functional clustering by bayesian wavelet methods summary we propose a nonparametric bayes wavelet model for clustering of functional data the wavelet based methodology is aimed at the resolution of generic global and local features during clustering and is suitable for clustering high dimensional data based on the dirichlet process the nonparametric bayes model extends the scope of traditional bayes wavelet methods to functional clustering and allows the elicitation of prior belief about the regularity of the functions and the number of clusters by suitably mixing the dirichlet processes posterior inference is carried out by gibbs sampling with conjugate priors which makes the computation straightforward we use simulated as well as real data sets to illustrate the suitability of the approach over other alternatives

rotation numbers for random dynamical systems on the circle in this paper we study rotation numbers of random dynamical systems on the circle we prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems as an application we prove a theorem on analytic conjugacy to a circle rotation

modelling the distribution of white matter hyperintensities due to ageing on mri images using bayesian inference white matter hyperintensities wmh also known as white matter lesions are localised white matter areas that appear hyperintense on mri scans wmh commonly occur in the ageing population and are often associated with several factors such as cognitive disorders cardiovascular risk factors cerebrovascular and neurodegenerative diseases despite the fact that some links between lesion location and parametric factors such as age have already been established the relationship between voxel wise spatial distribution of lesions and these factors is not yet well understood hence it would be of clinical importance to model the distribution of lesions at the population level and quantitatively analyse the effect of various factors on the lesion distribution model in this work we compare various methods including our proposed method to generate voxel wise distributions of wmh within a population with respect to various factors our proposed bayesian spline method models the spatio temporal distribution of wmh with respect to a parametric factor of interest in this case age within a population our probabilistic model takes as input the lesion segmentation binary maps of subjects belonging to various age groups and provides a population level parametric lesion probability map as output we used a spline representation to ensure a degree of smoothness in space and the dimension associated with the parameter and formulated our model using a bayesian framework we tested our algorithm output on simulated data and compared our results with those obtained using various existing methods with different levels of algorithmic and computational complexity we then compared the better performing methods on a real dataset consisting of 1000 subjects of the uk biobank divided in two groups based on hypertension diagnosis finally we applied our method on a clinical dataset of patients with vascular disease on simulated dataset the results from our algorithm showed a mean square error mse value of 7 27 10 5 which was lower than the mse value reported in the literature with the advantage of being robust and computationally efficient in the uk biobank data we found that the lesion probabilities are higher for the hypertension group compared to the non hypertension group and further verified this finding using a statistical t test finally when applying our method on patients with vascular disease we observed that the overall probability of lesions is significantly higher in later age groups which is in line with the current literature

the rotation number of the linear schrodinger equation with discontinuous almost periodic potentials abstract in this paper we study a linear schrodinger equation with a stepanov almost periodic potential where the potential is discontinuous from r to r we first show the existence of rotation numbers for the equation we then give the optimal estimate of rotation numbers

a matrix inequality and admissibility of linear estimators with respect to the mean square error matrix criterion abstract given matrices a b and vectors a b a necessary and sufficient condition is established for the lowner partial ordering am a am a bm b bm b to hold for all vectors m this result is then applied to derive a complete characterization of estimators that are admissible for a given vector of parametric functions among the set of all linear estimators under the general gauss markov model when the mean square error matrix is adopted as the criterion for evaluating the estimators

a nonparametric spatial model for periodontal data with nonrandom missingness periodontal disease pd progression is often quantified by clinical attachment level cal defined as the distance down a tooth s root that is detached from the surrounding bone measured at six locations per tooth throughout the mouth excluding the molars it gives rise to a dependent data setup these data are often reduced to a one number summary such as the whole mouth average or the number of observations greater than a threshold to be used as the response in a regression to identify important covariates related to the current state of a subject s periodontal health rather than a simple one number summary we set forward to analyze all available cal data for each subject exploiting the presence of spatial dependence nonstationarity and nonnormality also many subjects have a considerable proportion of missing teeth which cannot be considered missing at random because pd is the leading cause of adult tooth loss under a bayesian paradigm we propose a nonparametric flexible spatial joint

joint estimation of multiple graphical models from high dimensional time series in this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions we assume that the data are collected from n subjects each of which consists of t possibly dependent observations the graphical models of subjects vary but are assumed to change smoothly corresponding to a measure of closeness between subjects we propose a kernel based method for jointly estimating all graphical models theoretically under a double asymptotic framework where both t n and the dimension d can increase we provide the explicit rate of convergence in parameter estimation it characterizes the strength one can borrow across different individuals and the impact of data dependence on parameter estimation empirically experiments on both synthetic and real resting state functional magnetic resonance imaging rs fmri data illustrate the effectiveness of the proposed method

the rotation number for almost periodic potentials we define and analyze the rotation number for the almost periodic schrodinger operatorl d2 dx2 q x we use the rotation number to discuss i the spectrum ofl ii its relation to the korteweg de vries equation

finite mixture varying coefficient models for analyzing longitudinal heterogenous data this paper aims to develop a mixture model to study heterogeneous longitudinal data on the treatment effect of heroin use from a california civil addict program each component of the mixture is characterized by a varying coefficient mixed effect model we use the bayesian p splines approach to approximate the varying coefficient functions we develop markov chain monte carlo algorithms to estimate the smooth functions unknown parameters and latent variables in the model we use modified deviance information criterion to determine the number of components in the mixture a simulation study demonstrates that the modified deviance information criterion selects the correct number of components and the estimation of unknown quantities is accurate we apply the proposed model to the heroin treatment study furthermore we identify heterogeneous longitudinal patterns copyright 2011 john wiley sons ltd

matrix loss in comparison of linear experiments abstract the usual ordering of linear experiments was induced by estimation of some scalar parameters under quadratic risk new orderings based on estimation of vector parameters under quadratic and matrix risk respectively are defined and considered here

mixture of regression models for large spatial datasets abstractwhen a spatial regression model that links a response variable to a set of explanatory variables is desired it is unlikely that the same regression model holds throughout the domain when t

gaussian predictive process models for large spatial data sets with scientific data available at geocoded locations investigators are increasingly turning to spatial process models for carrying out statistical inference over the last decade hierarchical models implemented through markov chain monte carlo methods have become especially popular for spatial modelling given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics however fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations rendering such models infeasible for large spatial data sets this computational burden is exacerbated in multivariate settings with several spatially dependent response variables it is also aggravated when data are collected at frequent time points and spatiotemporal process models are used with regard to this challenge our contribution is to work with what we call predictive process models for spatial and spatiotemporal data every spatial or spatiotemporal process induces a predictive process model in fact arbitrarily many of them the latter models project process realizations of the former to a lower dimensional subspace thereby reducing the computational burden hence we achieve the flexibility to accommodate non stationary non gaussian possibly multivariate possibly spatiotemporal processes in the context of large data sets we discuss attractive theoretical properties of these predictive processes we also provide a computational template encompassing these diverse settings finally we illustrate the approach with simulated and real data sets

spatial modeling with spatially varying coefficient processes in many applications the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated in nearly all of this work the regression coefficients are assumed to be constant over the region however in some applications coefficients are expected to vary at the local or subregional level here we focus on the local case although parametric modeling of the spatial surface for the coefficient is possible here we argue that it is more natural and flexible to view the surface as a realization from a spatial process we show how such modeling can be formalized in the context of gaussian responses providing attractive interpretation in terms of both random effects and explaining residuals we also offer extensions to generalized linear models and to spatio temporal setting we illustrate both static and dynamic modeling with a dataset that attempts to explain log selling price of single family houses

continuity properties for random fields l auteur donne pour un champ aleatoire n dimensionnel donne une condition simple sur la fonction de covariance qui garantit l existence d une version du champ aleatoire dans laquelle les realisations sont partout continues la demonstration implique une approximation assez delicate du champ aleatoire par des polynomes d interpellation d ordre eleve

spatial homogeneity pursuit of regression coefficients for large datasets spatial regression models have been widely used to describe the relationship between a response variable and some explanatory variables over a region of interest taking into account the spatial de

estimation and experiments comparison with respect to the matrix risk given matrices a1 a2 b1 b2 and symmetric d a necessary and sufficient condition is established for the lowner partial ordering a1m b1 a1m b1 l a2m b2 a2m b2 d to hold for all matrices m this result is then applied to solve statistical problems of admissible linear estimation and experiments comparison under the general multivariate linear model when one of two kinds of a matrix risk function is adopted as the criterion

model choice a minimum posterior predictive loss approach summary model choice is a fundamental and much discussed activity in the analysis of datasets nonnested hierarchical models introducing random effects may not be handled by classical methods bayesian approaches using predictive distributions can be used though the formal solution which includes bayes factors as a special case can be criticised we propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values we obtain this criterion by minimising posterior loss for a given model and then for models under consideration selecting the one which minimises this criterion for a broad range of losses the criterion emerges as a form partitioned into a goodness of fit term and a penalty term we illustrate its performance with an application to a large dataset involving residential property transactions

ergodic properties and rotation number for linear hamiltonian systems abstract this paper is concerned with the dynamical behavior of the solutions of a class of linear hamiltonian systems including those to which kotani s theory applies we first present a symplectic l 2 perron transformation which takes these systems into skew symmetric form this allows us to study the average of the trajectories and the fourier coefficients of the solutions in addition from the construction of two invariant complex lagrange planes the differentiability of the rotation number is analyzed

penalized local polynomial regression for spatial data when performing spatial regression analysis in environmental data applications spatial heterogeneity in the regression coefficients is often observed spatially varying coefficient models including geographically weighted regression and spline models are standard tools for quantifying such heterogeneity in this paper we propose a spatially varying coefficient model that represents the spatially varying parameters as a mixture of local polynomials at selected locations the local polynomial parameters have attractive interpretations indicating various types of spatial heterogeneity instead of estimating the spatially varying regression coefficients directly we develop a penalized least squares regression procedure for the local polynomial parameter estimation which both shrinks the parameter estimation and penalizes the differences among parameters that are associated with neighboring locations we develop confidence intervals for the varying regression coefficients and prediction intervals for the response we apply the proposed method to characterize the spatially varying association between particulate matter concentrations pm2 5 and pollutant gases related to the secondary aerosol formulation in china the identified regression coefficients show distinct spatial patterns for nitrogen dioxide sulfur dioxide and carbon monoxide during different seasons

gmm estimation of 2d rca models with applications to texture image classification the 2d indexed random coefficients autoregressive 2d rca models are obtained by introducing appropriate random field coefficients to an ar model on mathrm z 2 the study of such models is motivated by their capability to capture the space varying behavior of the volatility a generalized method of moment approach is considered to estimate the 2d rca models consistency and asymptotic normality of the estimates are derived estimated parameters are used at a later stage as pixel features in texture image classification

the rotation number approach to the periodic fuc caron ik spectrum abstract in this paper we study the fucik spectrum of the problem q t x q t x 0 with the 2 periodic boundary condition where q t are 2 periodic after introducing a rotation number function for we prove using the hamiltonian structure and the positive homogeneity of that for any positive integer n the two boundary curves of the domain 1 n 2 in the plane are fucik curves of the result obtained in this paper shows that such a spectrum problem is much like that of the higher dimensional fucik spectrum with the dirichlet condition in particular it remains open if the fucik spectrum of is composed of only these curves

hierarchical spatially varying coefficient process model the spatially varying coefficient process model is a nonstationary approach to explaining spatial heterogen eity by allowing coefficients to vary across space in this article we develop a methodo

nonuniform nonresonance of semilinear differential equations abstract consider the dirichlet problem of nonlinear differential equations with the principal part the p laplacian when the nonlinearity satisfies some semilinearity conditions the usual nonuniform nonresonance conditions are obtained by comparing nonlinear equations with the classical eigenvalues in this article we will introduce some weighted eigenvalues the nonuniform nonresonance conditions proved in this article using weighted eigenvalues will improve the usual ones significantly

linear combinations of space time covariance functions and variograms the difference or a linear combination of two space time covariance functions or variograms is not necessarily a valid covariance function or variogram in general there seems no simple condition that makes a linear combination permissible unless its coefficients are non negative the permissibility is investigated in this paper for the linear combination of two spatial or spatio temporal covariance functions or variograms isotropic in space so that we obtain flexible classes of spatial or spatio temporal covariance functions with various properties such as long range dependence and having different signs

efficient parametrisations for normal linear mixed models summary the generality and easy programmability of modern sampling based methods for maximisation of likelihoods and summarisation of posterior distributions have led to a tremendous increase in the complexity and dimensionality of the statistical models used in practice however these methods can often be extremely slow to converge due to high correlations between or weak identifiability of certain model parameters we present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models in particular we study the two stage hierarchical normal linear model the laird ware model for longitudinal data and a general structure for hierarchically nested linear models using analytical arguments simulation studies and an example involving clinical markers of acquired immune deficiency syndrome aids we indicate when reparametrisation is likely to provide substantial gains in efficiency