by an idea introduced in fournier and printems 2010

bias reduction in nonlinear and dynamic panels in the presence of cross section dependence abstract fixed effects estimation of nonlinear dynamic panel models is subject to the incidental parameter issue leading to a biased asymptotic distribution while this problem has been studied extensively in the literature a general analysis allowing for both serial and cross sectional dependence is missing in this paper we investigate the large n t theory of the profile and integrated likelihood estimators allowing for dependence across both dimensions we show that under stronger dependence types the asymptotic bias disappears but a o p 1 t small sample bias remains we provide bias correction and inference methods and also obtain primitive conditions for asymptotic normality under various dependence settings

on robust analysis of a normal location parameter pericchi and smith considered a normal location parameter problem with double exponential and student t prior distributions these two prior distributions both belong to the class of scale mixtures of normal distributions and are useful in providing a robust analysis of the normal location parameter problem in this paper we extend the analysis to other scale mixtures of normal distributions such as the exponential power and the symmetric stable distributions

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

uniqueness and blow up for a stochastic viscous dyadic model we consider the dyadic model with viscosity and additive gaussian noise as a simplified version of the stochastic navier stokes equations with the purpose of studying uniqueness and emergence of singularities we prove pathwise uniqueness and absence of blow up in the intermediate intensity of the non linearity morally corresponding to the 3d case and blow up for stronger intensity moreover blow up happens with probability one for regular initial data

analysis of equilibrium states of markov solutions to the 3d navier stokes equations driven by additive noise we prove that every markov solution to the three dimensional navier stokes equations with periodic boundary conditions driven by additive gaussian noise is uniquely ergodic the convergence to the unique invariant measure is exponentially fast

estimating bayes factors via posterior simulation with the laplace metropolis estimator abstract the key quantity needed for bayesian hypothesis testing and model selection is the integrated or marginal likelihood of a model we describe a way to use posterior simulation output to estimate integrated likelihoods we describe the basic laplace metropolis estimator for models without random effects for models with random effects we introduce the compound laplace metropolis estimator we apply this estimator to data from the world fertility survey and show it to give accurate results batching of simulation output is used to assess the uncertainty involved in using the compound laplace metropolis estimator the method allows us to test for the effects of independent variables in a random effects model and also to test for the presence of the random effects

design of progressively censored group sampling plans for weibull distributions an optimization problem optimization algorithms provides efficient solutions to many statistical problems essentially the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints usually related to the quality levels required by the producer and the consumer an optimal acceptance sampling plan is developed in this paper for the weibull distribution with unknown scale parameter the proposed plan combines grouping of items sudden death testing in each group and progressive group removals and its decision criterion is based on the uniformly most powerful life test a mixed integer programming problem is first solved for determining the minimum number of failures required and the corresponding acceptance constant the optimal number of groups is then obtained by minimizing a balanced estimation of the expected test cost excellent approximately optimal solutions are also provided in closed forms the sampling plan is considerably flexible and allows to save experimental time and cost in general our methodology achieves solutions that are quite robust to small variations in the weibull shape parameter a numerical example about a manufacturing process of gyroscopes is included for illustration

a bayesian approach to logistic regression models having measurement error following a mixture distribution to estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error we take a bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value we allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure we apply the method to study the risk of alcohol consumption on breast cancer using the nurses health study data we estimate measurement error from a small subsample where we compare true with reported consumption some of the self reported non drinkers truly do not drink the resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error

stochastic tamed 3d navier stokes equations existence uniqueness and ergodicity in this paper we prove the existence of a unique strong solution to a stochastic tamed 3d navier stokes equation in the whole space as well as in the periodic boundary case then we also study the feller property of solutions and prove the existence of invariant measures for the corresponding feller semigroup in the case of periodic conditions moreover in the case of periodic boundary and degenerated additive noise using the notion of asymptotic strong feller property proposed by hairer and mattingly ann math 164 993 1032 2006 we prove the uniqueness of invariant measures for the corresponding transition semigroup

