advances on byy harmony learning information theoretic perspective generalized projection geometry and independent factor autodetermination the nature of bayesian ying yang harmony learning is reexamined from an information theoretic perspective not only its ability for model selection and regularization is explained with new insights but also discussions are made on its relations and differences from the studies of minimum description length mdl bayesian approach the bit back based mdl akaike information criterion aic maximum likelihood information geometry helmholtz machines and variational approximation moreover a generalized projection geometry is introduced for further understanding such a new mechanism furthermore new algorithms are also developed for implementing gaussian factor analysis fa and non gaussian factor analysis nfa such that selecting appropriate factors is automatically made during parameter learning

a latent class approach to fitting the weighted euclidean model clascal a weighted euclidean distance model for analyzing three way proximity data is proposed that incorporates a latent class approach in this latent class weighted euclidean model the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class this model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions and drastically reduces the number of parameters in the traditional indscal model the probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities the maximum likelihood function is optimized by means of an em algorithm a modified fisher scoring method is used to update the parameters in the m step a model selection strategy is proposed and illustrated on both real and artificial data

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

on model selection criteria in multimodel analysis 1 hydrologic systems are open and complex rendering them prone to multiple conceptualizations and mathematical descriptions there has been a growing tendency to postulate several alternative hydrologic models for a site and use model selection criteria to 1 rank these models 2 eliminate some of them and or 3 weigh and average predictions and statistics generated by multiple models this has led to some debate among hydrogeologists about the merits and demerits of common model selection also known as model discrimination or information criteria such as aic aicc bic and kic and some lack of clarity about the proper interpretation and mathematical representation of each criterion we examine the model selection literature to find that 1 all published rigorous derivations of aic and aicc require that the true model having generated the observational data be in the set of candidate models 2 though bic and kic were originally derived by assuming that such a model is in the set bic has been rederived by cavanaugh and neath 1999 without the need for such an assumption and 3 kic reduces to bic as the number of observations becomes large relative to the number of adjustable model parameters implying that it likewise does not require the existence of a true model in the set of alternatives we explain why kic is the only criterion accounting validly for the likelihood of prior parameter estimates elucidate the unique role that the fisher information matrix plays in kic and demonstrate through an example that it imbues kic with desirable model selection properties not shared by aic aicc or bic our example appears to provide the first comprehensive test of how aic aicc bic and kic weigh and rank alternative models in light of the models predictive performance under cross validation with real hydrologic data

estimating latent distributions in recurrent choice data this paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data these choice models are derived by specifying elements of the choice process at the individual level probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior due to the explicit consideration of random effect sources the choice models are parsimonious and readily interpretable an easy to implement em algorithm is presented for parameter estimation two applications illustrate the proposed approach

the camassa holm equation as a geodesic flow on the diffeomorphism group misiolek j geom phys 24 203 208 1998 has shown that the camassa holm equation is a geodesic flow on the bott virasoro group in this paper it is shown that the camassa holm equation for the case 0 is the geodesic spray of the weak riemannian metric on the diffeomorphism group of the line or the circle obtained by right translating the h1 inner product over the entire group this paper uses the right trivialization technique to rigorously verify that the euler poincare theory for lie groups can be applied to diffeomorphism groups the observation made in this paper has led to physically meaningful generalizations of the ch equation to higher dimensional manifolds

hierarchical classes models for three way three mode binary data interrelations and model selection several hierarchical classes models can be considered for the modeling of three way three mode binary data including the indclas model leenen van mechelen de boeck and rosenberg 1999 the tucker3 hiclas model ceulemans van mechelen and leenen 2003 the tucker2 hiclas model ceulemans and van mechelen 2004 and the tucker1 hiclas model that is introduced in this paper two questions then may be raised 1 how are these models interrelated and 2 given a specific data set which of these models should be selected and in which rank in the present paper we deal with these questions by 1 showing that the distinct hierarchical classes models for three way three mode binary data can be organized into a partially ordered hierarchy and 2 by presenting model selection strategies based on extensions of the well known scree test and on the akaike information criterion the latter strategies are evaluated by means of an extensive simulation study and are illustrated with an application to interpersonal emotion data finally the presented hierarchy and model selection strategies are related to corresponding work by kiers 1991 for principal component models for three way three mode real valued data

model selection principles in misspecified models summary model selection is of fundamental importance to high dimensional modelling featured in many contemporary applications classical principles of model selection include the bayesian principle and the kullback leibler divergence principle which lead to the bayesian information criterion and akaike information criterion respectively when models are correctly specified yet model misspecification is unavoidable in practice we derive novel asymptotic expansions of the two well known principles in misspecified generalized linear models which give the generalized bayesian information criterion and generalized akaike information criterion a specific form of prior probabilities motivated by the kullback leibler divergence principle leads to the generalized bayesian information criterion with prior probability gbicp which can be naturally decomposed as the sum of the negative maximum quasi log likelihood a penalty on model dimensionality and a penalty on model misspecification directly numerical studies demonstrate the advantage of the new methods for model selection in both correctly specified and misspecified models

