inference for mixtures of finite polya tree models mixtures of polya tree models provide a flexible alternative when a parametric model may only hold approximately i provide computational strategies for obtaining full semiparametric inference for mixtures of finite polya tree models given a standard parameterization including models that would be troublesome to fit using dirichlet process mixtures recommendations are put forth on choosing the level of a finite polya tree and model comparison is discussed several examples demonstrate the utility of finite polya tree modeling including data fit to generalized linear mixed models and several survival models

model comparison of generalized linear mixed models generalized linear mixed models glmms have been widely appreciated in biological and medical research maximum likelihood estimation has received a great deal of attention comparatively not much has been done on model comparison or hypotheses testing in this article we propose a path sampling procedure to compute the observed data log likelihood function so that the bayesian information criterion bic can be applied to model comparison or hypothesis testing advantages of the proposed path sampling procedure are discussed two medical data sets are analysed for providing illustrative examples of the proposed methodology

facilitating the gibbs sampler the gibbs stopper and the griddy gibbs sampler abstract the article briefly reviews the history literature and form of the gibbs sampler an importance sampling device is proposed for converting the output of the gibbs sampler to a sample from the exact posterior this gibbs stopper technique is also useful for assessing convergence of the gibbs sampler for moderate sized problems also presented is an approach for implementing the gibbs sampler in nonconjugate situations the basic idea is to approximate the true cdf of each conditional distribution by a piecewise linear function and then sample from the approximation questions relating to the number of nodes in the approximation gap size between successive nodes and the treatment of unbounded intervals for a given conditional are discussed the methodology is illustrated using a genetic linkage model a nonlinear regression model and the cox model

development of a formal likelihood function for improved bayesian inference of ephemeral catchments 1 the application of formal bayesian inferential approaches in hydrologic modeling is often criticized for requiring explicit assumptions to be made about the distribution of the errors via the likelihood function these assumptions can be adequate in some situations but often little attention is paid to the selection of an appropriate likelihood function this paper investigates the application of bayesian methods in modeling ephemeral catchments we consider two modeling case studies including a synthetically generated data set and a real data set of an arid australian catchment the case studies investigate some typical forms of the likelihood function which have been applied widely by previous researchers as well as introducing new implementations aimed at better addressing likelihood function assumptions in dry catchments the results of the case studies indicate the importance of explicitly accounting for model residuals that are highly positively skewed due to the presence of many zeros zero inflation arising from the dry spells experienced by the catchment specifically the form of the likelihood function was found to significantly impact the calibrated parameter posterior distributions which in turn have the potential to greatly affect the uncertainty estimates in each application the likelihood function that explicitly accounted for the nonconstant variance of the errors and the zero inflation of the errors resulted in 1 equivalent or better fits to the observed discharge in both timing and volume 2 superior estimation of the uncertainty as measured by the reliability and sharpness metrics and 3 more linear quantile quantile plots indicating the errors were more closely matched to the assumptions of this form of the likelihood function

marginal likelihood from the metropolis hastings output this article provides a framework for estimating the marginal likelihood for the purpose of bayesian model comparisons the approach extends and completes the method presented in chib 1995 by overcoming the problems associated with the presence of intractable full conditional densities the proposed method is developed in the context of mcmc chains produced by the metropolis hastings algorithm whose building blocks are used both for sampling and marginal likelihood estimation thus economizing on prerun tuning effort and programming experiments involving the logit model for binary data hierarchical random effects model for clustered gaussian data poisson regression model for clustered count data and the multivariate probit model for correlated binary data are used to illustrate the performance and implementation of the method these examples demonstrate that the method is practical and widely applicable

adaptive importance sampling monte carlo simulation for general multivariate probability laws we establish a parametric adaptive importance sampling variance reduction method for general multivariate probability laws employing the principle of bypass distributions makes it possible to develop adaptive algorithms without relying on particular properties of the target and proposal laws both of which in the proposed framework are as general as the uniform law on the unit hypercube without changing the sampling distribution at each iteration we establish the asymptotic normality of the estimator of the desired mean and of the importance sampling parameter as the number of observations tends to infinity although implementation of the proposed methodology requires a small amount of initial work it has the potential to yield substantial improvements in estimator efficiency in various general problem settings to illustrate the applicability and effectiveness we provide numerical results throughout in which we apply exponential and normal bypass distributions as well as demonstrate that well known adaptive importance sampling formulations in the literature can be easily rewritten in the proposed framework

hidden markov models for longitudinal comparisons medical researchers interested in temporal multivariate measurements of complex diseases have recently begun developing health state models which divide the space of patient characteristics into medically distinct clusters the current state of the art in health services research uses k means clustering to form the health states and a first order markov chain to describe transitions between the states this fitting procedure ignores information from temporally adjacent observations and prevents uncertainty from parameter estimation and cluster assignments from being incorporated into the analysis a natural way to address these issues is to combine clustering and longitudinal analyses using a hidden markov model we fit hidden markov models to longitudinal data using bayesian methods that account for all of the uncertainty in the parameters conditional only on the underlying correctness of the model potential lack of time homogeneity in the markov chain is accounted for by embedding transition probabi

