reconstruction of blurred orbits under finite resolution techniques to retrieve information about orbits of dynamical systems lost in the process of making measurements due to discretization sampling or noise are developed a general method of reprocessing the experimentally obtained data to effectively increase its information content the accuracy of measurements is proposed potential applications include many areas of applied mathematics such as inverse problems time series analysis ill posed problems etc the method can also be used to help construct new highly accurate measuring devices

bayesian inferences on umbrella orderings in regression applications with categorical predictors interest often focuses on comparing the null hypothesis of homogeneity to an ordered alternative this article proposes a bayesian approach for addressing this problem in the setting of normal linear and probit regression models the regression coefficients are assigned a conditionally conjugate prior density consisting of mixtures of point masses at 0 and truncated normal densities with a possibly unknown changepoint parameter included to accommodate umbrella ordering two strategies of prior elicitation are considered 1 a bayesian bonferroni approach in which the probability of the global null hypothesis is specified and local hypotheses are considered independent and 2 an approach which treats these probabilities as random a single gibbs sampling chain can be used to obtain posterior probabilities for the different hypotheses and to estimate regression coefficients and predictive quantities either by model averaging or under the preferred hypothesis the methods are applied to data from a carcinogenesis study

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

additive isotonic regression models in epidemiology stone s method for assessing disease risk around a point source through isotonic regression is routinely used in spatial epidemiology it is useful in situations where the relationship of risk with exposure distance being commonly used as a surrogate variable is assumed monotonic but otherwise of unknown form this paper extends this method to non spatial epidemiology where typically two or more risk factors are present the methodology described is based on the additive isotonic model approach of bacchetti versions appropriate to count poisson data and case control binomial data are described in both cases adjustment for covariates is incorporated and a monte carlo method of hypothesis testing and interval estimation is presented the methodology is illustrated through a case control example concerning the analysis of the possible effect of preconceptional external ionizing radiation doses on the sex ratio at birth among children of fathers working at the sellafield nuclear installation cumbria u k

nonparametric bayesian bioassay with prior constraints on the shape of the potency curve summary we consider the problem of implementing nonparametric bayesian analysis of bioassay problems when the prior constrains the form of the potency curve for example to be convex concave or ogive sampling based approaches to calculating posterior features of interest are detailed and illustrated extensions to prior constraints on hazard rates are outlined

analysis on binary responses with ordered covariates and missing data summary we consider the situation of two ordered categorical variables and a binary outcome variable where one or both of the categorical variables may have missing values the goal is to estimate the probability of response of the outcome variable for each cell of the contingency table of categorical variables while incorporating the fact that the categorical variables are ordered the probability of response is assumed to change monotonically as each of the categorical variables changes level a probability model is used in which the response is binomial with parameters pij for each cell i j and the number of observations in each cell is multinomial estimation approaches that incorporate gibbs sampling with order restrictions on pij induced via a prior distribution two dimensional isotonic regression and multiple imputation to handle missing values are considered the methods are compared in a simulation study using a fully bayesian approach with a strong prior distribution to induce ordering can lead to large gains in efficiency but can also induce bias utilizing isotonic regression can lead to modest gains in efficiency while minimizing bias and guaranteeing that the order constraints are satisfied a hybrid of isotonic regression and gibbs sampling appears to work well across a variety of scenarios the methods are applied to a pancreatic cancer case control study with two biomarkers copyright q 2007 john wiley sons ltd

phase transitions and equilibrium measures in random matrix models the paper is devoted to a study of phase transitions in the hermitian random matrix models with a polynomial potential in an alternative equivalent language we study families of equilibrium measures on the real line in a polynomial external field the total mass of the measure is considered as the main parameter which may be interpreted also either as temperature or time our main tools are differentiation formulas with respect to the parameters of the problem and a representation of the equilibrium potential in terms of a hyperelliptic integral using this combination we introduce and investigate a dynamical system system of odes describing the evolution of families of equilibrium measures on this basis we are able to systematically derive a number of new results on phase transitions such as the local behavior of the system at all kinds of phase transitions as well as to review a number of known ones