on the precision of the conditionally autoregressive prior in spatial models summary bayesian analyses of spatial data often use a conditionally autoregressive car prior which can be written as the kernel of an improper density that depends on a precision parameter that is typically unknown to include in the bayesian analysis the kernel must be multiplied by k for some k this article rigorously derives k n i 2 for the l2 norm car prior also called a gaussian markov random field model and k n i for the l1 norm car prior where n is the number of regions and i the number of islands disconnected groups of regions in the spatial map since i 1 for a spatial structure defining a connected graph this supports knorr held s 2002 in highly structured stochastic systems 260 264 suggestion that k n 1 2 in the l2 norm case instead of the more common k n 2 we illustrate the practical significance of our results using a periodontal example

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

integrable evolution equations on spaces of tensor densities and their peakon solutions we study a family of equations defined on the space of tensor densities of weight on the circle and introduce two integrable pde one of the equations turns out to be closely related to the inviscid burgers equation while the other has not been identified in any form before we present their lax pair formulations and describe their bihamiltonian structures we prove local wellposedness of the corresponding cauchy problem and include results on blow up as well as global existence of solutions moreover we construct peakon and multi peakon solutions for all 0 1 and shock peakons for 3 we argue that there is a natural geometric framework for these equations that includes other well known integrable equations and which is based on v arnold s approach to euler equations on lie groups

the two dimensional periodic b equation on the diffeomorphism group of the torus in this paper the two dimensional periodic b equation is discussed under geometric aspects i e as a geodesic flow on the diffeomorphism group of the torus in the framework of arnold s 1966 ann inst fourier grenoble 16 319 famous approach we achieve some well posedness results for the b equation and we perform explicit curvature computations for the 2d camassa holm equation which is obtained for b 2 finally we explain the special role of the choice b 2 by giving a rigorous proof that b 2 is the only case in which the associated geodesic flow is weakly riemannian

the robust sequential estimator a general approach and its application to surface organization in range data presents an autonomous statistically robust sequential function approximation approach to simultaneous parameterization and organization of possibly partially occluded surfaces in noisy outlier ridden not gaussian functional range data at the core of this approach is the robust sequential estimator a robust extension to the method of sequential least squares unlike most existing surface characterization techniques the authors method generates complete surface hypotheses in parameter space given a noisy depth map of an unknown 3 d scene the algorithm first selects appropriate seed points representing possible surfaces for each nonredundant seed it chooses the best approximating model from a given set of competing models using a modified akaike information criterion with this best model each surface is expanded from its seed over the entire image and this step is repeated for all seeds those points which appear to be outliers with respect to the model in growth are not included in the possibly disconnected surface point regions are deleted from each newly grown surface in the prune stage noise outliers or coincidental surface alignment may cause some points to appear to belong to more than one surface these ambiguities are resolved by a weighted voting scheme within a 5 spl times 5 decision window centered around the ambiguous point the isolated point regions left after the resolve stage are removed and any missing points in the data are filled by the surface having a majority consensus in an 8 neighborhood

generalized hunter saxton equation and the geometry of the group of circle diffeomorphisms we study an equation lying mid way between the periodic hunter saxton and camassa holm equations and which describes evolution of rotators in liquid crystals with external magnetic field and self interaction we prove that it is an euler equation on the diffeomorphism group of the circle corresponding to a natural right invariant sobolev metric we show that the equation is bihamiltonian and admits both cusped and smooth traveling wave solutions which are natural candidates for solitons we also prove that it is locally well posed and establish results on the lifespan of its solutions throughout the paper we argue that despite similarities to the kdv ch and hs equations the new equation manifests several distinctive features that set it apart from the other three

cluster number selection for a small set of samples using the bayesian ying yang model one major problem in cluster analysis is the determination of the number of clusters in this paper we describe both theoretical and experimental results in determining the cluster number for a small set of samples using the bayesian kullback ying yang byy model selection criterion under the second order approximation we derive a new equation for estimating the smoothing parameter in the cost function finally we propose a gradient descent smoothing parameter estimation approach that avoids complicated integration procedure and gives the same optimal result

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

bayesian spatial modeling of disease risk in relation to multivariate environmental risk fields the relationship between exposure to environmental chemicals during pregnancy and early childhood development is an important issue which has a spatial risk component in this context we have examined mental retardation and developmental delay mrdd outcome measures for children in a medicaid population in south carolina and sampled measures of soil chemistry e g as hg etc on a network of sites which are misaligned to the outcome residential addresses during pregnancy the true chemical concentration at the residential addresses is not observed directly and must be interpolated from soil samples in this study we have developed a bayesian joint model which interpolates soil chemical fields and estimates the associated mrdd risk simultaneously having multiple spatial fields to interpolate we have considered a low rank kriging method for the interpolation which requires less computation than bayesian kriging we performed a sensitivity analysis for a bivariate smoothing changing the number of knots and the smoothing parameter these analyses show that a low rank kriging method can be used as an alternative to a full rank kriging reducing computational burden however the number of knots for the low rank kriging model need to be selected with caution as a bivariate surface estimation can be sensitive to the choice of the number of knots