computing bayes factors using a generalization of the savage dickey density ratio abstract we present a simple method for computing bayes factors the method derives from observing that in general a bayes factor can be written as the product of a quantity called the savage dickey density ratio and a correction factor both terms are easily estimated from posterior simulation in some cases it is possible to do these computations without ever evaluating the likelihood

bayesian hypothesis testing in latent variable models hypothesis testing using bayes factors bfs is known not to be well defined under the improper prior in the context of latent variable models an additional problem with bfs is that they are difficult to compute in this paper a new bayesian method based on the decision theory and the em algorithm is introduced to test a point hypothesis in latent variable models the new statistic is a by product of the bayesian mcmc output and hence easy to compute it is shown that the new statistic is appropriately defined under improper priors because the method employs a continuous loss function in addition it is easy to interpret the method is illustrated using a one factor asset pricing model and a stochastic volatility model with jumps

nonparametric importance sampling abstract importance sampling is a widely used variance reduction simulation technique for the evaluation of high dimensional integrals a key step in the implementation of importance sampling is to choose a proper distribution function from which pseudorandom numbers are generated parametric sampling distributions if available at all are often inadequate for high dimensional integrals over irregular regions one possible remedy is to use a nonparametric method to estimate the unknown optimal sampling function we show that the nonparametric approach yields integral estimates that converge faster than estimates obtained from parametric approaches we also demonstrate that an adaptive method which has been used successfully in parametric settings does not yield better results than simple one step methods in the nonparametric setting

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

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

bayesian estimation and comparison of moment condition models in this article we develop a bayesian semiparametric analysis of moment condition models by casting the problem within the exponentially tilted empirical likelihood etel framework we use this f

bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations a bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation lco of a pitching airfoil in the transitional reynolds number regime at small angles of attack laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the lco the fluid structure interaction of the rigid but elastically mounted airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to lco the likelihood in the posterior parameter probability density function pdf is available semi analytically using the extended kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model the posterior parameter pdf is sampled using a parallel and adaptive markov chain monte carlo mcmc algorithm the posterior probability of each model is estimated using the chib jeliazkov method that directly uses the posterior mcmc samples for evidence marginal likelihood computation the bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind tunnel test data at various reynolds numbers

posterior simulation and bayes factors in panel count data models abstract this paper is concerned with the problems of posterior simulation and model choice for poisson panel data models with multiple random effects efficient algorithms based on markov chain monte carlo methods for sampling the posterior distribution are developed a new parameterization of the random effects and fixed effects is proposed and compared with a parameterization in common use and computation of marginal likelihoods and bayes factors via chib s 1995 method is also considered the methods are illustrated with two real data applications involving large samples and multiple random effects

spatial eigensolution analysis of energy stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness this study focuses on the dispersion and diffusion characteristics of high order energy stable flux reconstruction esfr schemes via the spatial eigensolution analysis framework proposed in 1 the analysis is performed for five esfr schemes where the parameter c dictating the properties of the specific scheme recovered is chosen such that it spans the entire class of esfr methods also referred to as vcjh schemes proposed in 2 in particular we used five values of c two that correspond to its lower and upper bounds and the others that identify three schemes that are linked to common high order methods namely the esfr recovering two versions of discontinuous galerkin methods and one recovering the spectral difference scheme the performance of each scheme is assessed when using different numerical intercell fluxes e g different levels of upwinding ranging from under to over upwinding in contrast to the more common temporal analysis the spatial eigensolution analysis framework adopted here allows one to grasp crucial insights into the diffusion and dispersion properties of fr schemes for problems involving non periodic boundary conditions typically found in open flow problems including turbulence unsteady aerodynamics and aeroacoustics

efficient bayes factor estimation from the reversible jump output summary we propose a class of estimators of the bayes factor which is based on an extension of the bridge sampling identity of meng wong 1996 and makes use of the output of the reversible jump algorithm of green 1995 within this class we give the optimal estimator and also a suboptimal one which may be simply computed on the basis of the acceptance probabilities used within the reversible jump algorithm for jumping between models the proposed estimators are very easily computed and lead to a substantial gain of efficiency in estimating the bayes factor over the standard estimator based on the reversible jump output this is illustrated through a series of monte carlo simulations involving a linear and a logistic regression model

a flexible approach to parametric inference in nonlinear and time varying time series models many structural break and regime switching models have been used with macroeconomic and financial data in this paper we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications we build on earlier work showing the relationship between flexible functional forms and random variation in parameters our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring reordered observations the range of priors produced in this way can accommodate a wide variety of nonlinear time series models including those with regime switching and structural breaks by allowing the amount of random variation in parameters to depend on the distance between reordered observations the parameters can evolve in a wide variety of ways allowing for everything from models exhibiting abrupt change e g threshold autoregressive models or standard structural break models to those which allow for a gradual evolution of parameters e g smooth transition autoregressive models or time varying parameter models bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering conditional on a hypothetical reordering and distance function a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation we use artificial data to show the advantages of our approach before providing two empirical illustrations involving the modeling of real gdp growth