bayesian covariance selection in generalized linear mixed models repeated measures and longitudinal data are commonly collected for analysis in epidemiology clinical trials biology sociology and economic sciences in such studies a response is measured repeatedly over time for each subject under study and the number and timing of the observations often varies among subjects in contrast to cross sectional studies that collect a single measurement per subject longitudinal studies have the extra complication of within subject dependence in the repeated measures such dependence can be thought to arise due to the impact of unmeasured predictors main effects of unmeasured predictors lead to variation in the average level of response among subjects while interactions with measured predictors lead to heterogeneity in the regression coefficients this justification has motivated random effects models which allow the intercept and slopes in a regression model to be subject specific random effects models are broadly useful for modeling of dependence not only for longitudinal data but also in multicenter studies meta analysis and functional data analysis

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

order restricted inferences in linear regression abstract regression analysis constitutes a large portion of the statistical repertoire in applications in cases where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem but in many applications we are interested in curve fitting with a simple parametric model to describe the structure of a system with some prior knowledge about the structure an important example of this occurs when the experimenter has a strong belief that the regression function changes monotonically with some or all of the predictor variables in a region of interest the analyses needed for statistical inferences under such constraints are nonstandard considering the present body of knowledge developed for unconstrained regression it will be an enormous task to derive the analogs of even a small fraction of this for the restricted case in this article we initiate the study with simple linear regression on a single variable the est

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

maximum likelihood estimation under order restrictions by the prior feedback method abstract algorithms for deriving isotonic regression estimators in order restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered we propose here an optimization method based on a sequence of formal bayes estimates whose variances converge to zero this method akin to simulated annealing can be applied universally that is as long as these bayes estimators can be derived by exact computation or markov chain monte carlo sampling approximation we then give an illustration of our method for two real life examples

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

extraction of dynamical equations from chaotic data abstract a method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise the equations facilitate calculation of fractal dimension lyapunov exponents and short term predictions the method is applied to data derived from numerical solutions of the logistic equation the henon equations with added noise the lorenz equations and the rossler equations

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

discrete time dynamical system under observational uncertainty abstract discrete time dynamical systems under observational uncertainty are studied as a result of the uncertainty points on an orbit are surrounded by uncertainty sets the problem of reconstructing the original orbit given the sequence of uncertainty sets is investigated the key property which makes the reconstruction possible is the sensitivity to initial conditions a general reconstructing algorithm is theoretically analyzed and experimentally tested on several low dimensional systems the technique is extended to coupled one dimensional maps with the goal of eventually developing retrospective techniques for partial differential equations exhibiting spatio temporal chaos provided the coupling strength remains small and the coupling term has bounded first derivatives it is conjectured that for dynamical systems with a positive liapunov exponent the observational uncertainty can be reduced exponentially with the length of the orbit used for reconstruction computer experiments with the coupled logistic map are consistent with this conjecture

bayesian nonparametric inference on stochastic ordering we consider bayesian inference about collections of unknown distributions subject to a partial stochastic ordering to address problems in testing of equalities between groups and estimation of group specific distributions we propose classes of restricted dependent dirichlet process priors these priors have full support in the space of stochastically ordered distributions and can be used for collections of unknown mixture distributions to obtain a flexible class of mixture models theoretical properties are discussed efficient methods are developed for posterior computation using markov chain monte carlo simulation and the methods are illustrated using data from a study of dna damage and repair

a simple approach to testing homogeneity of order constrained means abstract the likelihood ratio test for equality of partially ordered means first proposed by bartholomew is known to possess power characteristics that are generally superior to those of competing procedures a limitation of this test however is that the null distribution of the test statistic is heavily dependent on both the specific form of the order restriction and the group sample sizes it is not readily available for most orderings especially when the group sample sizes are unequal furthermore computation of the test statistics often involves intricate algorithms we propose a class of procedures based upon classical methods for combining independent tests these procedures are generally applicable and easily implemented a study of the power functions of the competing tests indicates that the power of the test based on fisher s combination method compares reasonably with that of the likelihood ratio test it is concluded that the procedure based on fisher s combination method is an effective

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

double scaling limit in random matrix models and a nonlinear hierarchy of differential equations we study the critical behaviour of a random hermitian one matrix model with nonsymmetric interaction at a critical point in which the eigenvalue density function has a zero of degree 2m m 1 inside a cut we prove that in the generic case m 1 the model exhibits a third order phase transition in temperature we formulate an ansatz for the double scaling limit of recurrence coefficients which is consistent with the quasiperiodic asymptotics of recurrence coefficients in the low temperature region and from this ansatz we derive the painleve ii hierarchy of ordinary differential equations for the recurrence coefficients in addition we derive an integral kernel which governs the double scaling limit of correlation functions

noise reduction finding the simplest dynamical system consistent with the data abstract a novel method is described for noise reduction in chaotic experimental data whose dynamics are low dimensional in addition we show how the approach allows experimentalists to use many of the same techniques that have been essential for the analysis of nonlinear systems of ordinary differential equations and difference equations

a class of bayesian shared gamma frailty models with multivariate failure time data nous proposons ici dans le cadre des donnees de survie une nouvelle classe de modeles a fragilite gamma partagee en appliquant la transformation de box cox a la fonction de hasard ainsi qu au produit du risque de base et de la fragilite cette nouvelle classe de modeles offre un large eventail de formes et relations entre la fonction de hasard et le risque de base et inclut en tant que cas particuliers le modele de cox usuel a fragilite gamma ainsi qu un nouveau modele additif a fragilite gamma de par la contrainte que le risque soit non negatif ce modele a fragilite gamma partagee presente un defi calculatoire dans le paradigme bayesien les distributions conjointes a priori sont definies par une distribution conditionnelle marginale ou la distribution conditionnelle est univariee cela permet d integrer les contraintes non lineaires sur les parametres la partie marginale de la distribution a priori quant a elle est libre de toute contrainte les distributions a priori permettent de programmer facilement l integralite des distributions conditionnelles requises pour l echantillonnage de gibbs tout en integrant les contraintes un jeu reel de donnees permet d illustrer cette classe de modeles a fragilite gamma partagee

construction and analysis of differential equations from experimental time series of oscillatory systems abstract we propose a novel method to derive an autonomous system of ordinary differential equations from an experimental time series this model describe quantitatively transient behaviour of a system with limit cycle dynamics and is simplified to an evolution equation for the amplitude and frequency the landau equation in addition the model is used for a qualitative prediction of the influence of periodic excitation on the experimental system using the van der pol transformation and floquet theory in particular the instability of the locking solution including the hopf bifurcation the intermittency scenario and the period doubling cascade is considered the method of constructing a differential equation from an experimental time signal is successfully applied to a velocity fluctuation of the laminar periodic wake behind a circular cylinder

problems in estimating dynamics from data abstract this paper discusses some difficulties in estimating dynamics from time delay embeddings of experimental data that can be characterized as low dimensional a new procedure is described to reduce noise by exploiting the properties of saddle periodic orbits on the reconstructed attractor

distributions on partitions point processes and the hypergeometric kernel we study a 3 parametric family of stochastic point processes on the one dimensional lattice originated from a remarkable family of representations of the infinite symmetric group we prove that the correlation functions of the processes are given by determinantal formulas with a certain kernel the kernel can be expressed through the gauss hypergeometric function we call it the hypergeometric kernel in a scaling limit our processes approximate the processes describing the decomposition of representations mentioned above into irreducibles as we showed in previous works the correlation functions of these limit processes also have determinantal form with so called whittaker kernel we show that the scaling limit of the hypergeometric kernel is the whittaker kernel integrable operator as defined by its izergin korepin and slavnov we argue that the hypergeometric kernel can be considered as a kernel defining a discrete integrable operator we also show that the hypergeometric kernel degenerates for certain values of parameters to the christoffel darboux kernel for meixner orthogonal polynomials this fact is parallel to the degeneration of the whittaker kernel to the christoffel darboux kernel for laguerre polynomials

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

reconstruction of chaotic orbits under finite resolution abstract in this paper it is shown how information about an orbit of a chaotic dynamical system can be recovered given only measurements with large error assuming that the imprecision of measurements manifests itself as a finite partition of the phase space general necessary and sufficient conditions under which it is possible to reconstruct orbits are presented two reconstructing methods and their pseudocodes are presented and analyzed the applicability of those methods is tested using a series of computer experiments for various one dimensional mappings on the unit interval potential applications are also discussed

confidence interval estimation subject to order restrictions this article deals with the construction of confidence intervals when the components of the location parameter mu of the random variable mathbf x which is elliptically symmetrically distributed are subject to order restrictions several domination results are proved by studying the derivative of the coverage probability of the confidence intervals centered at the improved point estimators consequently we strengthen the previously known results regarding the simple ordering and obtain several new results for other general forms of order restrictions including the simple tree ordering the umbrella ordering the simple and the double loop ordering and some combination of these these domination results are obtained under the assumption that sigma is a diagonal matrix when sigma is nondiagonal some new intervals are introduced which dominate the standard intervals centered at the unrestricted maximum likelihood estimator for various types of order restrictions similar results are obtained for scale parameters as well contrary to the location problems in case of the scale parameters satisfying the simple ordering we find that the restricted maximum likelihood estimator of the largest parameter fails to universally dominate the unrestricted maximum likelihood estimator a similar negative result is noted for simple tree order restriction

bayesian analysis of constrained parameter and truncated data problems using gibbs sampling abstract constrained parameter problems arise in a wide variety of applications including bioassay actuarial graduation ordinal categorical data response surfaces reliability development testing and variance component models truncated data problems arise naturally in survival and failure time studies ordinal data models and categorical data studies aimed at uncovering underlying continuous distributions in many applications both parameter constraints and data truncation are present the statistical literature on such problems is very extensive reflecting both the problems widespread occurrence in applications and the methodological challenges that they pose however it is striking that so little of this applied and theoretical literature involves a parametric bayesian perspective from a technical viewpoint this perhaps is not difficult to understand the fundamental tool for bayesian calculations in typical realistic models is multidimensional numerical integration which often is problem

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

additive isotonic models abstract additive isotonic models generalize linear models by replacing lines with isotonic nondecreasing transformations fitted transformations of several explanatory variables are added together and then transformed by a known function to yield fitted values of the response variable the isotonic transformations are chosen to minimize an explicit criterion such as the negative log likelihood by an algorithm that optimizes one transformation at a time while adjusting for the current fitted values of the others cycling until the criterion converges this approach can be used in various situations notably for generalizing ordinary linear regression and linear logistic regression at each step of the algorithm the needed optimal isotonic transformation is found using a simple generalization of the standard pool adjacent violators algorithm ayer brunk ewing reid and silverman 1955 the fitted transformations are always made up of flat steps so the technique is useful for finding optimal strati

monte carlo methods for bayesian analysis of constrained parameter problems summary constraints on the parameters in a bayesian hierarchical model typically make bayesian computation and analysis complicated posterior densities that contain analytically intractable integrals as normalising constants depending on the hyperparameters often make implementation of gibbs sampling or the metropolis algorithms difficult by using reweighting mixtures geyer 1995 we develop alternative simulation based methods to determine properties of the desired bayesian posterior distribution necessary theory and two illustrative examples are provided