approximating hidden gaussian markov random fields summary gaussian markov random field gmrf models are frequently used in a wide variety of applications in most cases parts of the gmrf are observed through mutually independent data hence the full conditional of the gmrf a hidden gmrf hgmrf is of interest we are concerned with the case where the likelihood is non gaussian leading to non gaussian hgmrf models several researchers have constructed block sampling markov chain monte carlo schemes based on approximations of the hgmrf by a gmrf using a second order expansion of the log density at or near the mode this is possible as the gmrf approximation can be sampled exactly with a known normalizing constant the markov property of the gmrf approximation yields computational efficiency the main contribution in the paper is to go beyond the gmrf approximation and to construct a class of non gaussian approximations which adapt automatically to the particular hgmrf that is under study the accuracy can be tuned by intuitive parameters to nearly any precision these non gaussian approximations share the same computational complexity as those which are based on gmrfs and can be sampled exactly with computable normalizing constants we apply our approximations in spatial disease mapping and model based geostatistical models with different likelihoods obtain procedures for block updating and construct metropolized independence samplers

integration of multimodal functions by monte carlo importance sampling abstract numerical integration of a multimodal integrand f is approached by monte carlo integration via importance sampling a mixture of multivariate t density functions is suggested as an importance function g for its easy random variate generation thick tails and high flexibility the number of components in the mixture is determined by the number of modes of f and the mixing weights and location and scale parameters of the component distributions are determined by numerical minimization of a monte carlo estimate of the squared variation coefficient of the weight function f g stratified importance sampling and control variates are shown to be particularly effective variance reduction techniques in this case the algorithm is applied to a 10 dimensional example and shown to yield significant improvement over usual integration schemes

composite likelihood bayesian information criteria for model selection in high dimensional data for high dimensional data sets with complicated dependency structures the full likelihood approach often leads to intractable computational complexity this imposes difficulty on model selection given that most traditionally used information criteria require evaluation of the full likelihood we propose a composite likelihood version of the bayes information criterion bic and establish its consistency property for the selection of the true underlying marginal model our proposed bic is shown to be selection consistent under some mild regularity conditions where the number of potential model parameters is allowed to increase to infinity at a certain rate of the sample size simulation studies demonstrate the empirical performance of this new bic especially for the scenario where the number of parameters increases with sample size technical proofs of our theoretical results are provided in the online supplemental materials

empirical supremum rejection sampling reference stat article 2002 003doi 10 1093 biomet 89 4 745view record in web of science record created on 2006 04 21 modified on 2017 05 12

spherical radial integration rules for bayesian computation abstract the common numerical problem in bayesian analysis is the numerical integration of the posterior in high dimensions this problem becomes too formidable for fixed quadrature methods and monte carlo integration is the usual approach through the use of modal standardization and a spherical radial transformation we reparameterize in terms of a radius r and point z on the surface of the sphere in d dimensions we propose two types of methods for spherical radial integration a completely randomized method uses randomly placed abscissas for the radial integration and for the sphere surface a mixed method uses fixed quadrature i e simpson s rule on the radius and randomized spherical integration the mixed methods show superior accuracy in comparisons require little or no assumptions and provide diagnostics to detect difficult problems moreover if the posterior is close to the multivariate normal then the mixed methods can give remarkable accuracy

fully exponential laplace approximations to expectations and variances of nonpositive functions abstract tierney and kadane 1986 presented a simple second order approximation for posterior expectations of positive functions they used laplace s method for asymptotic evaluation of integrals in which the integrand is written as f exp nh and the function h is approximated by a quadratic the form in which they applied laplace s method however was fully exponential the integrand was written instead as exp nh log f this allowed first order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second order expansion for the ratio other second order expansions hartigan 1965 johnson 1970 lindley 1961 1980 mosteller and wallace 1964 require computation of more derivatives of the log likelihood function in this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions to obtain a second order approximation to an expectation e g we use the fully exponential method to approximate

minimizing the area of a pareto confidence region abstract a constrained optimization problem is formulated and solved in order to determine the smallest confidence region for the parameters of the pareto distribution in a proposed family of sets the objective function is the area of the region whereas the constraints are related to the required confidence level explicit expressions for the area and confidence level of a given region are first deduced an efficient procedure based on minimizing the corresponding lagrangian function is then presented to solve the nonlinear programming problem the process is valid when some of the smallest and largest observations have been discarded or censored i e both single right or left and double censoring are allowed the optimal pareto confidence region is derived by simultaneously solving three four nonlinear equations in the right double censoring case in most practical situations newton s method with the balanced set as the starting point only needs a few iterations to find the global solution in general the reduction in area of the optimal pareto region with respect to the balanced set is considerable if the sample size n is small or moderately large which is usual in practice this reduction is sometimes impressive when n is quite small and the censoring degree is fairly high two numerical examples regarding component lifetimes and fire claims are included for illustrative and comparative purposes