filtering with state space localized kalman gain abstract it is well known that particle filters and markov chain monte carlo methods are too expensive for high dimensional models more robust techniques such as low rank versions of the kalman filter are usually applied in large scale models common feature of all the ensemble kalman type filters is that the model state and parameters are updated using the covariance matrix between the model states and the measurements often estimated by a finite number of samples in many nonlinear problems a global linearization of the model may be inadequate to describe the relationship between the observations and the model state and parameters hence the kalman type updates may cause severe bias in the posterior estimates in this paper we investigate the effect of using a local linearization motivated by local gaussian density estimation we describe ways to estimate the covariance locally in the state space resulting in local ensemble filters this is not to be confused with covariance localization which often refers to localization in the physical space the filters are tested on the three dimensional lorenz model and a three layer petroleum reservoir type model the results clearly show that using a kalman update based on local covariances allows resolution of small scale structures in the posterior distribution that cannot be resolved using a global covariance matrix in particular we show that the new local filters are able to approximate posterior distributions with multiple modes contrary to the ensemble kalman filter

antithetic acceleration of monte carlo integration in bayesian inference abstract it is proposed to sample antithetically rather than randomly from the posterior density in bayesian inference using monte carlo integration conditions are established under which the number of replications required with antithetic sampling relative to the number required with random sampling is inversely proportional to sample size as sample size increases the result is illustrated in an experiment using a bivariate vector autoregression

objective bayesian comparison of constrained analysis of variance models in the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints for instance when examining three group means mu 1 mu 2 mu 3 through an analysis of variance anova a model may specify that mu 1 mu 2 mu 3 while another one may state that mu 1 mu 3 mu 2 and finally a third model may instead suggest that all means are unrestricted this is a challenging problem because it involves a combination of nonnested models as well as nested models having the same dimension we adopt an objective bayesian approach requiring no prior specification from the user and derive the posterior probability of each model under consideration our method is based on the intrinsic prior methodology suitably modified to accommodate equality and inequality constraints focussing on normal anova models a comparative assessment is carried out through simulation studies we also present an application to real data collected in a psychological experiment

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

dealiasing techniques for high order spectral element methods on regular and irregular grids high order methods are becoming increasingly attractive in both academia and industry especially in the context of computational fluid dynamics however before they can be more widely adopted issues such as lack of robustness in terms of numerical stability need to be addressed particularly when treating industrial type problems where challenging geometries and a wide range of physical scales typically due to high reynolds numbers need to be taken into account one source of instability is aliasing effects which arise from the nonlinearity of the underlying problem in this work we detail two dealiasing strategies based on the concept of consistent integration the first uses a localised approach which is useful when the nonlinearities only arise in parts of the problem the second is based on the more traditional approach of using a higher quadrature the main goal of both dealiasing techniques is to improve the robustness of high order spectral element methods thereby reducing aliasing driven instabilities we demonstrate how these two strategies can be effectively applied to both continuous and discontinuous discretisations where in the latter both volumetric and interface approximations must be considered we show the key features of each dealiasing technique applied to the scalar conservation law with numerical examples and we highlight the main differences in terms of implementation between continuous and discontinuous spatial discretisations

inference for deterministic simulation models the bayesian melding approach abstract deterministic simulation models are used in many areas of science engineering and policy making typically these are complex models that attempt to capture underlying mechanisms in considerable detail and they have many user specified inputs the inputs are often specified by some form of trial and error approach in which plausible values are postulated the corresponding outputs inspected and the inputs modified until plausible outputs are obtained here we address the issue of more formal inference for such models a probabilistic approach called bayesian synthesis was shown to suffer from the borel paradox according to which the results can depend on the parameterization of the model we propose a modified approach called bayesian melding which takes into full account information and uncertainty about both inputs and outputs to the model while avoiding the borel paradox this is done by recognizing the existence of two priors one implicit and one explicit on each input and output

on the eddy resolving capability of high order discontinuous galerkin approaches to implicit les under resolved dns of euler turbulence we present estimates of spectral resolution power for under resolved turbulent euler flows obtained with high order discontinuous galerkin dg methods the 1 rule based on linear dispersion diffusion analysis introduced by moura et al 2015 10 is here adapted for 3d energy spectra and validated through the inviscid taylor green vortex problem the 1 rule estimates the wavenumber beyond which numerical diffusion induces an artificial dissipation range on measured energy spectra as the original rule relies on standard upwinding different riemann solvers are tested very good agreement is found for solvers which treat the different physical waves in a consistent manner relatively good agreement is still found for simpler solvers the latter however displayed spurious features attributed to the inconsistent treatment of different physical waves it is argued that in the limit of vanishing viscosity such features might have a significant impact on robustness and solution quality the estimates proposed are regarded as useful guidelines for no model dg based simulations of free turbulence at very high reynolds numbers