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

geodesic flows on semidirect product lie groups geometry of singular measure valued solutions the epdiff equation or dispersionless camassa holm equation in 1d is a well known example of geodesic motion on the diff group of smooth invertible maps diffeomorphisms its recent two component extension governs geodesic motion on the semidirect product mathrm diff circleds mathcal f where mathcal f denotes the space of scalar functions this paper generalizes the second construction to consider geodesic motion on mathrm diff circleds mathfrak g where mathfrak g denotes the space of scalar functions that take values on a certain lie algebra for example mathfrak g mathcal f otimes mathfrak so 3 measure valued delta like solutions are shown to be momentum maps possessing a dual pair structure thereby extending previous results for the epdiff equation the collective hamiltonians are shown to fit into the kaluza klein theory of particles in a yang mills field and these formulations are shown to apply also at the continuum pde level in the continuum description the kaluza klein approach produces the kelvin circulation theorem

discrepancy risk model selection test theory for comparing possibly misspecified or nonnested models a new model selection statistical test is proposed for testing the null hypothesis that two probability models equally effectively fit the underlying data generating process dgp the new model selection test called the discrepancy risk model selection test drmst extends previous work see vuong 1989 on this problem in four distinct ways first generalized goodness of fit measures which include log likelihood functions can be used second unlike the classical likelihood ratio test the models are not required to be fully nested where the nesting concept is defined for generalized goodness of fit measures the drmst also differs from the likelihood ratio test by not requiring that either competing model provides a completely accurate representation of the dgp and fourth the drmst may be used to compare competing time series models using correlated observations as well as data consisting of independent and identically distributed observations

a note on impact factor distribution revisited abstract motivated by huang 2017 we analyze impact factor data in all subject categories for each year from 2010 to 2015 the results are provided by subject categories and by years the two exponent distribution due to mansilla et al 2007 and the normal distribution are shown to give the best fits for the data sets the best fits are assessed in terms of probability plots quantile plots and five other criteria

spatial regression and spillover effects in cluster randomized trials with count outcomes this paper describes methodology for analyzing data from cluster randomized trials with count outcomes taking indirect effects as well spatial effects into account indirect effects are modeled using a novel application of a measure of depth within the intervention arm both direct and indirect effects can be estimated accurately even when the proposed model is misspecified we use spatial regression models with gaussian random effects where the individual outcomes have distributions overdispersed with respect to the poisson and the corresponding direct and indirect effects have a marginal interpretation to avoid spatial confounding we use orthogonal regression in which random effects represent spatial dependence using a homoscedastic and dimensionally reduced modification of the intrinsic conditional autoregression model we illustrate the methodology using spatial data from a pair matched cluster randomized trial against the dengue mosquito vector aedes aegypti done in trujillo venezuela

on the n 2 supersymmetric camassa holm and hunter saxton equations we consider n 2 supersymmetric extensions of the camassa holm and hunter saxton equations we show that they admit geometric interpretations as euler equations on the superconformal algebra of contact vector fields on the 1 2 dimensional supercircle we use the bi hamiltonian formulation to derive lax pairs moreover we present some simple examples of explicit solutions as a by product of our analysis we obtain a description of the bounded traveling wave solutions for the two component hunter saxton equation

dynamics of director fields an asymptotic equation for weakly nonlinear hyperbolic waves governed by variational principles is derived and analyzed the equation is used to study a nonlinear instability in the director field of a nematic liquid crystal it is shown that smooth solutions of the asymptotic equation break down in finite time also constructed are weak solutions of the equation that are continuous despite the fact that their spatial derivative blows up

range image segmentation using surface selection criterion in this paper we address the problem of recovering the true underlying model of a surface while performing the segmentation first and in order to solve the model selection problem we introduce a novel criterion which is based on minimising strain energy of fitted surfaces we then evaluate its performance and compare it with many other existing model selection techniques using this criterion we then present a robust range data segmentation algorithm capable of segmenting complex objects with planar and curved surfaces the presented algorithm simultaneously identifies the type order and geometric shape of each surface and separates all the points that are part of that surface this paper includes the segmentation results of a large collection of range images obtained from objects with planar and curved surfaces the resulting segmentation algorithm successfully segments various possible types of curved objects more importantly the new technique is capable of detecting the association between separated parts of a surface which has the same cartesian equation while segmenting a scene this aspect is very useful in some industrial applications of range data analysis

a maximum likelihood method for latent class regression involving a censored dependent variable the standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored this model is generalized by developing a conditional mixture maximum likelihood method for latent class censored regression the proposed method simultaneously estimates separate regression functions and subject membership in k latent classes or groups given a censored dependent variable for a cross section of subjects maximum likelihood estimates are obtained using an em algorithm the proposed method is illustrated via a consumer psychology application