optimal bayesian sampling acceptance plan with random censoring abstract the sampling acceptance scheme with censoring is one of the important life inspection problems in this article a general model of sampling acceptance plan for the exponential distribution with exponentially distributed random censoring is presented and investigated using bayesian decision theory we consider a loss function which includes the sampling cost time consuming cost and decision loss to determine the optimal sampling acceptance plan under mild assumptions the optimal bayes rule can be proved to be of a monotonic form moreover we obtain optimal bayes rules and explicit expressions of the bayes risk for two special decision loss functions finally a numerical example is given to demonstrate the model

optimum attributes component test plans for k out of n f weibull systems using prior information abstract assuming that the proportion defective in a production process p is variable and the component lifetimes are weibull distributed integer nonlinear programming problems are formulated and solved in order to determine the optimum component inspection scheme by attributes for k out of n f system reliability demonstration using available prior knowledge a limited beta prior model is adopted to reflect the random fluctuations on p the required quantity of components to test and the permissible number of component failures up to a specified censoring time are found by solving a minimisation problem with nonlinear constraints which are related to the tolerable average producer and consumer risks first order taylor polynomials of the operating characteristic function are used to derive a quite accurate approximate solution lower and upper bounds are also deduced optimal solutions are usually robust to small variations in the weibull parameters and prior information existing technical knowledge and experience are shown to be of great practical value in designing optimal sampling plans for lot acceptance purposes the proposed approach generalises the classical viewpoint to those cases in which appreciable prior information on the fraction of defective systems exists and also allows the analyst to determine the acceptability of a k out of n f system before assembly and to limit the range of p moreover the practitioners may attain substantial savings in sample size and improved assessments of the true producer and consumer risks a 4 out of 5 f system of independent water pumps for cooling a reactor is considered to illustrate the suggested component test plans

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

mixtures of g priors in generalized linear models abstractmixtures of zellner s g priors have been studied extensively in linear models and have been shown to have numerous desirable properties for bayesian variable selection and model averaging

exponential mixing for the 3d stochastic navier stokes equations we study the navier stokes equations in dimension 3 ns3d driven by a noise which is white in time we establish that if the noise is at the same time sufficiently smooth and non degenerate in space then the weak solutions converge exponentially fast to equilibrium

bayesian inference using record values from rayleigh model with application in this article based on a set of upper record values from a rayleigh distribution bayesian and non bayesian approaches have been used to obtain the estimators of the parameter and some lifetime parameters such as the reliability and hazard functions bayes estimators have been developed under symmetric squared error and asymmetric linex and general entropy ge loss functions these estimators are derived using the informative and non informative prior distributions for we compare the performance of the presented bayes estimators with known non bayesian estimators such as the maximum likelihood ml and the best linear unbiased blu estimators we show that bayes estimators under the asymmetric loss functions are superior to both the ml and blu estimators the highest posterior density hpd intervals for the rayleigh parameter and its reliability and hazard functions are presented also bayesian prediction intervals of the future record values are obtained and discussed finally practical examples using real record values are given to illustrate the application of the results

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness

markov selections for the 3d stochastic navier stokes equations we investigate the markov property and the continuity with respect to the initial conditions strong feller property for the solutions to the navier stokes equations forced by an additive noise first we prove by means of an abstract selection principle that there are markov solutions to the navier stokes equations due to the lack of continuity of solutions in the space of finite energy the markov property holds almost everywhere in time then depending on the regularity of the noise we prove that any markov solution has the strong feller property for regular initial conditions we give also a few consequences of these facts together with a new sufficient condition for well posedness

exponential ergodicity for stochastic burgers and 2d navier stokes equations abstract it is shown that transition measures of the stochastic navier stokes equation in 2 d converge exponentially fast to the corresponding invariant measures in the distance of total variation as a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state transformation analogous results are proved for the stochastic burgers equation