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

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

approximating posterior distributions by mixtures kernel density estimation techniques are used to smooth simulated samples from importance sampling function approximations to posterior distributions resulting in revised approximations that are mixtures of standard parametric forms usually multivariate normal or t distributions adaptive refinement of such mixture approximations involves repeating this process to home in successively on the posterior in fairly low dimensional problems this provides a general and automatic method of approximating posteriors by mixtures so that marginal densities and other summaries may be easily computed

the maximal smoothing principle in density estimation abstract we propose a widely applicable method for choosing the smoothing parameters for nonparametric density estimators it has come to be realized in recent years e g see hall and marron 1987 scott and terrell 1987 that cross validation methods for finding reasonable smoothing parameters from raw data are of very limited practical value their sampling variability is simply too large the alternative discussed here the maximal smoothing principle suggests that we consider using the most smoothing that is consistent with the estimated scale of our data this greatly generalizes and exploits a phenomenon noted in terrell and scott 1985 that measures of scale tend to place upper bounds on the smoothing parameters that minimize asymptotic mean integrated squared error of density estimates such as histograms and frequency polygons the method avoids the extreme sampling variability of cross validation by using ordinary scale estimators such as the standard deviation and interquartile range which

additive cubic spline regression with dirichlet process mixture errors abstract the goal of this article is to develop a flexible bayesian analysis of regression models for continuous and categorical outcomes in the models we study covariate or regression effects are modeled additively by cubic splines and the error distribution that of the latent outcomes in the case of categorical data is modeled as a dirichlet process mixture we employ a relatively unexplored but attractive basis in which the spline coefficients are the unknown function ordinates at the knots we exploit this feature to develop a proper prior distribution on the coefficients that involves the first and second differences of the ordinates quantities about which one may have prior knowledge we also discuss the problem of comparing models with different numbers of knots or different error distributions through marginal likelihoods and bayes factors which are computed within the framework of chib 1995 as extended to dpm models by basu and chib 2003 the techniques are illustrated with simulated and real data

inferential aspects of the skew exponential power distribution when the analysis of real data indicates that normality assumptions are untenable more flexible models that cope with the most prevalent deviations from normality can be adopted in this context the skew exponential power sep distribution warrants special attention because it encompasses distributions having both heavy tails and skewness it allows likelihood inference and it includes the normal model as a special case this article concerns likelihood inference about the parameters of the sep family in particular the information matrix of the maximum likelihood estimators mles is obtained and finite sample properties of the estimators are investigated numerically special attention is given to the properties of the mles and likelihood ratio statistics when the data are drawn from a normal distribution because this case is relevant for using the sep distribution to test for normality application of the sep distribution in robust estimation problems is considered for both independent and depend

spatial eigenanalysis of spectral hp continuous galerkin schemes and their stabilisation via dg mimicking spectral vanishing viscosity for high reynolds number flows abstract this study considers the spatial eigensolution analysis of spectral hp continuous galerkin cg schemes complementing a recent work by moura et al 2016 15 which addressed cg s temporal analysis while the latter assumes periodic boundary conditions the spatial approach presumes inflow outflow type conditions and therefore provides insights for a different class of problems the linear advection diffusion problem is considered for a wide range of peclet numbers allowing for viscous effects at different intensities the inviscid linear advection case receives particular attention owing to the manifestation of peculiar characteristics previously observed for discontinuous galerkin dg schemes in the limit of strong over upwinding these effects are discussed in detail due to their potential to negatively affect solution quality and numerical stability of under resolved simulations at high reynolds numbers the spectral vanishing viscosity svv technique is subsequently considered as a natural stabilization strategy in the context of linear advection an optimization procedure is employed to match svv diffusion levels to those of dg at appropriate polynomial orders the resulting cg svv discretisations are tested against under resolved computations of spatially developing vortex dominated flows and display excellent robustness at high reynolds numbers along with superior eddy resolving characteristics at higher polynomial orders this highlights the importance of appropriate stabilization techniques to improve the potential of spectral hp cg methods for high fidelity simulations of transitional and turbulent flows including implicit les under resolved dns approaches

analysis of multivariate probit models summary this paper provides a practical simulation based bayesian and non bayesian analysis of correlated binary data using the multivariate probit model the posterior distribution is simulated by markov chain monte carlo methods and maximum likelihood estimates are obtained by a monte carlo version of the em algorithm a practical approach for the computation of bayes factors from the simulation output is also developed the methods are applied to a dataset with a bivariate binary response to a four year longitudinal dataset from the six cities study of the health effects of air pollution and to a sevenvariate binary response dataset on the labour supply of married women from the panel survey of income dynamics

stochastic volatility with leverage fast and efficient likelihood inference this paper is concerned with the bayesian analysis of stochastic volatility sv models with leverage specifically the paper shows how the often used kim et al 1998 stochastic volatility likelihood inference and comparison with arch models review of economic studies 65 361 393 method that was developed for sv models without leverage can be extended to models with leverage the approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten component mixture of bivariate normal distributions the resulting posterior distribution is summarized by mcmc methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure the overall procedure is fast and highly efficient we illustrate the ideas on daily returns of the tokyo stock price index finally extensions of the method are described for superposition models where the log volatility is made up of a linear combination of heterogenous and independent autoregressions and heavy tailed error distributions student and log normal

on the properties of energy stable flux reconstruction schemes for implicit large eddy simulation we begin by investigating the stability order of accuracy and dispersion and dissipation characteristics of the extended range of energy stable flux reconstruction e esfr schemes in the context of implicit large eddy simulation iles we proceed to demonstrate that subsets of the e esfr schemes are more stable than collocation nodal discontinuous galerkin methods recovered with the flux reconstruction approach frdg for marginally resolved iles simulations of the taylorgreen vortex these schemes are shown to have reduced dissipation and dispersion errors relative to frdg schemes of the same polynomial degree and simultaneously have increased courantfriedrichslewy cfl limits finally we simulate turbulent flow over an sd7003 aerofoil using two of the most stable e esfr schemes identified by the aforementioned taylorgreen vortex experiments results demonstrate that subsets of e esfr schemes appear more stable than the commonly used frdg method have increased cfl limits and are suitable for iles of complex turbulent flows on unstructured grids

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

quantile hydrologic model selection and model structure deficiency assessment 1 theory a theory for quantile based hydrologic model selection and model structure deficiency assessment is presented the paper demonstrates that the degree to which a model selection problem is constrained by the model structure measured by the lagrange multipliers of the constraints quantifies structural deficiency this leads to a formal definition of model structure deficiency or rigidity model structure deficiency introduces a bias in the prediction of an observed quantile which is often not equal across quantiles structure deficiency is therefore diagnosed when any two quantile predictions for a given model structure cross since unequal bias across quantiles result in quantile predictions crossing the analysis further suggests that the optimal value of quantile specific loss functions order different model structures by its structure deficiencies over a range of quantiles in addition to such novelties quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

computationally efficient nonparametric importance sampling the variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution a good choice is often hard to achieve especially for high dimensional integration problems nonparametric estimation of the optimal importance sampling distribution known as nonparametric importance sampling is a reasonable alternative to parametric approaches in this article nonparametric variants of both the self normalized and the unnormalized importance sampling estimator are proposed and investigated a common critique of nonparametric importance sampling is the increased computational burden compared with parametric methods we solve this problem to a large degree by utilizing the linear blend frequency polygon estimator instead of a kernel estimator mean square error convergence properties are investigated leading to recommendations for the efficient application of nonparametric importance sampling particularly we show that nonparametric importance sampling as

identification of mechanical properties of elastically restrained laminated composite plates using vibration data abstract a nondestructive evaluation method using vibration data to determine mechanical properties material and spring constants of elastically restrained laminated composite plates is presented the rayleigh ritz method in which a set of legendre s polynomials is adopted to approximate the plate deflection is used to determine the theoretical natural frequencies of the elastically restrained laminated composite plates a number of natural frequencies extracted from the impulse vibration test data of the laminated composite plates supported by elastic restraints at both the edges and centers of the plates are used in the present method to determine the mechanical properties of the plates the sum of the squared differences function which measures the differences between the experimentally and theoretically predicted natural frequencies of the elastically restrained laminated composite plates is established the identification of the plate mechanical properties is then formulated as a constrained minimization problem in which the mechanical properties are determined by making the sum of the squared differences function a global minimum the feasibility and accuracy of the proposed method are studied by means of several numerical examples on the mechanical properties identification of elastically restrained laminated composite plates with different layups made of various composite materials experimental investigation of the mechanical properties identification of several elastically restrained laminated composite plates has been performed to illustrate the applications of the present method it has been shown that the present method can produce good estimates of the mechanical properties of the elastically restrained laminated composite plates in an efficient and effective way

on monte carlo methods for estimating ratios of normalizing constants recently estimating ratios of normalizing constants has played an important role in bayesian computations applications of estimating ratios of normalizing constants arise in many aspects of bayesian statistical inference in this article we present an overview and discuss the current monte carlo methods for estimating ratios of normalizing constants then we propose a new ratio importance sampling method and establish its theoretical framework we find that the ratio importance sampling method can be better than the current methods for example the bridge sampling method meng and wong and the path sampling method gelman and meng in the sense of minimizing asymptotic relative mean square errors of estimators an example is given for illustrative purposes finally we present two special applications and the general implementation issues for estimating ratios of normalizing constants

simulation of underresolved turbulent flows by adaptive filtering using the high order discontinuous galerkin spectral element method scale resolving simulations of turbulent flows in complex domains demand accurate and efficient numerical schemes as well as geometrical flexibility for underresolved situations the avoidance of aliasing errors is a strong demand for stability for continuous and discontinuous galerkin schemes an effective way to prevent aliasing errors is to increase the quadrature precision of the projection operator to account for the non linearity of the operands polynomial dealiasing overintegration but this increases the computational costs extensively in this work we present a novel spatially and temporally adaptive dealiasing strategy by projection filtering we show this to be more efficient for underresolved turbulence than the classical overintegration strategy for this novel approach we discuss the implementation strategy and the indicator details show its accuracy and efficiency for a decaying homogeneous isotropic turbulence and the transitional taylor green vortex and compare it to the original overintegration approach and a state of the art variational multi scale eddy viscosity formulation

review papers recent developments in nonparametric density estimation abstract advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where re

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

local adaptive importance sampling for multivariate densities with strong nonlinear relationships abstract we consider adaptive importance sampling techniques that use kernel density estimates at each iteration as importance sampling functions these can provide more nearly constant importance weights and more precise estimates of quantities of interest than the sampling importance resampling algorithm when the initial importance sampling function is diffuse relative to the target we propose a new method that adapts to the varying local structure of the target when the target has unusual structure such as strong nonlinear relationships between variables this method provides estimates with smaller mean squared error than alternative methods

quantile regression methods for recursive structural equation models abstract two classes of quantile regression estimation methods for the recursive structural equation models of chesher 2003 identification in nonseparable models econometrica 71 1405 1441 are investigated a class of weighted average derivative estimators based directly on the identification strategy of chesher is contrasted with a new control variate estimation method the latter imposes stronger restrictions achieving an asymptotic efficiency bound with respect to the former class an application of the methods to the study of the effect of class size on the performance of dutch primary school students shows that i reductions in class size are beneficial for good students in language and for weaker students in mathematics ii larger classes appear beneficial for weaker language students and iii the impact of class size on both mean and median performance is negligible

on hydrological model complexity its geometrical interpretations and prediction uncertainty knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk this may be considered equivalent to minimizing an upper bound on prediction error defined here as the mathematical expectation of empirical risk in this paper we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time we demonstrate that hydrological model complexity as defined in the presented theoretical framework plays an important role in determining the upper bound the model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill posed we provide an algorithm for computing complexity of any arbitrary hydrological model we also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space the presented theory is applied to quantify complexities of two hydrological model structures sac sma and sixpar it detects that sac sma is indeed more complex than sixpar we also develop an algorithm to estimate the upper bound on prediction error which is applied on five different rainfall runoff model structures that vary in complexity we show that a model selection problem is stabilized by regularizing it with model complexity complexity regularized model selection yields models that are robust in predicting future but yet unseen data

bayesian analysis of the differences of count data paired count data usually arise in medicine when before and after treatment measurements are considered in the present paper we assume that the correlated paired count data follow a bivariate poisson distribution in order to derive the distribution of their difference the derived distribution is shown to be the same as the one derived for the difference of the independent poisson variables thus recasting interest on the distribution introduced by skellam using this distribution we remove correlation which naturally exists in paired data and we improve the quality of our inference by using exact distributions instead of normal approximations the zero inflated version is considered to account for an excess of zero counts bayesian estimation and hypothesis testing for the models considered are discussed an example from dental epidemiology is used to illustrate the proposed methodology

inference in semiparametric dynamic models for binary longitudinal data this article deals with the analysis of a hierarchical semiparametric model for dynamic binary longitudinal responses the main complicating components of the model are an unknown covariate function and serial correlation in the errors existing estimation methods for models with these features are of o n3 where n is the total number of observations in the sample therefore nonparametric estimation is largely infeasible when the sample size is large as in typical in the longitudinal setting here we propose a new o n markov chain monte carlo based algorithm for estimation of the nonparametric function when the errors are correlated thus contributing to the growing literature on semiparametric and nonparametric mixed effects models for binary data in addition we address the problem of model choice to enable the formal comparison of our semiparametric model with competing parametric and semiparametric specifications the performance of the methods is illustrated with detailed studies involving simul

discretized and interpolated kernel density estimates abstract the kernel estimate of a probability density function inherits its smoothness properties from the kernel density chosen by the investigator nevertheless for computational and especially graphical reasons exact kernel density estimates are often presented in piecewise constant discretized or piecewise linear interpolated form using the exact estimate only at some grid of points the asymptotic integrated mean squared error properties of these modifications are studied it is seen that discretization may adversely affect the order of magnitude of this risk criterion so care needs to be taken in practice to limit the degree of discretization employed this roughness effect essentially disappears when interpolation is used instead then it takes a remarkably coarse grid to result in more than a negligible deterioration in the estimate s performance data discretization prior to applying the kernel density estimation prescription is also addressed such prebinning does not affect the smoot

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

linear dispersion diffusion analysis and its application to under resolved turbulence simulations using discontinuous galerkin spectral hp methods we investigate the potential of linear dispersion diffusion analysis in providing direct guidelines for turbulence simulations through the under resolved dns sometimes called implicit les approach via spectral hp methods the discontinuous galerkin dg formulation is assessed in particular as a representative of these methods we revisit the eigensolutions technique as applied to linear advection and suggest a new perspective to the role of multiple numerical modes peculiar to spectral hp methods from this new perspective secondary eigenmodes are seen to replicate the propagation behaviour of a primary mode so that dg s propagation characteristics can be obtained directly from the dispersion diffusion curves of the primary mode numerical dissipation is then appraised from these primary eigencurves and its effect over poorly resolved scales is quantified within this scenario a simple criterion is proposed to estimate dg s effective resolution in terms of the largest wavenumber it can accurately resolve in a given hp approximation space also allowing us to present points per wavelength estimates typically used in spectral and finite difference methods although strictly valid for linear advection the devised criterion is tested against 1d burgers turbulence and found to predict with good accuracy the beginning of the dissipation range on the energy spectra of under resolved simulations the analysis of these test cases through the proposed methodology clarifies why and how the dg formulation can be used for under resolved turbulence simulations without explicit subgrid scale modelling in particular when dealing with communication limited hardware which forces one to consider the performance for a fixed number of degrees of freedom the use of higher polynomial orders along with moderately coarser meshes is shown to be the best way to translate available degrees of freedom into resolution power

eigensolution analysis of spectral hp continuous galerkin approximations to advection diffusion problems this study addresses linear dispersion diffusion analysis for the spectral hp continuous galerkin cg formulation in one dimension first numerical dispersion and diffusion curves are obtained for the advection diffusion problem and the role of multiple eigencurves peculiar to spectral hp methods is discussed from the eigencurves behaviour we observe that cg might feature potentially undesirable non smooth dispersion diffusion characteristics for under resolved simulations of problems strongly dominated by either convection or diffusion subsequently the linear advection equation augmented with spectral vanishing viscosity svv is analysed dispersion and diffusion characteristics of cg with svv based stabilization are verified to display similar non smooth features in flow regions where convection is much stronger than dissipation or vice versa owing to a dependency of the standard svv operator on a local peclet number first a modification is proposed to the traditional svv scaling that enforces a globally constant peclet number so as to avoid the previous issues in addition a new svv kernel function is suggested and shown to provide a more regular behaviour for the eigencurves along with a consistent increase in resolution power for higher order discretizations as measured by the extent of the wavenumber range where numerical errors are negligible the dissipation characteristics of cg with the svv modifications suggested are then verified to be broadly equivalent to those obtained through upwinding in the discontinuous galerkin dg scheme nevertheless for the kernel function proposed the full upwind dg scheme is found to have a slightly higher resolution power for the same dissipation levels these results show that improved cg svv characteristics can be pursued via different kernel functions with the aid of optimization algorithms

monte carlo approximations in bayesian decision theory abstract in decision making problems the bayesian action and its posterior expected loss usually cannot be obtained analytically in this article we study a monte carlo method for approximating the bayesian action and its posterior expected loss the monte carlo approximation to the bayesian action is obtained through a approximating the posterior expected loss function by using the monte carlo integration method and b searching the minimum of the approximated posterior expected loss function as the monte carlo sample size diverges to infinity the monte carlo approximations are shown to be convergent in general situations the rates of the convergence are also obtained under some regularity conditions on the loss function two accuracy measures of the monte carlo approximations are proposed some examples are presented for illustration

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

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

improvement of a large analytical model using test data a method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure the method directly identifies without iteration a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements an application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure the resulting changes in the model are judged to be small compared to expectations of error in the analysis thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics in addition it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structure nomenclature analytical matrix matrix of changes identity matrix full improved stiffness and mass matrices n x n full analytical k m matrices n x n partitions of ka ma corresponding to test coordinates partitions of ka ma corresponding to coupling elements partitions of ka ma corresponding to unmea sured coordinates number of measured modes number of degrees of freedom in the model measures of changes eqs 15 17 matrix norm sum of the squares of all the elements rectangular modal matrix normalized n x m th mode th column of measured and unmeasured partitions of diagonal matrix of measured natural frequencies m xm natural frequency of th mode 12 17 sum of the squares of all elements of matrix

statistical models for overdispersion in the frequency of peaks over threshold data for a flow series 1 in a peaks over threshold analysis of a series of river flows a sufficiently high threshold is used to extract the peaks of independent flood events this paper reviews existing and proposes new statistical models for both the annual counts of such events and the process of event peak times the most common existing model for the process of event times is a homogeneous poisson process this model is motivated by asymptotic theory however empirical evidence suggests that it is not the most appropriate model since it implies that the mean and variance of the annual counts are the same whereas the counts appear to be overdispersed i e have a larger variance than mean this paper describes how the homogeneous poisson process can be extended to incorporate time variation in the rate at which events occur and so help to account for overdispersion in annual counts through the use of regression and mixed models the implications of these new models on the implied probability distribution of the annual maxima are also discussed the models are illustrated using a historical flow series from the river thames at kingston

monte carlo state space likelihoods by weighted posterior kernel density estimation maximum likelihood estimation and likelihood ratio tests for nonlinear non gaussian state space models require numerical integration for likelihood calculations several methods including monte carlo mc expectation maximization mc likelihood ratios direct mc integration and particle filter likelihoods are inefficient for the motivating problem of stage structured population dynamics models in experimental settings an mc kernel likelihood mckl method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of bayesian posteriors mckl is derived by using bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals mc error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed zooming in on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant based approximation of mode bias a simulated example show

dispersion and dissipation properties of the 1d spectral volume method and application to a p multigrid algorithm in this article the wave propagation properties of the 1d spectral volume method are studied through analysis of the fourier footprint of the schemes a p multigrid algorithm for the spectral volume method is implemented restriction and prolongation operators are discussed and the efficiency of the smoothing operators is analyzed the results are verified for simple 1d advection problems and for a quasi 1d euler flow it is shown that a significant decrease in computational effort is possible with the p multigrid algorithm

two stage importance sampling with mixture proposals for importance sampling is multiple proposals can be combined to address different aspects of a target distribution there are various methods for is with multiple proposals including hesterberg s stratified is estimator owen and zhou s regression estimator and tan s maximum likelihood estimator for the problem of efficiently allocating samples to different proposals it is natural to use a pilot sample to select the mixture proportions before the actual sampling and estimation however most current discussions are in an empirical sense for such a two stage procedure in this article we establish a theoretical framework of applying the two stage procedure for various methods including the asymptotic properties and the choice of the pilot sample size by our simulation studies these two stage estimators can outperform estimators with naive choices of mixture proportions furthermore while owen and zhou s and tan s estimators are designed for estimating normalizing constants we extend their usa

quantile hydrologic model selection and model structure deficiency assessment 2 applications quantile hydrologic model selection and structure deficiency assessment is applied in three case studies the performance of quantile model selection problem is rigorously evaluated using a model structure on the french broad river basin data set the case study shows that quantile model selection encompasses model selection strategies based on summary statistics and that it is equivalent to maximum likelihood estimation under certain likelihood functions it also shows that quantile model predictions are fairly robust the second case study is of a parsimonious hydrological model for dry land areas in western india the case study shows that an intuitive improvement in the model structure leads to reductions in asymmetric loss function values for all considered quantiles the asymmetric loss function is a quantile specific metric that is minimized to obtain a quantile specific prediction model the case study provides evidence that a quantile wise reduction in the asymmetric loss function is a robust indicator of model structure improvement finally a case study of modeling daily streamflow for the guadalupe river basin is presented a model structure that is least deficient for the study area is identified from nine different model structures based on quantile structural deficiency assessment the nine model structures differ in interception routing overland flow and base flow conceptualizations the three case studies suggest that quantile model selection and deficiency assessment provides a robust mechanism to compare deficiencies of different model structures and helps to identify better model structures in addition to its novelty quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

a formal likelihood function for parameter and predictive inference of hydrologic models with correlated heteroscedastic and non gaussian errors estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions residual errors are often assumed to be independent and to be adequately described by a gaussian probability distribution with a mean of zero and a constant variance here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed a formal generalized likelihood function is presented which extends the applicability of previously used likelihood functions to situations where residual errors are correlated heteroscedastic and non gaussian with varying degrees of kurtosis and skewness the approach focuses on a correct statistical description of the data and the total model residuals without separating out various error sources application to bayesian uncertainty analysis of a conceptual rainfall runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors when applied to daily rainfall runoff data from a humid basin we find that 1 residual errors are much better described by a heteroscedastic first order auto correlated error model with a laplacian distribution function characterized by heavier tails than a gaussian distribution and 2 compared to a standard least squares approach proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference application to daily rainfall runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that 1 multiplicative bias factors can be used to compensate for some of the largest errors and 2 a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near zero flows we conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well

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

variable selection and functional form uncertainty in cross country growth regressions regression analyses of cross country economic growth data are complicated by two main forms of model uncertainty the uncertainty in selecting explanatory variables and the uncertainty in specifying the functional form of the regression function most discussions in the literature address these problems independently yet a joint treatment is essential we present a new framework that makes such a joint treatment possible using flexible nonlinear models specified by gaussian process priors and addressing the variable selection problem by means of bayesian model averaging using this framework we extend the linear model to allow for parameter heterogeneity of the type suggested by new growth theory while taking into account the uncertainty in selecting explanatory variables controlling for variable selection uncertainty we confirm the evidence in favor of parameter heterogeneity presented in several earlier studies however controlling for functional form uncertainty we find that the effects of many of the explanatory variables identified in the literature are not robust across countries and variable selections

multi objective parameter identification of euler bernoulli beams under axial load abstract identification of physical parameters of the partial differential equation describing transverse vibrations of an axially loaded euler bernoulli beam ebb is proposed via a multi objective optimization formulation and solved by a genetic algorithm conflicting objectives such as performance and stability are specifically formulated and optimized simultaneously stability is quantified in terms of the solution s time growth factor physical parameter sets in the resulting pareto front approximation represent best trade offs with respect to the multiple objectives to compute output error performance objectives the ebb equation is discretized via finite differences in space and time and reformulated to a state space system identifiability is verified by checking regularity of the so called fisher information matrix the identification methodology is capable of determining material parameters including damping as well as the axial load from few spatially concentrated measurements its features are demonstrated and successfully validated on specific simulation data and measurement data obtained from a laboratory testbed

bayesian model choice via markov chain monte carlo methods summary markov chain monte carlo mcmc integration methods enable the fitting of models of virtually unlimited complexity and as such have revolutionized the practice of bayesian data analysis however comparison across models may not proceed in a completely analogous fashion owing to violations of the conditions sufficient to ensure convergence of the markov chain in this paper we present a framework for bayesian model choice along with an mcmc algorithm that does not suffer from convergence difficulties our algorithm applies equally well to problems where only one model is contemplated but its proper size is not known at the outset such as problems involving integer valued parameters multiple changepoints or finite mixture distributions we illustrate our approach with two published examples

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea