a time series ddp for functional proteomics profiles using a new type of array technology the reverse phase protein array rppa we measure time course protein expression for a set of selected markers that are known to co regulate biological functions in a pathway structure to accommodate the complex dependent nature of the data including temporal correlation and pathway dependence for the protein markers we propose a mixed effects model with temporal and protein specific components we develop a sequence of random probability measures rpm to account for the dependence in time of the protein expression measurements marginally for each rpm we assume a dirichlet process dp model the dependence is introduced by defining multivariate beta distributions for the unnormalized weights of the stick breaking representation we also acknowledge the pathway dependence among proteins via a conditionally autoregressive car model applying our model to the rppa data we reveal a pathway dependent functional profile for the set of proteins as well as marginal expression profiles over time for individual markers

order based dependent dirichlet processes in this article we propose a new framework for bayesian nonparametric modeling with continuous covariates in particular we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick breaking representation we focus mostly on the class of random distributions that induces a dirichlet process at each covariate value we derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering two main constructions with analytically known correlation structures are proposed practical and efficient computational methods are introduced we apply our framework through mixtures of these processes to regression modeling the modeling of stochastic volatility in time series data and spatial geostatistical modeling

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

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

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

multiple imputation of missing categorical and continuous values via bayesian mixture models with local dependence abstractwe present a nonparametric bayesian joint model for multivariate continuous and categorical variables with the intention of developing a flexible engine for multiple imputation of missing values the model fuses dirichlet process mixtures of multinomial distributions for categorical variables with dirichlet process mixtures of multivariate normal distributions for continuous variables we incorporate dependence between the continuous and categorical variables by 1 modeling the means of the normal distributions as component specific functions of the categorical variables and 2 forming distinct mixture components for the categorical and continuous data with probabilities that are linked via a hierarchical model this structure allows the model to capture complex dependencies between the categorical and continuous data with minimal tuning by the analyst we apply the model to impute missing values due to item nonresponse in an evaluation of the redesign of the survey of income and program partic

a bayesian population model with hierarchical mixture priors applied to blood count data abstract population pharmacokinetic and pharmacodynamic studies require analyzing nonlinear growth curves fit to multiple measurements from study subjects we propose a class of nonlinear population models with nonparametric second stage priors for analyzing such data the proposed models apply a flexible class of mixtures to implement the nonparametric second stage the discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles i e blood counts measured over time of cancer patients undergoing chemotherapy we describe a full posterior analysis in a bayesian framework this includes prediction of future observations profiles and end points for new patients estimation of the mean response function for observed individuals and inference on population characteristics the mixture model is specified and given a hyperprior distribution by means of a dirichlet processes prior on the mixing measure estimation is implemented by a combination of various m

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

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

bayesian isotonic density regression density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions and are well supported in many applications a rich variety of bayesian methods have been proposed for density regression but it is not clear whether such priors have full support so that any true data generating model can be accurately approximated this article develops a new class of density regression models that incorporate stochastic ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor theory is developed showing large support methods are developed for hypothesis testing with posterior computation relying on a simple gibbs sampler frequentist properties are illustrated in a simulation study and an epidemiology application is considered

theory and numerical analysis for exact distributions of functionals of a dirichlet process the distribution of a mean or more generally of a vector of means of a dirichlet process is considered some characterizing aspects of this paper are i a review of a few basic results providing new formulations free from many of the extra assumptions considered to date in the literature and giving essentially new simpler and more direct proofs ii new numerical evaluations with any prescribed error of approximation of the distribution at issue iii a new form for the law of a vector of means moreover as applications of these results we give iv the sharpest condition sufficient for the distribution of a mean to be symmetric v forms for the probability distribution of the variance of the dirichlet random measure vi some hints for determining the finite dimensional distributions of a random function connected with bayesian methods for queuing models

