an exact likelihood analysis of the multinomial probit model abstract we develop new methods for conducting a finite sample likelihood based analysis of the multinomial probit model using a variant of the gibbs sampler an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors this approach avoids direct evaluation of the likelihood and thus avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches both simulated and actual consumer panel data are used to fit six dimensional choice models we also develop methods for analyzing random coefficient and multiperiod probit models

azumaya algebras with involutions res 2wr zbr s cores br r 1 one could ask whether this sequence is exact indeed if r and s are fields and char r 2 the exactness of the above sequence is proved in cl corollary 4 6 p 4731 let a be an azumaya s algebra whose class a belongs to kernel cores br s br r for a to belong to res br r it is necessary and sufficient that there exists an azumaya s algebra b brauer equivalent to a admitting involutions of first and second kinds which commute results of saltman assert lo that there exist algebras bi i 1 2 brauer equivalent to a which support involutions of the first and second kind respectively we construct section 4 a homomorphism h ker cores br s br r pic rjcores pit s whose kernel consists precisely of classes of azumaya s algebras which support commuting involutions of both kinds thus h is a measure of the obstruction to the sequence 1 being exact in particular if pit r cores pit s 1 is exact

bayesian random effects meta analysis of trials with binary outcomes methods for the absolute risk difference and relative risk scales when conducting a meta analysis of clinical trials with binary outcomes a normal approximation for the summary treatment effect measure in each trial is inappropriate in the common situation where some of the trials in the meta analysis are small or the observed risks are close to 0 or 1 this problem can be avoided by making direct use of the binomial distribution within trials a fully bayesian method has already been developed for random effects meta analysis on the log odds scale using the bugs implementation of gibbs sampling in this paper we demonstrate how this method can be extended to perform analyses on both the absolute and relative risk scales within each approach we exemplify how trial level covariates including underlying risk can be considered data from 46 trials of the effect of single dose ibuprofen on post operative pain are analysed and the results contrasted with those derived from classical and bayesian summary statistic methods the clinical interpretation of the odds ratio scale is not straightforward the advantages and flexibility of a fully bayesian approach to meta analysis of binary outcome data considered on an absolute risk or relative risk scale are now available

reference bayesian methods for generalized linear mixed models abstract bayesian methods furnish an attractive approach to inference in generalized linear mixed models in the absence of subjective prior information for the random effect variance components these analyses are typically conducted using either the standard invariant prior for normal responses or diffuse conjugate priors previous work has pointed out serious difficulties with both strategies and we show here that as in normal mixed models the standard invariant prior leads to an improper posterior distribution for generalized linear mixed models this article proposes and investigates two alternative reference i e objective or noninformative priors an approximate uniform shrinkage prior and an approximate jeffreys s prior we give conditions for the existence of the posterior distribution under any prior for the variance components in conjunction with a uniform prior for the fixed effects the approximate uniform shrinkage prior is shown to satisfy these conditions for several families of d

a note on the existence of the posterior distribution for a class of mixed models for binomial responses summary necessary and sufficient conditions are given for the existence of the posterior distribution of the variance components in a class of mixed models for binomial responses the implications of our results are illustrated through an example

linear mixed models for skew normal independent bivariate responses with an application to periodontal disease bivariate clustered correlated data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model framework with underlying normality assumptions of the random effects and within subject errors however such normality assumptions might be questionable if the data set particularly exhibit skewness and heavy tails using a bayesian paradigm we use the skew normal independent sni distribution as a tool for modeling clustered data with bivariate non normal responses in a linear mixed model framework the sni distribution is an attractive class of asymmetric thick tailed parametric structure which includes the skew normal distribution as a special case we assume that the random effects follows multivariate skew normal independent distributions and the random errors follow symmetric normal independent distributions which provides substantial robustness over the symmetric normal process in a linear mixed model framework specific distributions obtained as special cases viz the skew t the skew slash and the skew contaminated normal distributions are compared along with the default skew normal density the methodology is illustrated through an application to a real data which records the periodontal health status of an interesting population using periodontal pocket depth ppd and clinical attachment level cal

bilinear mixed effects models for dyadic data this article discusses the use of a symmetric multiplicative interaction effect to capture certain types of third order dependence patterns often present in social networks and other dyadic datasets such an effect along with standard linear fixed and random effects is incorporated into a generalized linear model and a markov chain monte carlo algorithm is provided for bayesian estimation and inference in an example analysis of international relations data accounting for such patterns improves model fit and predictive performance