a note on multi dimensional camassa holm type systems on the torus we present a 2n component nonlinear evolutionary pde which includes the n dimensional versions of the camassa holm and the hunter saxton systems as well as their partially averaged variations our goal is to apply arnold s geometric formalism arnold 1966 ann inst fourier grenoble 16 319 61 ebin and marsden 1970 ann math 92 102 63 to this general equation in order to obtain results on well posedness conservation laws or stability of its solutions following the line of arguments of kohlmann 2011 j phys a math theor 44 465205 we present geometric aspects of a two dimensional periodic b equation on the diffeomorphism group of the torus in this context

partitioning degrees of freedom in hierarchical and other richly parameterized models hodges and sargent 2001 have developed a measure of a hierarchical model s complexity degrees of freedom df that is consistent with definitions for scatterplot smoothers is interpretable in terms of simple models and enables control of a fit s complexity by means of a prior distribution on complexity but although df describes the complexity of the whole fitted model in general it remains unclear how to allocate df to individual effects here we present a new definition of df for arbitrary normal error linear hierarchical models consistent with that of hodges and sargent that naturally partitions the n observations into df for individual effects and for error the new conception of an effect s df is the ratio of the effect s modeled variance matrix to the total variance matrix this provides a way to describe the sizes of different parts of a model e g spatial clustering vs heterogeneity to place df based priors on smoothing parameters and to describe how a smoothed effect competes with

effects of residual smoothing on the posterior of the fixed effects in disease mapping models disease mapping models for areal data often have fixed effects to measure the effect of spatially varying covariates and random effects with a conditionally autoregressive car prior to account for spatial clustering in such spatial regressions the objective may be to estimate the fixed effects while accounting for the spatial correlation but adding the car random effects can cause large changes in the posterior mean and variance of fixed effects compared to the nonspatial regression model this article explores the impact of adding spatial random effects on fixed effect estimates and posterior variance diagnostics are proposed to measure posterior variance inflation from collinearity between the fixed effect covariates and the car random effects and to measure each region s influence on the change in the fixed effect s estimates by adding the car random effects a new model that alleviates the collinearity between the fixed effect covariates and the car random effects is developed and extensions of these methods to point referenced data models are discussed

application of model selection criteria to some problems in multivariate analysis a review of model selection criteria is presented with a view toward showing their similarities it is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model selection criteria consideration is given to application of model selection criteria to some problems of multivariate analysis especially the clustering of variables factor analysis and more generally describing a complex of variables

deriving ultrametric tree structures from proximity data confounded by differential stimulus familiarity this paper presents a new procedure called treefam for estimating ultrametric tree structures from proximity data confounded by differential stimulus familiarity the objective of the proposed treefam procedure is to quantitatively filter out the effects of stimulus unfamiliarity in the estimation of an ultrametric tree a conditional alternating maximum likelihood procedure is formulated to simultaneously estimate an ultrametric tree under the unobserved condition of complete stimulus familiarity and subject specific parameters capturing the adjustments due to differential unfamiliarity we demonstrate the performance of the treefam procedure under a variety of alternative conditions via a modest monte carlo experimental study an empirical application provides evidence that the treefam outperforms traditional models that ignore the effects of unfamiliarity in terms of superior tree recovery and overall goodness of fit

well posedness global existence and blowup phenomena for a periodic quasi linear hyperbolic equation we establish the local well posedness of a recently derived model for small amplitude shallow water waves for a large class of initial data we prove global existence of the corresponding solution criteria guaranteeing the development of singularities in finite time for strong solutions with smooth initial data are obtained and an existence and uniqueness result for a class of global weak solutions is also given c 1998 john wiley sons inc

a model based approach for visualizing the dimensional structure of ordered successive categories preference data a cyclical conditional maximum likelihood estimation procedure is developed for the multidimensional unfolding of two or three way dominance data e g preference choice consideration measured on ordered successive category rating scales the technical description of the proposed model and estimation procedure are discussed as well as the rather unique joint spaces derived we then conduct a modest monte carlo simulation to demonstrate the parameter recovery of the proposed methodology as well as investigate the performance of various information heuristics for dimension selection a consumer psychology application is provided where the spatial results of the proposed model are compared to solutions derived from various traditional multidimensional unfolding procedures this application deals with consumers intending to buy new luxury sport utility vehicles suvs finally directions for future research are discussed

spatial analyses of periodontal data using conditionally autoregressive priors having two classes of neighbor relations attachment loss the extent of a tooth s root in millimeters that is no longer attached to surrounding bone by periodontal ligament is often used to measure the current state of a patient s periodontal disease and monitor disease progression attachment loss data can be analyzed using a conditionally autoregressive car prior distribution that smooths fitted values toward neighboring values however it may be desirable to have more than one class of neighbor relation in the spatial structure so the different classes of neighbor relations can induce different degrees of smoothing for example we may wish to allow smoothing of neighbor pairs bridging the gap between teeth to differ from smoothing of pairs that do not bridge such gaps adequately modeling the spatial structure may improve the monitoring of periodontal disease progression this article develops a two neighbor relation car model to handle this situation and presents associated theory to help explain the sometimes unusual posterior distr

the byy annealing learning algorithm for gaussian mixture with automated model selection bayesian ying yang byy learning has provided a new mechanism that makes parameter learning with automated model selection via maximizing a harmony function on a backward architecture of the byy system for the gaussian mixture however since there are a large number of local maxima for the harmony function any local searching algorithm such as the hard cut em algorithm does not work well in order to overcome this difficulty we propose a simulated annealing learning algorithm to search the global maximum of the harmony function being expressed as a kind of deterministic annealing em procedure it is demonstrated by the simulation experiments that this byy annealing learning algorithm can efficiently and automatically determine the number of clusters or gaussians during the learning process moreover the byy annealing learning algorithm is successfully applied to two real life data sets including iris data classification and unsupervised color image segmentation

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

a simple derivation of deletion diagnostic results for the general linear model with correlated errors a general simple and intuitive derivation is provided for diagnostics associated with the deletion of arbitrary subsets for the linear model with general covariance structure these are seen to be most simply expressed even for the well studied case of independent and identically distributed data in terms of a residual known variously as the conditional residual the deletion prediction residual and the cross validation residual particularly simple specializations arise when the subsets are of size 1 and of size 2 but the method is easy to apply for all subsets and to conditional deletions

on a completely integrable nonlinear hyperbolic variational equation abstract we show that the nonlinear partial differential equation u t uu x xx 1 2 u x 2 x is a completely integrable bi variational bi hamiltonian system the corresponding equation for w u xx belongs to the harry dym hierarchy this equation arises in two different physical contexts in two nonequivalent variational forms it describes the propagation of weakly nonlinear orientation waves in a massive nematic liquid crystal director field and it is the high frequency limit of the camassa holm equation which is an integrable model equation for shallow water waves using the bi hamiltonian structure we derive a recursion operator a lax pair and an infinite family commuting hamiltonian flows together with the associated conservation laws we also give the transformation to action angle coordinates smooth solutions of the partial differential equation break down because their derivative blows up in finite time nevertheless the hamiltonian structure and complete integrability appear to remain valid globally in time even after smooth solutions break down we show this fact explicitly for finite dimensional invariant manifolds consisting of conservative piecewise linear solutions we compute the bi hamiltonian structure on this invariant manifold which is obtained by restricting the bi hamiltonian structure of the partial differential equation

bayesian modeling of multivariate spatial binary data with applications to dental caries dental research gives rise to data with potentially complex correlation structure assessments of dental caries yield a binary outcome indicating the presence or absence of caries experience for each surface of each tooth in a subject s mouth in addition to this nesting caries outcome exhibit spatial structure among neighboring teeth we develop a bayesian multivariate model for spatial binary data using random effects autologistic regression that controls for the correlation within tooth surfaces and spatial correlation among neighboring teeth using a sample from a clinical study conducted at the medical university of south carolina we compare this autologistic model with covariates to alternative models to demonstrate the improvement in predictions and also to assess the effects of covariates on caries experience

data model conclusion doing it again this paper explores the robustness of conclusions from a statistical model against variations in model choice rather than variations in random sampling and random assignment to treatments which are the usual variations covered by inferential statistics after the problem formulation in section 1 section 2 presents an example from box and tiao in which variation in parent distribution is modeled for a one sample location problem an adaptive bayesian procedure permits to use a weighted mixture of parent distributions rather than choosing just one such as a normal or a uniform distribution in section 3 similar considerations are applied to an event history model for the influence of education and gender on age at first marriage but here the conclusions are hardly influenced by the choice of the duration distribution in section 4 a brief discussion of model choice in factor analysis and structural equation models is followed by a more elaborate treatment of the choice of integer valued slopes for item response functions in the oplm model which is an extension of the rasch model a modest simulation study suggests that adaptive bayesian modeling with a mixture of sets of slopes works better than fixing one set of postulated slopes the paper concludes with some remarks on the roles and sources of prior distributions followed by a short epilogue which argues that simultaneous consideration of a class of models for the same data is sometimes superior to exclusively analyzing the data under one specific model chosen from such a class

facaic model selection algorithm for the orthogonal factor model using aic and caic this paper describes the authors fortran algorithm facaic for choosing the number of factors for an orthogonal factor model using akaike s information criterion facaic utilizes the imsl subroutine ofcomm

on the choice of a model to fit data from an exponential family let x 1 cdots x n be iid observations coming from an exponential family the problem of interest is this given a finite number of models m j smoothly curved manifolds in mathbb r k choose the best model to fit the observations with some penalty for choosing models with dimensions which are too large a result of schwarz is made more specific and is extended to the case where the models are curved manifolds if s y n j is up to a constant c n independent of the model the log of the posterior probability of the j th model where the sample mean y n 1 n sum n i 1 x i has been replaced by y schwarz suggested an asymptotic expansion of s y n j whose leading terms are gamma y n j n sup psi in m j cap theta y psi b psi frac 1 2 k j log n in the case where the models are affine subspaces of mathbb r k we establish a similar asymptotic expansion including the next term with uniform bounds for y in a compact neighborhood of nabla b theta where theta is the true value of the parameter we suggest a criterion for the choice of the best model that consists of maximizing the three leading terms in the expansion s y n j we show that the criterion gives the correct model with probabilities p n theta rightarrow 1 as n rightarrow infty

prediction diagnostics for spatial linear models case deletion diagnostics are developed for detecting observations that are influential for prediction in linear models with a general covariance matrix a primary application of such results is in universal kriging and the related methodologies of ordinary kriging and intrinsic random function kriging in these applications the linear model and the covariance matrix of the data are determined by the locations at which observations are taken computational formulae are given that make the procedures feasible the diagnostics are illustrated using an example

bootstrap choice of estimators in parametric and semiparametric families an extension of eic ishiguro sakamoto et kitagawa 1997 ont propose le eic comme une extension du critere d akaike aic le eic est construit en corrigeant le biais de la log vraisemblance consideree comme un estimateur de l information de kullback leibler par la technique du bootstrap nous developpons ce critere dans un cadre d estimation semi parametrique multivarie et nous montrons qu il peut etre utilise pour choisir un estimateur parmi une famille d estimateurs parametriques et semi parametriques une etude de simulation basee sur un modele de regression montre que l eic est meilleur que les criteres usuels bien que la validation croisee appliquee a la vraisemblance donne des resulats tres proches sauf dans le cas d echantillons de faible taille nous avons applique le eic afin d estimer l evolution moyenne de la charge virale d enfants infectes par le vih

model order selection rules for covariance structure classification in radar the adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper this represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties the considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of model order selection mos is exploited to devise suitable decision rules several mos techniques such as the akaike takeuchi and bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed at the analysis stage illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

on the geometric approach to the motion of inertial mechanical systems according to the principle of least action the spatially periodic motions of one dimensional mechanical systems with no external forces are described in the lagrangian formalism by geodesics on a manifold configuration space the group d of smooth orientation preserving diffeomorphisms of the circle the periodic inviscid burgers equation is the geodesic equation on d with the l 2 right invariant metric however the exponential map for this right invariant metric is not a c 1 local diffeomorphism and the geometric structure is therefore deficient on the other hand the geodesic equation on d for the h 1 rightinvariant metric is also a re expression of a model in mathematical physics we show that in this case the exponential map is a c 1 local diffeomorphism and that if two diffeomorphisms are sufficiently close on d t heycan be joined by a unique length minimizing geodesic a state of the system is transformed to another nearby state by going through a uniquely determined flow that minimizes the energy we also analyse for both metrics the breakdown of the geodesic flow

admissible selection of an accurate and parsimonious normal linear regression model let mo be a normal linear regression model and let m1 mk be distinct proper linear submodels of mo let k e 0 k be a model selection rule based on observed data from the true model given k let the unknown parameters of the selected model ms be fitted by the maximum likelihood method a loss function is introduced which depends additively on two parts i a measure of the difference between the fitted model ms and the true model and ii a measure cs of the complexity of the selected model a natural model selection rule k which minimizes an empirical version of this loss is shown to be admissible and very nearly bayes

weak geodesic flow on a semidirect product and global solutions to the periodic hunter saxton system abstract we give explicit solutions for the two component hunter saxton system on the unit circle moreover we show how global weak solutions can be naturally constructed using the geometric interpretation of this system as a re expression of the geodesic flow on the semidirect product of a suitable subgroup of the diffeomorphism group of the circle with the space of smooth functions on the circle these spatially and temporally periodic solutions turn out to be conservative

case deletion diagnostics for mixed models mixed linear models arise in many areas of application standard estimation methods for mixed models are sensitive to bizarre observations such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions we develop case deletion diagnostics for detecting influential observations in mixed linear models diagnostics for both fixed effects and variance components are proposed computational formulas are given that make the procedures feasible the methods are illustrated using examples

on the cauchy problem for the two component euler poincare equations abstract in the paper we first use the energy method to establish the local well posedness as well as blow up criteria for the cauchy problem on the two component euler poincare equations in multi dimensional space in the case of dimensions 2 and 3 we show that for a large class of smooth initial data with some concentration property the corresponding solutions blow up in finite time by using constantin escher lemma and littlewood paley decomposition theory then for the one component case a more precise blow up estimate and a global existence result are also established by using similar methods next we investigate the zero density limit and the zero dispersion limit at the end we also briefly demonstrate a liouville type theorem for the stationary weak solution

filter order selection in adaptive maximum likelihood estimation the choice of the number of parameters is an important problem in adaptive filtering in the general ground of maximum likelihood ml parameter estimation akaike criterion has proved to be a very useful tool significant results and the importance of the kullback information measure as the implicit measure of distance associated with ml estimation are discussed application of these results to adaptive filtering is then considered for time invariant and time varying parametric models the corresponding practical forms of akaike criterion are given in the time varying case this criterion may be used as a way to fit the model into the nonstationarity of an exact filter the possible generalization of the akaike criterion to non ml estimation is discussed and application is made for weighted least squares estimation a more general approach to the nonstationary case is given by assuming a linear stochastic model for the vector of the filter coefficients in which case the ml estimate is computed recursively using the kalman filtering equation then the random sequence of kalman gains is close to a deterministic average sequence this sequence may be precomputed and gives an optimal choice for the gain matrices in an adaptive gradient type filter

identification of piecewise affine systems based on statistical clustering technique this paper is concerned with the identification of a class of piecewise affine systems called a piecewise affine autoregressive exogenous pwarx model the pwarx model is composed of arx sub models each of which corresponds to a polyhedral region of the regression space under the temporary assumption that the number of sub models is known a priori the input output data are collected into several clusters by using a statistical clustering algorithm we utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space in each cluster the parameter vector of the sub model is obtained by the least squares method it turns out that the present statistical clustering approach enables us to estimate the number of sub models based on the information criteria such as caic and mdl the estimate of the number of sub models is performed by applying the identification procedure several times to the same data set after having fixed the number of sub models to different values finally we verify the applicability of the present identification method through a numerical example of a hammerstein model

on model selection and the arc sine laws generalizations of the arc sine laws are shown to provide insight into the operating characteristics of certain techniques for selecting models to fit a given data set when the available models are nested as a corollary one sees that a popular technique may be expected to include about one superfluous parameter even if the sample size is large

biclustering models for two mode ordinal data the work in this paper introduces finite mixture models that can be used to simultaneously cluster the rows and columns of two mode ordinal categorical response data such as those resulting from likert scale responses we use the popular proportional odds parameterisation and propose models which provide insights into major patterns in the data model fitting is performed using the em algorithm and a fuzzy allocation of rows and columns to corresponding clusters is obtained the clustering ability of the models is evaluated in a simulation study and demonstrated using two real data sets

the chic model a global model for coupled binary data often problems result in the collection of coupled data which consist of different n way n mode data blocks that have one or more modes in common to reveal the structure underlying such data an integrated modeling strategy with a single set of parameters for the common mode s that is estimated based on the information in all data blocks may be most appropriate such a strategy implies a global model consisting of different n way n mode submodels and a global loss function that is a weighted sum of the partial loss functions associated with the different submodels in this paper such a global model for an integrated analysis of a three way three mode binary data array and a two way two mode binary data matrix that have one mode in common is presented a simulated annealing algorithm to estimate the model parameters is described and evaluated in a simulation study an application of the model to real psychological data is discussed

high snr consistent linear model order selection and subset selection high snr consistency of model order selection criteria in linear regression models has attracted a lot of attention in the signal processing community recently it is now known that exponentially embedded family versions of minimum description length etc are high snr consistent however a general framework for high snr consistency in linear regression is still missing this paper fills this gap by deriving necessary and sufficient conditions nscs for model order selection criteria in both known and unknown noise variance situations to be high snr consistent many popular model order selection criteria are proved to be high snr consistent using these nscs we also provide a convergence rate analysis to discriminate between various high snr consistent model order selection criteria a direct application of model order selection techniques to the very important subset selection problem is computationally infeasible this paper establish the high snr consistency of an existing t statistics based index ordering scheme that allows the conversion of a subset selection problem into a model order selection problem combining this index ordering with high snr consistent model order selection criteria leads to a novel subset selection procedure ssp that is numerically shown to outperform existing high snr consistent ssps

semiparametric estimation of count regression models this paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity we use the generalized laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a poisson mixture model we establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated censored and zero inflated count regression models monte carlo evidence shows that the finite sample behavior of the estimator is quite good the paper applies the method to a model of individual shopping behavior

factor analysis and aic the information criterion aic was introduced to extend the method of maximum likelihood to the multimodel situation it was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis the use of the aic criterion in the factor analysis is particularly interesting when it is viewed as the choice of a bayesian model this observation shows that the area of application of aic can be much wider than the conventional i i d type models on which the original derivation of the criterion was based the observation of the bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings

optimal product positioning based on paired comparison data a new approach for analyzing paired comparison data is proposed which combines a probabilistic ideal point model with product positioning issues unlike traditional approaches based on paired comparison data the same formulation is used for estimating a joint space representation of consumer segments and products as well as for determining optimal new product positioning options in a relevant product market a monte carlo experiment is presented and real world coffee market data are used to show advantages of the new approach

mixtures of constrained ultrametric trees this paper presents a new methodology concerned with the estimation of ultrametric trees calibrated on subjects pairwise proximity judgments of stimuli capturing subject heterogeneity using a finite mixture formulation we assume that a number of unobserved classes of subjects exist each having a different ultrametric tree structure underlying the pairwise proximity judgments a new likelihood based estimation methodology is presented for those finite mixtures of ultrametric trees that accommodates ultrametric as well as other external constraints various assumptions on the correlation of the error of the dissimilarities are accommodated the performance of the method to recover known ultrametric tree structures is investigated on synthetic data an empirical application to published data from schiffman reynolds and young 1981 is provided the ability to deal with external constraints on the tree topology is demonstrated and a comparison with an alternative clustering based method is made

selecting a separable parametric spatiotemporal covariance structure for longitudinal imaging data longitudinal imaging studies allow great insight into how the structure and function of a subject s internal anatomy changes over time unfortunately the analysis of longitudinal imaging data is complicated by inherent spatial and temporal correlation the temporal from the repeated measures and the spatial from the outcomes of interest being observed at multiple points in a patients body we propose the use of a linear model with a separable parametric spatiotemporal error structure for the analysis of repeated imaging data the model makes use of spatial exponential spherical and matern and temporal compound symmetric autoregressive 1 toeplitz and unstructured parametric correlation functions a simulation study inspired by a longitudinal cardiac imaging study on mitral regurgitation patients compared different information criteria for selecting a particular separable parametric spatiotemporal correlation structure as well as the effects on type i and ii error rates for inference on fixed effects when the specified model is incorrect information criteria were found to be highly accurate at choosing between separable parametric spatiotemporal correlation structures misspecification of the covariance structure was found to have the ability to inflate the type i error or have an overly conservative test size which corresponded to decreased power an example with clinical data is given illustrating how the covariance structure procedure can be done in practice as well as how covariance structure choice can change inferences about fixed effects

restricted spatial regression methods implications for inference the issue of spatial confounding between the spatial random effect and the fixed effects in regression analyses has been identified as a concern in the statistical literature multiple authors have

the geometry of loop groups l espace g des boucles basees sur un groupe de lie compact admet une metrique de kahler on exprime sa courbure en termes d operateurs de toeplitz et on definit des classes de chern par analogie avec la theorie de chern weil aux dimensions finies il y a une structure de fredhohn naturelle sur g induite a partir de la famille des operateurs de toeplitz on obtient des formules explicites pour su n

least informative distributions in maximum q log likelihood estimation abstract we use the maximum q log likelihood estimation for least informative distributions lids in order to estimate the parameters in probability density functions pdfs efficiently and robustly when data include outlier s lids are derived by using convex combinations of two pdfs a convex combination of two pdfs is composed of an underlying distribution and a contamination the optimal criterion is obtained by minimizing the change of maximum q log likelihood function when the data contain small amount of contamination in this paper we make a comparison between ordinary maximum likelihood estimation maximum q log likelihood estimation mqle and lids based on mqle for parameter estimation from data with outliers we derive a new fisher information matrix based on the score function for lid from m function and use it for choice of optimal estimator in the class of mqle the model selection is done by the robust information criteria we test the methods on the real data with outliers and estimate shape and scale parameters of probability distributions as a result we show that the lids based on mqle provide the most robust and efficient estimation of the model parameters

dimension reduction and alleviation of confounding for spatial generalized linear mixed models summary non gaussian spatial data are very common in many disciplines for instance count data are common in disease mapping and binary data are common in ecology when fitting spatial regressions for such data one needs to account for dependence to ensure reliable inference for the regression coefficients the spatial generalized linear mixed model offers a very popular and flexible approach to modelling such data but this model suffers from two major shortcomings variance inflation due to spatial confounding and high dimensional spatial random effects that make fully bayesian inference for such models computationally challenging we propose a new parameterization of the spatial generalized linear mixed model that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects we illustrate the application of our approach to simulated binary count and gaussian spatial data sets and to a large infant mortality data set

almost nonparametric inference for repeated measures in mixture models summary we consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions we require a vector of observations on each subject this vector is mapped into a vector of os and 1 s and summed the resulting distribution of sums can be modelled as a mixture of binomials we then work with the binomial mixture the efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when typically the true underlying mixture distribution is different it is shown that in many cases the approach based on simple binomial mixtures is superior let pi x and p2 x be probability distributions with ai and a2 positive real numbers that sum to 1 then p x al pi x a2 p2 x defines a two component mixture distribution with com ponents pl x and p2 x and mixture weights al and a2 mixture distributions arise when observations come from different populations each with a different distribution and the population sampled is unobserved interesting examples include those in the social sciences in which important variables are latent and unobserved as an example consider the problem of trying to infer the solution strategies which young children employ in solving a cognitive task when different solution strategies can be employed a group of same age children can be considered a sample from a mixture distribution in which the components correspond to the various strategies see thomas and horton 1997 recently there has been an expanding interest in mixtures and there is now a large literature examples and theory may be found in many sources including lindsay 1995 mclachlan and basford 1988 titterington et al 1985 and everitt and hand 1981 computational issues in estimating the model parameters rely mainly on the em algorithm see mclachlan and krishnan 1997 for a detailed account two main issues remain unresolved in applications of mixtures one is the specification of the number of components although there may sometimes be substantive theory to guide this specification in exploratory settings