analysis and design of variable structure systems using a geometric approach multivariable variable structure systems in the sliding mode are studies using a geometric approach the properties of system order reduction and disturbance rejection are proved using projector theory new design methods for the choice of switching hyperplanes are derived for the closed loop eigenvalue eigenvector assignment problem

controlling the reinforcement in bayesian non parametric mixture models summary the paper deals with the problem of determining the number of components in a mixture model we take a bayesian non parametric approach and adopt a hierarchical model with a suitable non parametric prior for the latent structure a commonly used model for such a problem is the mixture of dirichlet process model here we replace the dirichlet process with a more general non parametric prior obtained from a generalized gamma process the basic feature of this model is that it yields a partition structure for the latent variables which is of gibbs type this relates to the well known exchangeable product partition models if compared with the usual mixture of dirichlet process model the advantage of the generalization that we are examining relies on the availability of an additional parameter belonging to the interval 0 1 it is shown that such a parameter greatly influences the clustering behaviour of the model a value of that is close to 1 generates a large number of clusters most of which are of small size then a reinforcement mechanism which is driven by acts on the mass allocation by penalizing clusters of small size and favouring those few groups containing a large number of elements these features turn out to be very useful in the context of mixture modelling since it is difficult to specify a priori the reinforcement rate it is reasonable to specify a prior for hence the strength of the reinforcement mechanism is controlled by the data

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

a semiparametric bayesian model for randomised block designs summary a model is proposed for a bayesian semiparametric analysis of randomised block experiments the model is a hierarchical model in which a dirichlet process is inserted at the middle stage for the distribution of the block effects this model allows an arbitrary distribution of block effects and it results in effective estimates of treatment contrasts block effects and the distribution of block effects an effective computational strategy is presented for describing the posterior distribution

hochschild homology of affine hecke algebras abstract let h h r q be an affine hecke algebra with complex possibly unequal parameters q which are not roots of unity we compute the hochschild and the cyclic homology of h it turns out that these are independent of q and that they admit an easy description in terms of the extended quotient of a torus by a weyl group both of which are canonically associated to the root datum r for positive q we also prove that the representations of the family of algebras h r q c come in families which depend analytically on analogous results are obtained for graded hecke algebras and for schwartz completions of affine hecke algebras

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

nonparametric bayes testing of changes in a response distribution with an ordinal predictor in certain biomedical studies one may anticipate changes in the shape of a response distribution across the levels of an ordinal predictor for instance in toxicology studies skewness and modality might change as dose increases to address this issue we propose a bayesian nonparametric method for testing for distribution changes across an ordinal predictor using a dynamic mixture of dirichlet processes we allow the response distribution to change flexibly at each level of the predictor in addition by assigning mixture priors to the hyperparameters we can obtain posterior probabilities of no effect of the predictor and identify the lowest dose level for which there is an appreciable change in distribution the method also provides a natural framework for performing tests across multiple outcomes we apply our method to data from a genotoxicity experiment

the multivariate beta process and an extension of the polya tree model we introduce a novel stochastic process that we term the multivariate beta process the process is defined for modelling dependent random probabilities and has beta marginal distributions we use this process to define a probability model for a family of unknown distributions indexed by covariates the marginal model for each distribution is a polya tree prior an important feature of the proposed prior is the easy centring of the nonparametric model around any parametric regression model we use the model to implement nonparametric inference for survival distributions the nonparametric model that we introduce can be adopted to extend the support of prior distributions for parametric regression models

estimation of sliding mode domains of uncertain variable structure systems with bounded controllers the problem of estimating regions of asymptotic stability ras of uncertain dynamical systems with bounded controllers and the sliding model requirement is discussed the notion of combining different lyapunov functions is utilized different lyapunov functions are found and for each lyapunov function an estimate of the ras is found different regions are combined in order to find an improved ras the combined region is not in general a convex region and cannot be found analytically by using just a single lyapunov function a class of uncertain linear time invariant multivariable control systems is considered and a transformation for decoupling the system into two subsystems is used the transformation simplifies the ras estimation problem stability domains are estimated for a linear variable structure control system with sliding mode performance in the case of a discontinuous bounded controller