misspecifying the covariance structure in a linear mixed model under mar drop out misspecification of the covariance structure in a linear mixed model lmm can lead to biased population parameters estimates under mar drop out in our motivating example of modeling cd4 cell counts during untreated hiv infection random intercept and slope lmms are frequently used in this article we evaluate the performance of lmms with specific covariance structures in terms of bias in the fixed effects estimates under specific mar drop out mechanisms and adopt a bayesian model comparison criterion to discriminate between the examined approaches in real data applications we analytically show that using a random intercept and slope structure when the true one is more complex can lead to seriously biased estimates with the degree of bias depending on the magnitude of the mar drop out under misspecified covariance structure we compare in terms of induced bias the approach of adding a fractional brownian motion bm process on top of random intercepts and slopes with the approach of using splines for the random effects in general the performance of both approaches was satisfactory with the bm model leading to smaller bias in most cases a simulation study is carried out to evaluate the performance of the proposed bayesian criterion in identifying the model with the correct covariance structure overall the proposed method performs better than the aic and bic criteria under our specific simulation setting the models under consideration are applied to real data from the cascade study the most plausible model is identified by all examined criteria

cyclic galois extensions and normal bases a kummer theory is presented which does not need roots of unity in the ground ring for r commutative with p i e r we study the group of cyclic galois extensions of fixed degree pn in detail our theory is well suited for dealing with cyclic pn extensions of a number field k which are unramified outside p we then consider the group gal 6f p i cpn of all such extensions and its subgroup nb k k p1 cpn of extensions with integral normal basis outside p for the size of the latter we get a simple asymptotic formula n oo and the discrepancy between the two groups is in some way measured by the defect a in leopoldt s conjecture introduction this work begins with a general study of galois extensions of a commutative ring r with finite abelian galois group g part i the results are applicable in a number theoretical setting part ii and give theorems concerning the existence of p integral normal bases in cpn extensions and zp extensions of an arbitrary number field k here p is an odd prime cpn is the cyclic group of order pn and p integral means integral outside places over p let us start by describing the general situation let r be a commutative ring with 1 and g a finite abelian group we study the finite abelian group gal r g which consists of the isomorphism classes of g galois ring extensions of r such extensions were defined by chase harrison and rosenberg 4 the group structure on gal r g is due to harrison 13 and goes back to hasse 14 for the case r k a field in that case the basic idea is to admit some nonfields galois algebras in order to form gal k g the principal link between general galois theory of rings and number theory is the study of ramification let l be a g galois field extension of the number field k x a set of finite places of k and r the ring of x integers in k then the integral closure s of r in l is a g galois extension of r if and only if l k is unramified at all finite places outside x see 4 remark 1 5d in particular 6 l is galois over k iff l k is unramified except at infinity received by the editors june 13 1989 1980 mathematics subject classification 1985 revision primary 1 lr33 1 lr27 13b05

hierarchical poisson regression modeling abstract the poisson model and analyses here feature nonexchangeable gamma distributions although exchangeable following a scale transformation for individual parameters with standard deviations proportional to means a relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components when tested in simulation studies the resulting procedure provides better coverage probabilities and smaller risk than several other published rules and thus works well from bayesian and frequentist perspectives alike the computations provide fast accurate density approximations to individual parameters and to structural regression coefficients the computer program is publicly available through statlib

illustration of bayesian inference in normal data models using gibbs sampling abstract the use of the gibbs sampler as a method for calculating bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models including variance components unordered and ordered means hierarchical growth curves and missing data in a crossover trial in all cases the approach is straightforward to specify distributionally and to implement computationally with output readily adapted for required inference summaries

bayesian multivariate logistic regression bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes in addition difficulties arise when simple noninformative priors are chosen for the covariance parameters motivated by these problems we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data the model for individual outcomes has a marginal logistic structure simplifying interpretation we follow a bayesian approach to estimation and inference developing an efficient data augmentation algorithm for posterior computation the method is illustrated with application to a neurotoxicology study

a note on a albert and j a anderson s conditions for the existence of maximum likelihood estimates in logistic regression models summary this note expands the paper by albert anderson 1984 on the existence and uniqueness of maximum likelihood estimates in logistic regression models their three possible mutually exclusive data pattems i overlap ii complete separation and iii quasiseparation are considered the maximum likelihood estimate exists only in i modifications of the statement and proofs of albert anderson s results are given for ii and iii the identifiability for a more general model arising in the study of iii is discussed together with the maximization of the corresponding likelihood a linear program is presented which determines whether data is of type i ii or iii and in the case of iii identifies albert anderson s minimal set qm

inference of nested variance components in a longitudinal myopia intervention trial this paper was motivated by a double blind randomized clinical trial of myopia intervention in addition to the primary goal of comparing treatment effects we are concerned with the modelling of correlation that may come from two possible sources one among the longitudinal observations and the other between measurements taken from both eyes per subject the data are nested repeated measurements we suggest three models for analysis each one expresses the correlation differently in various covariance structures we articulate their differences and describe the implementations in estimation using commercial statistical software the computer output can be further utilized to perform model selection with schwarz criterion simulation studies are conducted to evaluate the performance under each model data of the myopia intervention trial are reanalysed with these models for illustration the results indicate that atropine is more effective in reducing the progression rate the rates are homogeneous across subjects and among the suggested models the one with independent random effects of two eyes fits best we conclude that model selection is a crucial step before making inference with estimates otherwise the correlation may be attributed incorrectly to a different mechanism the same conclusion applies to other variance components as well copyright 2005 john wiley sons ltd

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

the hodge conjecture for self products of certain k3 surfaces abstract we use a result of van geemen 2008 vg4 to determine the endomorphism algebra of the kuga satake variety of a k3 surface with real multiplication this is applied to prove the hodge conjecture for self products of double covers of p 2 which are ramified along six lines

critical and multicritical o n models soluble o n models on the square lattice are found via the yang baxter equations in a parameter space of three coupling constants a number of distinct soluble cases are found for each value of n some of these constitute critical or multicritical points in the phase diagram for all solutions the free energy per spin can be determined using the bethe ansatz by studying the finite size corrections at the critical points the critical exponents and the central charge can be found in some cases analytically and failing that numerically by extrapolation of exact results for finite size systems

discretely holomorphic parafermions and integrable loop models we define parafermionic observables in various lattice loop models including examples where no kramers wannier duality holds for a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these variables are discretely holomorphic they satisfy a lattice version of the cauchy riemann equations as long as the boltzmann weights satisfy certain linear constraints in the cases considered the weights then also satisfy the critical yang baxter equations with the spectral parameter being related linearly to the angle of the elementary rhombus

the effect of improper priors on gibbs sampling in hierarchical linear mixed models abstract often either from a lack of prior information or simply for convenience variance components are modeled with improper priors in hierarchical linear mixed models although the posterior distributions for these models are rarely available in closed form the usual conjugate structure of the prior specification allows for painless calculation of the gibbs conditionals thus the gibbs sampler may be used to explore the posterior distribution without ever having established propriety of the posterior an example is given showing that the output from a gibbs chain corresponding to an improper posterior may appear perfectly reasonable thus one cannot expect the gibbs output to provide a red flag informing the user that the posterior is improper the user must demonstrate propriety before a markov chain monte carlo technique is used a theorem is given that classifies improper priors according to the propriety of the resulting posteriors applications concerning bayesian analysis of animal breeding

multilevel modeling with correlated effects when there exist omitted effects measurement error and or simultaneity in multilevel models explanatory variables may be correlated with random components and standard estimation methods do not provide consistent estimates of model parameters this paper introduces estimators that are consistent under such conditions by employing generalized method of moments gmm estimation techniques in multilevel modeling the authors present a series of estimators along a robust to efficient continuum this continuum depends on the assumptions that the analyst makes regarding the extent of the correlated effects it is shown that the gmm approach provides an overarching framework that encompasses well known estimators such as fixed and random effects estimators and also provides more options these gmm estimators can be expressed as instrumental variable iv estimators which enhances their interpretability moreover by exploiting the hierarchical structure of the data the current technique does not require additional variables unlike traditional iv methods further statistical tests are developed to compare the different estimators a simulation study examines the finite sample properties of the estimators and tests and confirms the theoretical order of the estimators with respect to their robustness and efficiency it further shows that not only are regression coefficients biased but variance components may be severely underestimated in the presence of correlated effects empirical standard errors are employed as they are less sensitive to correlated effects when compared to model based standard errors an example using student achievement data shows that gmm estimators can be effectively used in a search for the most efficient among unbiased estimators

bayesian inference in semiparametric mixed models for longitudinal data we consider bayesian inference in semiparametric mixed models spmms for longitudinal data spmms are a class of models that use a nonparametric function to model a time effect a parametric function to model other covariate effects and parametric or nonparametric random effects to account for the within subject correlation we model the nonparametric function using a bayesian formulation of a cubic smoothing spline and the random effect distribution using a normal distribution and alternatively a nonparametric dirichlet process dp prior when the random effect distribution is assumed to be normal we propose a uniform shrinkage prior usp for the variance components and the smoothing parameter when the random effect distribution is modeled nonparametrically we use a dp prior with a normal base measure and propose a usp for the hyperparameters of the dp base measure we argue that the commonly assumed dp prior implies a nonzero mean of the random effect distribution even when a base measure with mean zero is specified this implies weak identifiability for the fixed effects and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function we propose an adjustment using a postprocessing technique we show that under mild conditions the posterior is proper under the proposed usp a flat prior for the fixed effect parameters and an improper prior for the residual variance we illustrate the proposed approach using a longitudinal hormone dataset and carry out extensive simulation studies to compare its finite sample performance with existing methods

discretely holomorphic parafermions and integrable boundary conditions in two dimensional statistical models possessing a discretely holomorphic parafermion we introduce a modified discrete cauchy riemann equation on the boundary of the domain and we show that the solution of this equation yields integrable boundary boltzmann weights this approach is applied to i the square lattice o n loop model where the exact locations of the special and ordinary transitions are recovered and ii the fateev zamolodchikov spin model where a new rotation invariant integrable boundary condition is discovered for generic n

discrete holomorphicity at two dimensional critical points after a brief review of the historical role of analyticity in the study of critical phenomena an account is given of recent discoveries of discretely holomorphic observables in critical two dimensional lattice models these are objects whose correlation functions satisfy a discrete version of the cauchy riemann relations their existence appears to have a deep relation with the integrability of the model and they are presumably the lattice versions of the truly holomorphic observables appearing in the conformal field theory cft describing the continuum limit this hypothesis sheds light on the connection between cft and integrability and if verified can also be used to prove that the scaling limit of certain discrete curves in these models is described by schramm loewner evolution sle

hierarchical models a current computational perspective 2000 hierarchical models a current computational perspective journal of the american statistical association vol 95 no 452 pp 1312 1316

corestriction for algebras with group action abstract we define a corestriction map for equivariant brauer groups in the sense of frohlich and wall which contain as a special case the brauer clifford groups introduced by turull we show that this corestriction map has similar properties as the corestriction map in group cohomology especially galois cohomology in particular composing corestriction and restriction associated to a subgroup h g amounts to powering with the index g h

an assessment of estimation methods for generalized linear mixed models with binary outcomes two main classes of methodology have been developed for addressing the analytical intractability of generalized linear mixed models likelihood based methods and bayesian methods likelihood based methods such as the penalized quasi likelihood approach have been shown to produce biased estimates especially for binary clustered data with small clusters sizes more recent methods using adaptive gaussian quadrature perform well but can be overwhelmed by problems with large numbers of random effects and efficient algorithms to better handle these situations have not yet been integrated in standard statistical packages bayesian methods although they have good frequentist properties when the model is correct are known to be computationally intensive and also require specialized code limiting their use in practice in this article we introduce a modification of the hybrid approach of capanu and begg 2011 biometrics 67 371 380 as a bridge between the likelihood based and bayesian approaches by employing bayesian estimation for the variance components followed by laplacian estimation for the regression coefficients we investigate its performance as well as that of several likelihood based methods in the setting of generalized linear mixed models with binary outcomes we apply the methods to three datasets and conduct simulations to illustrate their properties simulation results indicate that for moderate to large numbers of observations per random effect adaptive gaussian quadrature and the laplacian approximation are very accurate with adaptive gaussian quadrature preferable as the number of observations per random effect increases the hybrid approach is overall similar to the laplace method and it can be superior for data with very sparse random effects copyright 2013 john wiley sons ltd

conserved currents in the six vertex and trigonometric solid on solid models we construct quasi local conserved currents in the six vertex model with anisotropy parameter by making use of the quantum group approach of bernard and felder from these currents we construct parafermionic operators with spin that obey a discrete integral condition around lattice plaquettes embedded into the complex plane these operators are identified with primary fields in a c 1 compactified free boson conformal field theory we then consider a vertex face correspondence that takes the six vertex model to a trigonometric sos model and construct sos operators that are the image of the six vertex currents under this correspondence we define corresponding sos parafermionic operators with spins s 1 and that obey discrete integral conditions around sos plaquettes embedded into the complex plane we consider in detail the cyclic sos case corresponding to the choice with coprime we identify our sos parafermionic operators in terms of the screening operators and primary fields of the associated conformal field theory

crossed random effect models for multiple outcomes in a study of teratogenesis human teratogens often manifest themselves through a broad spectrum of adverse effects although often not serious when considered individually such outcomes taken together may represent a syndrome that can lead to serious developmental problems accordingly studies that investigate the effect of human teratogens on fetal development typically record the presence or absence of a multitude of abnormalities resulting in the data of multivariate binary form for each infant such studies typically have three objectives 1 estimate an overall effect of exposure across outcomes 2 identify subjects having the syndrome and 3 identify those outcomes that constitute the syndrome so that doctors know what to look for when diagnosing the syndrome in other exposed newborns this article proposes the use of a logistic regression model with crossed random effect structure to address all three questions simultaneously we use the proposed models to analyze data from a study investigating the effects of in uter

bayesian methods of analysis for cluster randomized trials with binary outcome data we explore the potential of bayesian hierarchical modelling for the analysis of cluster randomized trials with binary outcome data and apply the methods to a trial randomized by general practice an approximate relationship is derived between the intracluster correlation coefficient icc and the between cluster variance used in a hierarchical logistic regression model by constructing an informative prior for the icc on the basis of available information we are thus able implicitly to specify an informative prior for the between cluster variance the approach also provides us with a credible interval for the icc for binary outcome data several approaches to constructing informative priors from empirical icc values are described we investigate the sensitivity of results to the prior specified and find that the estimate of intervention effect changes very little in this data set while its interval estimate is more sensitive the bayesian approach allows us to assume distributions other than normality for the random effects used to model the clustering this enables us to gain insight into the robustness of our parameter estimates to the classical normality assumption in a model with a more complex variance structure bayesian methods can provide credible intervals for a difference between two variance components in order for example to investigate whether the effect of intervention varies across clusters we compare our results with those obtained from classical estimation discuss the relative merits of the bayesian framework and conclude that the flexibility of the bayesian approach offers some substantial advantages although selection of prior distributions is not straightforward

a closer look at combining data among a small number of binomial experiments in a regulatory environment the regulators and the regulated may not be able to agree on the use of subjective prior information for a clinical trial the use of a data based prior offers a greater possibility for agreement however the degree of importance given to the prior data may still be contentious the use of a hierarchical model to link the prior data and the current trial is shown to provide a relatively objective method for assigning weight to the prior data using a series of examples combining two binomial experiments the effect of a hierarchical model on estimating rates on the degree to which data is combined and on hypothesis testing is illustrated in addition the phenomenon in which combining data reduces the precision is explained simpler models based on finite mixtures of beta distributions are shown to work as well as the more computationally intensive continuous mixtures lastly an example combining three concurrent studies is illustrated published in 2001 by john wiley sons ltd

nonconjugate bayesian analysis of variance component models we consider the usual normal linear mixed model for variance components from a bayesian viewpoint with conjugate priors and balanced data gibbs sampling is easy to implement however simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors thus leading one to consider alternative markov chain monte carlo schemes we propose and investigate a method for posterior simulation based on an independence chain the method is customized to exploit the structure of the variance component model and it works with arbitrary prior distributions as a default reference prior we use a version of jeffreys prior based on the integrated restricted likelihood we demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data

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

on the residue fields of henselian valued stable fields abstract let k v be a henselian valued field satisfying the following conditions for a given prime number p i central division k algebras of finite p primary dimensions have schur indices equal to their exponents ii the value group v k properly includes its subgroup p v k the paper shows that if k is the residue field of k v and r is an intermediate field of the maximal p extension k p k then the natural homomorphism br k br r of brauer groups maps surjectively the p component br k p on br r p it proves that br k p is divisible if p 2 or k is a nonreal field and that br k 2 is of order 2 when k is formally real we also obtain that r embeds as a k subalgebra in a central division k algebra if and only if the degree r k divides the index of

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

conformal invariance of spin correlations in the planar ising model we rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi point spin correlations in the critical ising model on arbitrary simply connected planar domains this solves a number of conjectures coming from the physical and the mathematical literature the proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques

scaling dimensions and conformal anomaly in anisotropic lattice spin models the effect of anisotropic interactions on the eigenvalue spectrum of the row to row transfer matrix of critical lattice spin models is investigated it is verified that the predictions of conformal theory apply to anisotropic systems if one allows for spatial rescaling by incorporating an anisotropy factor zeta ay ax sin theta where ay and ax are lattice spacings and theta is an angle describing the anisotropy for exactly solvable models these anisotropy angles can be calculated analytically using corner transfer matrices this is done for the eight vertex model hard hexagons and interacting hard squares and it is found that theta pi u lambda 10u 3 and 5u respectively where u is the spectral parameter and lambda is the crossing parameter for each of these models the amplitude of the finite size corrections to the free energy at criticality is found to be of the form pi zeta c 6n2 where zeta is the anisotropy factor and the central charge or conformal anomaly is given by c 1 4 5 and 7 10 respectively this is an analytic result for the eight vertex model for the hard hexagon and square models the largest eigenvalues are found accurately by numerically solving their inversion identities for various anisotropies and strip widths up to n 48 finally the authors argue that the anisotropy angle for magnetic hard squares and the q state potts models is also given by theta pi u lambda so this result is quite general

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

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 selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

rhombic embeddings of planar quad graphs given a finite or infinite planar graph all of whose faces have degree 4 we study embeddings in the plane in which all edges have length 1 that is in which every face is a rhombus we give a necessary and sucient condition for the existence of such an embedding as well as a description of the set of all such embeddings r etant donne un graphe planaire fini ou infini dont toutes les faces sont de degre 4 onetudie ses plongements dans le plan dont toutes les aretes sont de longueur 1 c estdire dont toutes les faces sont des losanges on donne une condition necessaire et susante pour l existence d un tel plongement et on decrit l ensemble de ces plongements

integrability as a consequence of discrete holomorphicity loop models it has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical boltzmann weights in a number of lattice models remarkably the solutions of these linear equations also solve the yang baxter equations we extend this analysis for the zn model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi for two rhombi this leads to a quadratic equation in the boltzmann weights and for three rhombi a cubic equation the two rhombus equation implies the inversion relations the star triangle relation follows from the three rhombus equation we also show that these weights are self dual as a consequence of discrete holomorphicity this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

induced orthogonal representations of galois groups abstract we prove a result showing the connection between induced orthogonal representations and corestrictions of group extensions derived from their clifford groups by the means of the corestriction map we then obtain new obstructions to the p embedding problems given by the group extensions of the modular p group and to one 2 embedding problem given by a group extension of the dihedral group

isotropic trialitarian algebraic groups abstract by modifying a construction from knus et al we construct all isotropic algebraic groups of type 3 d 4 and 6 d 4 over an arbitrary field of characteristic 2 we also provide a nice isomorphism criterion for such groups the results of this paper extend the main results of allison using entirely different methods to fields of nonzero characteristic and algebraic groups

the energy density in the planar ising model we study the critical ising model on the square lattice in bounded simply connected domains with and free boundary conditions we relate the energy density of the model to a discrete fermionic spinor and compute its scaling limit by discrete complex analysis methods as a consequence we obtain a simple exact formula for the scaling limit of the energy field one point function in terms of the hyperbolic metric this confirms the predictions originating in physics but also provides a higher precision

testing random effects in the linear mixed model using approximate bayes factors deciding which predictor effects may vary across subjects is a difficult issue standard model selection criteria and test procedures are often inappropriate for comparing models with different numbers of random effects due to constraints on the parameter space of the variance components testing on the boundary of the parameter space changes the asymptotic distribution of some classical test statistics and causes problems in approximating bayes factors we propose a simple approach for testing random effects in the linear mixed model using bayes factors we scale each random effect to the residual variance and introduce a parameter that controls the relative contribution of each random effect free of the scale of the data we integrate out the random effects and the variance components using closed form solutions the resulting integrals needed to calculate the bayes factor are low dimensional integrals lacking variance components and can be efficiently approximated with laplace s method we propose a default prior distribution on the parameter controlling the contribution of each random effect and conduct simulations to show that our method has good properties for model selection problems finally we illustrate our methods on data from a clinical trial of patients with bipolar disorder and on data from an environmental study of water disinfection by products and male reproductive outcomes

universality in the 2d ising model and conformal invariance of fermionic observables it is widely believed that the celebrated 2d ising model at criticality has a universal and conformally invariant scaling limit which is used in deriving many of its properties however no mathematical proof has ever been given and even physics arguments support a priori weaker mobius invariance we introduce discrete holomorphic fermions for the 2d ising model at criticality on a large family of planar graphs we show that on bounded domains with appropriate boundary conditions those have universal and conformally invariant scaling limits thus proving the universality and conformal invariance conjectures

additive multilevel item structure models with random residuals item modeling for explanation and item generation an additive multilevel item structure amis model with random residuals is proposed the model includes multilevel latent regressions of item discrimination and item difficulty parameters on covariates at both item and item category levels with random residuals at both levels the amis model is useful for explanation purposes and also for prediction purposes as in an item generation context the parameters can be estimated with an alternating imputation posterior algorithm that makes use of adaptive quadrature and the performance of this algorithm is evaluated in a simulation study

how vague is vague a simulation study of the impact of the use of vague prior distributions in mcmc using winbugs there has been a recent growth in the use of bayesian methods in medical research the main reasons for this are the development of computer intensive simulation based methods such as markov chain monte carlo mcmc increases in computing power and the introduction of powerful software such as winbugs this has enabled increasingly complex models to be fitted the ability to fit these complex models has led to mcmc methods being used as a convenient tool by frequentists who may have no desire to be fully bayesian often researchers want the data to dominate when there is no prior information and thus attempt to use vague prior distributions however with small amounts of data the use of vague priors can be problematic the results are potentially sensitive to the choice of prior distribution in general there are fewer problems with location parameters the main problem is with scale parameters with scale parameters not only does one have to decide the distributional form of the prior distribution but also whether to put the prior distribution on the variance standard deviation or precision we have conducted a simulation study comparing the effects of 13 different prior distributions for the scale parameter on simulated random effects meta analysis data we varied the number of studies 5 10 and 30 and compared three different between study variances to give nine different simulation scenarios one thousand data sets were generated for each scenario and each data set was analysed using the 13 different prior distributions the frequentist properties of bias and coverage were investigated for the between study variance and the effect size the choice of prior distribution was crucial when there were just five studies there was a large variation in the estimates of the between study variance for the 13 different prior distributions with a large number of studies the choice of prior distribution was less important the effect size estimated was not biased but the precision with which it was estimated varied with the choice of prior distribution leading to varying coverage intervals and potentially to different statistical inferences again there was less of a problem with a larger number of studies there is a particular problem if the between study variance is close to the boundary at zero as mcmc results tend to produce upwardly biased estimates of the between study variance particularly if inferences are based on the posterior mean the choice of vague prior distribution can lead to a marked variation in results particularly in small studies sensitivity to the choice of prior distribution should always be assessed

high dimensional exploratory item factor analysis by a metropolis hastings robbins monro algorithm a metropolis hastings robbins monro mh rm algorithm for high dimensional maximum marginal likelihood exploratory item factor analysis is proposed the sequence of estimates from the mh rm algorithm converges with probability one to the maximum likelihood solution details on the computer implementation of this algorithm are provided the accuracy of the proposed algorithm is demonstrated with simulations as an illustration the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children it is shown that when the dimensionality is high mh rm has advantages over existing methods such as numerical quadrature based em algorithm extensions of the algorithm to other modeling frameworks are discussed

estimability and likelihood inference for generalized linear mixed models using data cloning maximum likelihood estimation for generalized linear mixed models glmm an important class of statistical models with substantial applications in epidemiology medical statistics and many other fields poses significant computational difficulties in this article we use data cloning a simple computational method that exploits advances in bayesian computation in particular the markov chain monte carlo method to obtain maximum likelihood estimators of the parameters in these models this method also leads to a simple estimator of the asymptotic variance of the maximum likelihood estimators determining estimability of the parameters in a mixed model is in general a very difficult problem data cloning provides a simple graphical test to not only check if the full set of parameters is estimable but also and perhaps more importantly if a specified function of the parameters is estimable one of the goals of mixed models is to predict random effects we suggest a frequentist method to obtain predict