minimally informative prior distributions for non parametric bayesian analysis summary we address the problem of how to conduct a minimally informative non parametric bayesian analysis the central question is how to devise a model so that the posterior distribution satisfies a few basic properties the concept of local mass provides the key to the development of the limiting dirichlet process model this model is then used to provide an engine for inference in the compound decision problem and for multiple comparisons inference in a one way analysis of variance setting our analysis in this setting may be viewed as a limit of the analyses that were developed by escobar and by gopalan and berry computations for the analysis are described and the predictive performance of the model is compared with that of mixture of dirichlet processes models

bayesian nonparametric estimation for incomplete data via successive substitution sampling in the problem of estimating an unknown distribution function f in the presence of censoring one can use a nonparametric estimator such as the kaplan meier estimator or one can consider parametric modeling there are many situations where physical reasons indicate that a certain parametric model holds approximately in these cases a nonparametric estimator may be very inefficient relative to a parametric estimator on the other hand if the parametric model is only a crude approximation to the actual model then the parametric estimator may perform poorly relative to the nonparametric estimator and may even be inconsistent the bayesian paradigm provides a reasonable framework for this problem in a bayesian approach one would try to put a prior distribution on f that gives most of its mass to small neighborhoods of the entire parametric family we show that certain priors based on the dirichlet process prior can be used to accomplish this for these priors the posterior distribution of f given the censored data appears to be analytically intractable we provide a method for approximating this posterior distribution through the use of a successive substitution sampling algorithm we also show convergence of the algorithm

marginal likelihood and bayes factors for dirichlet process mixture models we present a method for comparing semiparametric bayesian models constructed under the dirichlet process mixture dpm framework with alternative semiparameteric or parameteric bayesian models a distinctive feature of the method is that it can be applied to semiparametric models containing covariates and hierarchical prior structures and is apparently the first method of its kind formally the method is based on the marginal likelihood estimation approach of chib 1995 and requires estimation of the likelihood and posterior ordinates of the dpm model at a single high density point an interesting computation is involved in the estimation of the likelihood ordinate which is devised via collapsed sequential importance sampling extensive experiments with synthetic and real data involving semiparametric binary data regression models and hierarchical longitudinal mixed effects models are used to illustrate the implementation performance and applicability of the method

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

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

bayesian density regression summary the paper considers bayesian methods for density regression allowing a random probability distribution to change flexibly with multiple predictors the conditional response distribution is expressed as a non parametric mixture of regression models with the mixture distribution changing with predictors a class of weighted mixture of dirichlet process priors is proposed for the uncountable collection of mixture distributions it is shown that this specification results in a generalized polya urn scheme which incorporates weights that are dependent on the distance between subjects predictor values to allow local dependence in the mixture distributions we propose a kernel based weighting scheme a gibbs sampling algorithm is developed for posterior computation the methods are illustrated by using simulated data examples and an epidemiologic application

the collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem abstract this article describes a method of grouping and collapsing in using the gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial the norms of the forward operators associated with the corresponding nonreversible markov chains are used to discriminate among different simulation schemes when applied to bayesian missing data problems the idea of collapsing suggests skipping the steps of sampling parameter s values in standard data augmentation by doing this we obtain a predictive update version of the gibbs sampler a procedure of calculating the posterior odds ratio via the collapsed gibbs sampler when incomplete observations are involved is presented as an illustration of possible applications three examples along with a bayesian treatment for identifying common protein binding sites in unaligned dna sequences are provided

regression density estimation using smooth adaptive gaussian mixtures we model a regression density flexibly so that at each value of the covariates the density is a mixture of normals with the means variances and mixture probabilities of the components changing smo

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

isomorphisms between affine hecke algebras of type a2 abstract we prove that two affine hecke algebras h p and h q of type a 2 with nonzero parameters p q c are not isomorphic whenever p q and p q 1 theorem 3 1 however they are isomorphic locally more precisely we prove that the quotient algebras h s q and h t p are isomorphic provided that n s q n t p for type a 2 theorem 2 4

fully nonparametric regression for bounded data using dependent bernstein polynomials abstractwe propose a novel class of probability models for sets of predictor dependent probability distributions with bounded domain the proposal extends the dirichlet bernstein prior for single density estimation by using dependent stick breaking processes a general model class and two simplified versions are discussed in detail appealing theoretical properties such as continuity association structure marginal distribution large support and consistency of the posterior distribution are established for all models the behavior of the models is illustrated using simulated and real life data the simulated data are also used to compare the proposed methodology to existing methods supplementary materials for this article are available online

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

bayesian nonparametric longitudinal data analysis abstractpractical bayesian nonparametric methods have been developed across a wide variety of contexts here we develop a novel statistical model that generalizes standard mixed models for longitudinal data that include flexible mean functions as well as combined compound symmetry cs and autoregressive ar covariance structures ar structure is often specified through the use of a gaussian process gp with covariance functions that allow longitudinal data to be more correlated if they are observed closer in time than if they are observed farther apart we allow for ar structure by considering a broader class of models that incorporates a dirichlet process mixture dpm over the covariance parameters of the gp we are able to take advantage of modern bayesian statistical methods in making full predictive inferences and about characteristics of longitudinal profiles and their differences across covariate combinations we also take advantage of the generality of our model which provides for estimation

a bayesian hierarchical model for related densities by using polya trees bayesian hierarchical models are used to share information between related samples and to obtain more accurate estimates of sample level parameters common structure and variation between samples when the parameter of interest is the distribution or density of a continuous variable a hierarchical model for continuous distributions is required various such models have been described in the literature using extensions of the dirichlet process and related processes typically as a distribution on the parameters of a mixing kernel we propose a new hierarchical model based on the polya tree which enables direct modelling of densities and enjoys some computational advantages over the dirichlet process the polya tree also enables more flexible modelling of the variation between samples providing more informed shrinkage and permitting posterior inference on the dispersion function which quantifies the variation between sample densities we also show how the model can be extended to cluster samples in situations where the observed samples are believed to have been drawn from several latent populations

properties of min max controllers in uncertain dynamical systems we discuss properties of min max controllers previously obtained for uncertain dynamical systems in particular we present a new model for switching action and re examine asymptotic stability we demonstrate the attractiveness of switching surfaces and comment on the insensitivity of solutions in those surfaces to the uncertainty

bayesian regression with nonparametric heteroskedasticity abstract this paper studies large sample properties of a semiparametric bayesian approach to inference in a linear regression model the approach is to model the distribution of the regression error term by a normal distribution with the variance that is a flexible function of covariates the main result of the paper is a semiparametric bernstein von mises theorem under misspecification even when the distribution of the regression error term is not normal the posterior distribution of the properly recentered and rescaled regression coefficients converges to a normal distribution with the zero mean and the variance equal to the semiparametric efficiency bound

autoregressive mixture models for dynamic spatial poisson processes application to tracking intensity of violent crime this article develops a set of tools for smoothing and prediction with dependent point event patterns the methodology is motivated by the problem of tracking weekly maps of violent crime events but is designed to be straightforward to adapt to a wide variety of alternative settings in particular a bayesian semiparametric framework is introduced for modeling correlated time series of marked spatial poisson processes the likelihood is factored into two independent components the set of total integrated intensities and a series of process densities for the former it is assumed that poisson intensities are realizations from a dynamic linear model in the latter case a novel class of dependent stick breaking mixture models are proposed to allow nonparametric density estimates to evolve in discrete time this a simple and flexible new model for dependent random distributions is based on autoregressive time series of marginally beta random variables applied as correlated stick breaking proportions the

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

rao blackwellisation of sampling schemes summary this paper proposes a post simulation improvement for two common monte carlo methods the accept reject and metropolis algorithms the improvement is based on a rao blackwellisation method that integrates over the uniform random variables involved in the algorithms and thus post processes the standard estimators we show how the rao blackwellised versions of these algorithms can be implemented and through examples illustrate the improvement in variance brought by these new procedures we also compare the improved version of the metropolis algorithm with ordinary and rao blackwellised importance sampling procedures for independent and general metropolis set ups

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

retrospective markov chain monte carlo methods for dirichlet process hierarchical models inference for dirichlet process hierarchical models is typically performed using markov chain monte carlo methods which can be roughly categorized into marginal and conditional methods the former integrate out analytically the infinite dimensional component of the hierarchical model and sample from the marginal distribution of the remaining variables using the gibbs sampler conditional methods impute the dirichlet process and update it as a component of the gibbs sampler since this requires imputation of an infinite dimensional process implementation of the conditional method has relied on finite approximations in this paper we show how to avoid such approximations by designing two novel markov chain monte carlo algorithms which sample from the exact posterior distribution of quantities of interest the approximations are avoided by the new technique of retrospective sampling we also show how the algorithms can obtain samples from functionals of the dirichlet process the marginal and the conditional methods are compared and a careful simulation study is included which involves a non conjugate model different datasets and prior specifications

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

robust control synthesis for uncertain nonlinear dynamical systems this paper addresses the problem of robust output feedback controller design for uncertain and nonlinear dynamic systems first a robust state feedback nonlinear control law is synthesized this control strategy practically stabilizes the closed loop system then a state estimator for the nonlinear uncertain plant is designed and its performance analyzed finally the control law and the estimator are combined and the practical stability region is estimated the results are illustrated by their application to a benchmark problem for robust control design proposed by wie and bernstein 1990

stick breaking autoregressive processes this paper considers the problem of defining a time dependent nonparametric prior for use in bayesian nonparametric modelling of time series a recursive construction allows the definition of priors whose marginals have a general stick breaking form the processes with poisson dirichlet and dirichlet process marginals are investigated in some detail we develop a general conditional markov chain monte carlo mcmc method for inference in the wide subclass of these models where the parameters of the marginal stick breaking process are nondecreasing sequences we derive a generalised polya urn scheme type representation of the dirichlet process construction which allows us to develop a marginal mcmc method for this case we apply the proposed methods to financial data to develop a semi parametric stochastic volatility model with a time varying nonparametric returns distribution finally we present two examples concerning the analysis of regional gdp and its growth

posterior simulation in countable mixture models for large datasets mixture models or convex combinations of a countable number of probability distributions offer an elegant framework for inference when the population of interest can be subdivided into latent clusters having random characteristics that are heterogeneous between but homogeneous within the clusters traditionally the different kinds of mixture models have been motivated and analyzed from very different perspectives and their common characteristics have not been fully appreciated the inferential techniques developed for these models usually necessitate heavy computational burdens that make them difficult if not impossible to apply to the massive data sets increasingly encountered in real world studies this paper introduces a flexible class of models called generalized polya urn gpu processes many common mixture models including finite mixtures hidden markov models and dirichlet processes are obtained as special cases of gpu processes other important special cases include finite dimensional

semiparametric bayesian density estimation with disparate data sources a meta analysis of global childhood undernutrition undernutrition resulting in restricted growth and quantified here using height for age z scores is an important contributor to childhood morbidity and mortality since all levels of mild moderate and severe undernutrition are of clinical and public health importance it is of interest to estimate the shape of the z scores distributions we present a finite normal mixture model that uses data on 4 3 million children to make annual country specific estimates of these distributions for under 5 year old children in the world s 141 low and middle income countries between 1985 and 2011 we incorporate both individual level data when available as well as aggregated summary statistics from studies whose individual level data could not be obtained we place a hierarchical bayesian probit stick breaking model on the mixture weights the model allows for nonlinear changes in time and it borrows strength in time in covariates and within and across regional country clusters to make estimates where data are

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions