choice of column scores for testing independence in ordered 2 x k contingency tables the numerous statistical methods for testing no association between a binary response rows and k ordered categories columns group naturally into two classes those that require preassigned numerical column scores and those that do not an example of the former would be a logistic regression analysis and of the latter would be a wilcoxon rank sum test in this paper we demonstrate that the perceived advantage of not preassigning scores is illusory we do this by presenting an example from our consulting experience in which the midrank scores used by the rank tests that do not require preassigned scores are clearly inappropriate our recommendations are to assign reasonable column scores whenever possible and to consider equally spaced scores when the choice is not apparent midranks as scores should always be examined for their appropriateness before a rank test is applied

assessing proportionality in the proportional odds model for ordinal logistic regression the proportional odds model for ordinal logistic regression provides a useful extension of the binary logistic model to situations where the response variable takes on values in a set of ordered categories the model may be represented by a series of logistic regressions for dependent binary variables with common regression parameters reflecting the proportional odds assumption key to the valid application of the model is the assessment of the proportionality assumption an approach is described arising from comparisons of the separate correlated fits to the binary logistic models underlying the overall model based on asymptotic distributional results formal goodness of fit measures are constructed to supplement informal comparisons of the different fits a number of proposals including application of bootstrap simulation are discussed and illustrated with a data example

discrimination and classification overview publisher summary this chapter discusses discrimination and classification the problem of discrimination and classification is mainly concerned with differentiating between g g 2 mutually exclusive populations and with classifying subjects or objects on the basis of multivariate observation the emphasis of the problem is on deriving a rule that can be used to optimally classify a new subject it is an important problem in statistics and applied mathematics as its applications are found in many diverse areas in practice the distributions are rarely known and if the form of the distributions are known or assumed the parameters are seldom known thus the problem for practical applications is to develop a sample based rule for discrimination and classification the earliest and most well known method is based on the linear discriminant function due to fisher

order restricted score parameters in association models for contingency tables abstract the row effects and column effects models for two way contingency tables have parameters for the row and column categories pertaining to the association between the variables for classifications having ordered categories it is often reasonable to assume that the association parameters have a corresponding ordering this article proposes order restricted estimates of the association parameters in these models the maximum likelihood solution can be determined by the solution of a simple isotonic regression of some of the model sufficient statistics the models are primarily log linear in form and can be expressed in terms of odds ratios for 2 2 subtables consisting of adjacent rows and adjacent columns for the order restricted solution these local log odds ratios have uniform sign goodness of fit statistics for this solution are related to corresponding statistics for collapsed tables and to statistics for testing equality of sets of the parameters the row effects model discussed in this art

25th order high temperature expansion results for three dimensional ising like systems on the simple cubic lattice 25th order high temperature series are computed for a general nearest neighbor three dimensional ising model with arbitrary potential on the simple cubic lattice in particular we consider three improved potentials characterized by suppressed leading scaling corrections critical exponents are extracted from high temperature series specialized to improved potentials obtaining gamma 1 2373 2 nu 0 63012 16 alpha 0 1096 5 eta 0 03639 15 beta 0 32653 10 delta 4 7893 8 moreover biased analyses of the 25th order series of the standard ising model provide the estimate delta 0 52 3 for the exponent associated with the leading scaling corrections by the same technique we study the small magnetization expansion of the helmholtz free energy the results are then applied to the construction of parametric representations of the critical equation of state using a systematic approach based on a global stationarity condition accurate estimates of several universal amplitude ratios are also presented

hypothesis testing in the polychotomous logistic model with an application to detecting gastrointestinal cancer we discuss the use of the trichotomous logistic model to discriminate between patients with gastrointestinal gi cancer patients with benign gi disease and normal subjects using symptoms and the concentrations of some serum proteins that are potentially indicative of malignancy as covariates a parsimonious model can be obtained by invoking an indistinguishability hypothesis which is appropriate when a covariate is considered to have no predictive value between categories it is shown that the polychotomous model can be re parameterised under the null hypothesis to give a reduced form which can be fitted by maximum likelihood the validity of the use of the same methods for retrospective sampling is discussed the approach is illustrated by the development of a logistic model to identify symptomatic and asymptomatic subjects with a high risk of gi cancer

random rates in anisotropic regression in the context of minimax theory we propose a new kind of risk normalized by a random variable measurable with respect to the data we present a notion of optimality and a method to construct optimal procedures accordingly we apply this general setup to the problem of selecting significant variables in gaussian white noise in particular we show that our method essentially improves the accuracy of estimation in the sense of giving explicit improved confidence sets in l2 norm links to adaptive estimation are discussed 1 introduction searching for significant variables is certainly one of the oldest and most popular problems in statistics one of the simplest models where the issue of selecting significant variables was first stated mathematically is linear regression a vast literature has been devoted to this topic since and different approaches have been proposed over the last forty years both for estimation and for hypothesis testing among many authors we refer to akaike 1 breiman and freedman 3 chernoff 5 csiszar and korner 6 dychakov 10 patel 42 renyi 46 freidlina 13 meshalkin 35 malyutov and tsitovich 34 schwarz 47 and stone 48 in classical parametric regression if we consider a linear model we first have to measure the possible gain of searching for a limited number of significant variables if the model comes from a specific field of application then only an adequate description together with its solution is relevant however from a mathematical point of view a theory of selecting significant variables does not lead at least asymptotically to a substantial improvement of the accuracy of estimation in a regular parametric model the classical n rate of convergence is not affected by the number of significant variables however even in this setup let us emphasize that asymptotically has to be understood as up to a constant and that the correct choice of significant variables may possibly improve this constant if instead of a linear model we consider a nonparametric regression model the search for significant variables becomes crucial for estimating the regression function the rate of convergence explicitly depends on the set of significant variables let us develop this statement with the following example of multivariate regression suppose we observe z n xi y i i 1 n in the model

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

inference after model selection typical modeling strategies involve model selection which has a significant effect on inference of estimated parameters common practice is to use a selected model ignoring uncertainty introduced by the process of model selection this could yield overoptimistic inferences resulting in false discovery in this article we develop a general methodology via optimal approximation for estimating the mean and variance of complex statistics that involve the process of model selection this allows us to make approximately unbiased inferences taking into account the selection process we examine the operating characteristics of the proposed methodology via asymptotic analyses and simulations these results show that the proposed methodology yields correct inferences and outperforms common alternatives

a log linear model for ordinal data to characterize differential change among treatments we propose a family of log linear models for ordinal data that contain parameters reflecting change patterns to compare treatments relative to change from baseline under the most general model rates of change can depend not only upon the direction of change but also upon the level of the baseline classification we describe methods for selection of a parsimonious model and for tests of hypotheses concerning treatment differences interpretation of treatment differences in the follow up response profiles within baseline strata employs the concept of stochastic ordering data from two clinical trials illustrate the proposed procedure

a two stage regression model for epidemiological studies with multivariate disease classification data polytomous logistic regression is commonly used to analyze epidemiological data with disease subtype information in this approach effects of exposures on different disease subtypes are studied through separate exposure odds ratios comparing different case groups to the common control group this article considers the situation where disease subtypes can be defined using multiple characteristics of a disease for efficient analysis of such data a two stage modeling approach is proposed at the first stage a standard polytomous logistic regression model is considered for all possible distinct disease subtypes that can be defined by the cross classification of the different disease characteristics at the second stage the exposure odds ratio parameters for the first stage disease subtypes are further modeled in terms of the defining characteristics of the subtypes when the total number of first stage disease subtypes is small standard maximum likelihood methods can be used for inference in the proposed

decision combination in multiple classifier systems a multiple classifier system is a powerful solution to difficult pattern recognition problems involving large class sets and noisy input because it allows simultaneous use of arbitrary feature descriptors and classification procedures decisions by the classifiers can be represented as rankings of classifiers and different instances of a problem the rankings can be combined by methods that either reduce or rerank a given set of classes an intersection method and union method are proposed for class set reduction three methods based on the highest rank the borda count and logistic regression are proposed for class set reranking these methods have been tested in applications of degraded machine printed characters and works from large lexicons resulting in substantial improvement in overall correctness

retrospective prospective symmetry in the likelihood and bayesian analysis of case control studies summary prentice pyke 1979 established that the maximum likelihood estimate of an odds ratio in a case control study is the same as would be found by fitting a logistic regression in other words for this specific target the incorrect prospective model is inferentially equivalent to the correct retrospective model similar results have been obtained for other models and conditions have also been identified under which the corresponding bayesian property holds namely that the posterior distribution of the odds ratio is the same whether it is computed using the prospective or the retrospective likelihood in this article we demonstrate how these results follow directly from certain parameter independence properties of the models and priors and identify prior laws that support such reverse analysis for both standard and stratified designs somekeywords case controlstudy conditionalindependence hypermarkovlaw logisticregression retrospective likelihood

critical adsorption and critical casimir forces in the canonical ensemble critical properties of a liquid film between two planar walls are investigated in the canonical ensemble within which the total number of fluid particles rather than their chemical potential is kept constant the effect of this constraint is analyzed within mean field theory mft based on a ginzburg landau free energy functional as well as via monte carlo simulations of the three dimensional ising model with fixed total magnetization within mft and for finite adsorption strengths at the walls the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the lagrange multiplier associated with the constraint however due to a nonintegrable divergence of the mean field order parameter profile near a wall the limit of infinitely strong adsorption turns out to be not well defined within mft because it would necessarily violate the constraint the critical casimir force ccf acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles for instance the canonical ccf in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart we derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case but with the chemical potential playing the role of the lagrange multiplier associated with the constraint the different behavior of the ccf in the two ensembles is rationalized within mft by showing that for a prescribed value of the thermodynamic control parameter of the film i e density or chemical potential the film pressures are identical in the two ensembles while the corresponding bulk pressures are not

generalized estimating equations to estimate the ordered stereotype logit model for panel data by modeling the effects of predictor variables as a multiplicative function of regression parameters being invariant over categories and category specific scalar effects the ordered stereotype logit model is a flexible regression model for ordinal response variables in this article we propose a generalized estimating equations gee approach to estimate the ordered stereotype logit model for panel data based on working covariance matrices which are not required to be correctly specified a simulation study compares the performance of gee estimators based on various working correlation matrices and working covariance matrices using local odds ratios estimation of the model is illustrated using a real world dataset the results from the simulation study suggest that gee estimation of this model is feasible in medium sized and large samples and that estimators based on local odds ratios as realized in this study tend to be less efficient compared with estimators based on a working correlation matrix for low true correlations the efficiency gains seem to be rather small and if the working covariance structure is too flexible the corresponding estimator may even be less efficient compared with the gee estimator assuming independence like for gee estimators more generally if the true correlations over time are high then a working covariance structure which is close to the true structure can lead to considerable efficiency gains compared with assuming independence

accurate estimates of 3d ising critical exponents using the coherent anomaly method abstract an analysis of the critical behavior of the three dimensional ising model using the coherent anomaly method cam is presented various sources of errors in cam estimates of critical exponents are discussed and an improved scheme for the cam data analysis is tested using a set of mean field type approximations based on the variational series expansion approach accuracy comparable to the most precise conventional methods has been achieved our results for the critical exponents are given by 0 108 5 0 327 4 1 237 4 and 4 77 5

analysis of cohort studies with multivariate and partially observed disease classification data complex diseases like cancers can often be classified into subtypes using various pathological and molecular traits of the disease in this article we develop methods for analysis of disease incidence in cohort studies incorporating data on multiple disease traits using a two stage semiparametric cox proportional hazards regression model that allows one to examine the heterogeneity in the effect of the covariates by the levels of the different disease traits for inference in the presence of missing disease traits we propose a generalization of an estimating equation approach for handling missing cause of failure in competing risk data we prove asymptotic unbiasedness of the estimating equation method under a general missing at random assumption and propose a novel influence function based sandwich variance estimator the methods are illustrated using simulation studies and a real data application involving the cancer prevention study ii nutrition cohort

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter

red bond exponents of the critical and the tricritical ising model in three dimensions using the wolff and geometric cluster algorithms and finite size scaling analysis we investigate the critical ising and the tricritical blume capel models with nearest neighbor interactions on the simple cubic lattice the sampling procedure involves the decomposition of the ising configuration into geometric clusters each of which consists of a set of nearest neighboring spins of the same sign connected with bond probability p these clusters include the well known kasteleyn fortuin clusters as a special case for p 1 exp 2k where k is the ising spin spin coupling along the critical line k kc the size distribution of geometric clusters is investigated as a function of p we observe that unlike in the case of two dimensional tricriticality the percolation threshold in both models lies at pc 1 exp 2kc further we determine the corresponding red bond exponents as yr 0 757 2 and 0 501 5 for the critical ising and the tricritical blume capel models respectively on this basis we conjecture yr 1 2 for the latter model

a goodness of fit test for the ordered stereotype model this paper presents a new goodness of fit test for an ordered stereotype model used for an ordinal response variable the proposed test is based on the well known hosmer lemeshow test and its version for the proportional odds regression model the latter test statistic is calculated from a grouping scheme assuming that the levels of the ordinal response are equally spaced which might be not true one of the main advantages of the ordered stereotype model is that it allows us to determine a new uneven spacing of the ordinal response categories dictated by the data the proposed test takes the use of this new adjusted spacing to partition data a simulation study shows good performance of the proposed test under a variety of scenarios finally the results of the application in two examples are presented copyright 2016 john wiley sons ltd

the grouped continuous model for multivariate ordered categorical variables and covariate adjustment the grouped continuous model for multivariate ordered categorical data is described this is based on partitioning an underlying multivariate normal distribution straightforward maximum likelihood estimation is really feasible only for one and two way tables we introduce an estimation system based on maximum likelihood estimation in the one and two way marginal tables of higher order tables this is computationally feasible and an example involving aspects of bird colouring is given the approach is extended to provide a regression model for multivariate ordered categorical data with an estimation scheme again based on the one and two way marginal tables the above example is developed to investigate the covariate effect of time the asymptotic efficiency of these sampling schemes is discussed it appears that they have high efficiency

multivariate logistic models for incomplete binary responses abstract in this article we describe a likelihood based regression model appropriate for analyzing incomplete multivariate binary responses we focus on marginal models that is models where the marginal mean or expectation of the binary response is related to a set of covariates the association between the binary responses is modeled in terms of conditional log odds ratios when the nonresponse mechanism is ignorable it is not necessary to specify a nonresponse model and valid inferences can be obtained provided that the likelihood for the responses has been correctly specified but when the nonresponse mechanism is nonignorable valid inferences can only be obtained by incorporating a model for nonresponse an unresolved issue with nonignorable models concerns the identifiability of the parameters so far no general and practically useful necessary and sufficient conditions for identifiability are available here we suggest some simple procedures for examining the identifiability status of nonign

high temperature series for scalar field lattice models generation and analysis an implementation of the free embedding scheme for high temperature series generation on the body centered cubic family of lattices in arbitrary dimensiond is described series to order 21 in inverse temperature are tabulated for several scalar field models both for the magnetic susceptibility and for the second moment of the spin correlation function the critical behavior of a family of 3 dimensional double gaussian models which interpolate continuously between the spin 1 2 ising model and the gaussian model is analyzed in detail away from the gaussian model limit using confluent inhomogeneous secondorder differential approximants with our best estimate of the correction to scaling exponent 0 52 0 03 the leading exponents for the susceptibility and correlation length for this family are consistent with universality and are given by 1 237 0 002 and 0 630 0 0015 respectively and 2 0 0359 0 0007

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

simultaneous analysis of several models in the three dimensional ising universality class we investigate several three dimensional lattice models believed to be in the ising universality class by means of monte carlo methods and finite size scaling these models include spin 1 models with nearestneighbor interactions on the simple cubic and on the diamond lattice for the simple cubic lattice we also include models with third neighbor interactions of varying strength and some equivalent neighbor models also included are a spin 1 model and a hard core lattice gas separate analyses of the numerical data confirm the ising like critical behavior of these systems on this basis we analyze all these data simultaneously such that the universal parameters occur only once this leads to an improved accuracy the thermal magnetic and irrelevant exponents are determined as y t51 5868 3 y h52 4816 1 and y i520 821 5 respectively the binder ratio is estimated as q5 m 2 2 m 4 50 62 341 4

regression and ordered categorical variables read before the royal statistical society by professor r l plackett on behalf of the late professor anderson at a meeting organized by the research section on wednesday october 5th 1983 professor j b copas in the chair summary a general approach to regression modelling for ordered categorical response variables y is given which is equally applicable to ordered and unordered y the regressor variables xt xi x may be continuous or categorical the method is based on the logistic family which contains a hierarchy of regression models ranging from ordered to unordered models ordered properties of the former the stereotype model are established the choice between models is made empirically on the basis of model fit this is particularly important for assessed ordered categorical response variables where it is not obvious a priori whether or not the ordering is relevant to the regression relationship model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x the models are fitted iteratively using the method of maximum likelihood examples are given

computing exact distributions for polytomous response data abstract this article presents an efficient method for computing exact conditional distributions of the sufficient statistics for the parameters of four polytomous response models for nominal response two baseline category logit models and for ordinal response two adjacent categories logit models are considered the method consists of recursive generation of the joint distribution of the sufficient statistics augmented by a technique to slice off portions of the evolving sample space so as to eventually yield the required conditional distribution two actual data sets are analyzed to illustrate the method

finite size scaling of the three dimensional conserved order parameter ising model via wang landau algorithm abstract the critical properties of the conserved order parameter cop version of the three dimensional ising model with zero magnetization were investigated by means of the monte carlo mc wang landau algorithm the study was carried out in appropriate restricted but dominant energy subspaces the main effort was focused on the specific heat and binder energy cumulant by using the density of states of the model for lattices with linear size l 4 60 by applying finite size scaling analysis the estimated values for the thermal critical exponent y t and critical temperature k c are in agreement with the considered as best values leading to the conclusion that this model belongs to the ising universality class the analysis revealed the necessity of corrections to scaling functions for interpreting correctly the mc data

the analysis of longitudinal polytomous data generalized estimating equations and connections with weighted least squares in recent years methods have been developed for modelling repeated observations of a categorical response obtained over time on the same individual although situations in which the repeated response is binary or poisson have been studied extensively relatively little attention has been given to polytomous categorical response variable in this paper we extend the estimating equations initially developed for clustered discrete data by liang and zeger 1986 biometrika 73 13 22 and subsequently extended by prentice 1988 biometrics 44 1033 1048 to polytomous response variables under certain assumptions we illustrate that these estimating equations simplify to the weighted least squares wls equations formalized by koch et al 1977 biometrics 33 133 158 this connection provides a formal framework for obtaining iterated weighted least squares model parameter estimates cumulative logit models are developed and applied to a representative longitudinal data set simulation results comparing wls an iterative form of wls and independence estimating equations using a robust estimate of the variance are presented

solutions of renormalization group flow equations with full momentum dependence we demonstrate the power of a recently proposed approximation scheme for the nonperturbative renormalization group that gives access to correlation functions over their full momentum range we solve numerically the leading order flow equations obtained within this scheme and compute the two point functions of the o n theories at criticality in two and three dimensions excellent results are obtained for both universal and nonuniversal quantities at modest numerical cost

a class of logistic regression models for multivariate binary time series abstract a logistic model for multivariate binary time series is proposed first we establish the equivalence between a log linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others the logistic formulation is used to describe a markov chain for each series which implies a markov model for the vector of time series a pseudolikelihood estimation procedure is presented the methods are illustrated with data on psychosomatic and psychological diagnoses for families in a health maintenance plan

prediction intervals factor analysis models and high dimensional empirical linear prediction abstract we discuss a technique that provides prediction intervals based on a model called an empirical linear model the technique high dimensional empirical linear prediction help involves principal component analysis factor analysis and model selection in fact a special case of the empirical model is the factor analysis model a factor analysis model does not generally aim at prediction however therefore help can be viewed as a technique that provides prediction and confidence intervals based on a factor analysis model or a more generalized model possibly with unknown dimension to be estimated although factor analysis models do not typically have justifiable theory due to nonidentifiability we show that our intervals are justifiable asymptotically an interval for a future response is called a prediction interval an interval for the mean of the future response is called a confidence interval these intervals were compared to the intervals of hwang and liu which were derived using stand

ordinal association in contingency tables some interpretive aspects abstract two families of models for ordered contingency tables goodman s association models and canonical correlation models are investigated and compared with respect to the interpretation of their parameters we show that the two families of models actually refer to different kinds of ordinal association stochastic order extremity for correlation models and stochastic order entropy for association models this difference is related to the way the two models scale interaction the scale difference is proven to be of substantial consequence especially under strong association

critical phenomena of the hard sphere lattice gas on the simple cubic lattice abstract we study the critical phenomena of the hard sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion by the monte carlo method we get the critical exponents v 0 313 9 and v 2 37 2 where is the critical exponent for the staggered density for the staggered compressibility and v for the correlation length

bayesian inference for the stereotype regression model application to a case control study of prostate cancer the stereotype regression model for categorical outcomes proposed by anderson j roy statist soc b 1984 46 1 30 is nested between the baseline category logits and adjacent category logits model with proportional odds structure the stereotype model is more parsimonious than the ordinary baseline category or multinomial logistic model due to a product representation of the log odds ratios in terms of a common parameter corresponding to each predictor and category specific scores the model could be used for both ordered and unordered outcomes for ordered outcomes the stereotype model allows more flexibility than the popular proportional odds model in capturing highly subjective ordinal scaling which does not result from categorization of a single latent variable but are inherently multi dimensional in nature as pointed out by greenland statist med 1994 13 1665 1677 an additional advantage of the stereotype model is that it provides unbiased and valid inference under outcome stratified sampling as in case control studies in addition for matched case control studies the stereotype model is amenable to classical conditional likelihood principle whereas there is no reduction due to sufficiency under the proportional odds model in spite of these attractive features the model has been applied less as there are issues with maximum likelihood estimation and likelihood based testing approaches due to non linearity and lack of identifiability of the parameters we present comprehensive bayesian inference and model comparison procedure for this class of models as an alternative to the classical frequentist approach we illustrate our methodology by analyzing data from the flint men s health study a case control study of prostate cancer in african american men aged 40 79 years we use clinical staging of prostate cancer in terms of tumors nodes and metastasis as the categorical response of interest

missing exposure data in stereotype regression model application to matched case control study with disease subclassification with advances in modern medicine and clinical diagnosis case control data with characterization of finer subtypes of cases are often available in matched case control studies missingness in exposure values often leads to deletion of entire stratum and thus entails a significant loss in information when subtypes of cases are treated as categorical outcomes the data are further stratified and deletion of observations becomes even more expensive in terms of precision of the category specific odds ratio parameters especially using the multinomial logit model the stereotype regression model for categorical responses lies intermediate between the proportional odds and the multinomial or baseline category logit model the use of this class of models has been limited as the structure of the model implies certain inferential challenges with nonidentifiability and nonlinearity in the parameters we illustrate how to handle missing data in matched case control studies with finer disease subclassification within the cases under a stereotype regression model we present both monte carlo based full bayesian approach and expectation conditional maximization algorithm for the estimation of model parameters in the presence of a completely general missingness mechanism we illustrate our methods by using data from an ongoing matched case control study of colorectal cancer simulation results are presented under various missing data mechanisms and departures from modeling assumptions

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

conditional predictive inference post model selection we give a finite sample analysis of predictive inference procedures after model selection in regression with random design the analysis is focused on a statistically challenging scenario where the number of potentially important explanatory variables can be infinite where no regularity conditions are imposed on unknown parameters where the number of explanatory variables in a good model can be of the same order as sample size and where the number of candidate models can be of larger order than sample size the performance of inference procedures is evaluated conditional on the training sample under weak conditions on only the number of candidate models and on their complexity and uniformly over all data generating processes under consideration we show that a certain prediction interval is approximately valid and short with high probability in finite samples in the sense that its actual coverage probability is close to the nominal one and in the sense that its length is close to the length of an infeasible interval that is constructed by actually knowing the best candidate model similar results are shown to hold for predictive inference procedures other than prediction intervals like for example tests of whether a future response will lie above or below a given threshold

discussion on model confidence bounds for variable selection by yang li yuetian luo davide ferrari xiaonan hu and yichen qin

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

on the coupling time of the heat bath process for the fortuin kasteleyn random cluster model we consider the coupling from the past implementation of the random cluster heat bath process and study its random running time or coupling time we focus on hypercubic lattices embedded on tori in dimensions one to three with cluster fugacity at least one we make a number of conjectures regarding the asymptotic behaviour of the coupling time motivated by rigorous results in one dimension and monte carlo simulations in dimensions two and three amongst our findings we observe that for generic parameter values the distribution of the appropriately standardized coupling time converges to a gumbel distribution and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time perhaps surprisingly we observe these results to hold both off criticality where the coupling time closely mimics the coupon collector s problem and also at the critical point provided the cluster fugacity is below the value at which the transition becomes discontinuous finally we consider analogous questions for the single spin ising heat bath process

constrained latent class analysis simultaneous classification and scaling of discrete choice data a reparameterization of a latent class model is presented to simultaneously classify and scale nominal and ordered categorical choice data latent class specific probabilities are constrained to be equal to the preference probabilities from a probabilistic ideal point or vector model that yields a graphical multidimensional representation of the classification results in addition background variables can be incorporated as an aid to interpreting the latent class specific response probabilities the analyses of synthetic and real data sets illustrate the proposed method

critical properties of the three dimensional equivalent neighbor model and crossover scaling in finite systems accurate numerical results are presented for the three dimensional equivalent neighbor model on a cubic lattice for 12 different interaction ranges coordination number between 18 and 250 these results allow the determination of the range dependences of the critical temperature and various critical amplitudes which are compared to renormalization group predictions in addition the analysis yields an estimate for the interaction range at which the leading corrections to scaling vanish for the spin 1 2 model and confirms earlier conclusions that the leading wegner correction must be negative for the three dimensional nearest neighbor ising model by complementing these results with monte carlo data for systems with coordination numbers as large as 52 514 the full finite size crossover curves between classical and ising like behavior are obtained as a function of a generalized ginzburg parameter also the crossover function for the effective magnetic exponent is determined

computer simulation studies of critical phenomena abstract the recent strides which have been made in the use of computer simulations to study phase transitions and critical phenomena are reviewed we describe how the use of a combination of recently developed histogram techniques and sophisticated monte carlo simulation algorithms have allowed the determination of the static critical behavior of the d 3 ising and heisenberg models with unprecedented precision we also discuss the study of dynamic critical behavior in simple spin models by both monte carlo and spin dynamics methods recent estimates for dynamic critical exponents are reviewed including the first high precision estimate for true dynamics

estimation of critical behavior from the density of states in classical statistical models we present a simple and efficient approximation scheme which greatly facilitates the extension of wang landau sampling or similar techniques in large systems for the estimation of critical behavior the method presented in an algorithmic approach is based on a very simple idea familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem it is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters it is proposed that the extensions of the finite size critical part of the energy space determining the specific heat satisfy a scaling law involving the thermal critical exponent the method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic ising lattices the proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space the density of states of the zero field ising model on these lattices is obtained via a multirange wang landau sampling

analysis of ordinal data in a study of endometrial cancer under a matched pairs case control design while estimating odds ratios ors in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer the categories formed by the levels of the exposure are ordinal in nature in the literature the binary logistic model is used for estimating or for each category relative to the baseline category we describe the use of two ordinal logistic models the cumulative logit and continuation ratio logit models to estimate the ors for the matched pairs case control data set of the los angeles endometrial cancer study a test for equality of the cumulative ors across the exposure levels is proposed the test statistic follows asymptotically the chi square distribution

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

unimodal models to relate species to environment to assess the impact of environmental change on biological communities knowledge about species environment relationships is indispensable ecologists attempt to uncover the relationships between species and environment from data obtained from field surveys in the survey species are scored on their presence or their abundance at each of several sampling sites and environmental variables that ecologists believe to be important are measured the research that led to this thesis aimed to unravel the assumptions required for the application of statistical methods that are popular among ecologists to analyse such data from a statistical point of view species data are difficult to analyse there are many species involved 10 500 many species occur at a few sites only so the data contain numerous zeroes relations between species and environmental variables are not linear but unimodal a plant for example preferably grows under for that species optimal moisture conditions and is encountered less frequently at drier or wetter sites a mathematical model for a unimodal relationship is the gaussian response model standard statistical methods such as linear regression principal components analysis and canonical correlation analysis are often inappropriate for analysing species data because they are based on linear relationships one of the methods that ecologists use instead is correspondence analysis this thesis contributes to the understanding of the underlying response model with correspondence analysis species and sites are arranged to discover the structure in the data ordination and the arrangement is subsequently related to environmental variables it is an indirect method to detect relations between species and environment hence r h whittaker s term indirect gradient analysis correspondence analysis has been invented around 1935 but did not receive interest from ecologists before 1973 when m o hill derived the technique once more as the repeated application of weighted averaging a method that was familiar to ecologists ever since 1930 weighted averaging has the advantage of being simple to apply the method can be used for two different aims 1 to estimate the optimum of a species for an environmental variable and 2 to estimate the value of an environmental variable at a site from known optima of the species present calibration in chapter 2 estimating optima by weighted averaging is compared with the results of non linear regression on the basis of the gaussian response model under particular conditions both methods agree precisely in other cases weighted averaging gives a biased estimate of the optimum and non linear regression is the method to be preferred an additional advantage of non linear regression is that it can also be used to fit response models with more than one environmental variable in chapter 3 weighted averaging to estimate the value of an environmental variable is compared with calibration on the basis of the gaussian response model also in this context the techniques are sometimes equivalent chapter 4 deals with correspondence analysis it is shown that under particular conditions correspondence analysis approximates ordination on the basis of the gaussian response model which is computationally much more complicated to detect relations indirect methods have an important disadvantage the impact of some environmental variables on the species composition can be so large that the impact of other interesting environmental variables may fail to be detected this problem can be overcome by using non linear regression but with many species and environmental variables this is laborious in chapter 5 a simpler direct method is proposed canonical correspondence analysis in chapter 6 canonical correspondence analysis turns out to be a multivariate extension of weighted averaging the results can be displayed graphically in chapter 7 an extension with covariables is discussed which leads to partial canonical correspondence analysis chapter 7 also shows that gaussian models and hence canonical correspondence analysis are relevant to the analysis of contingency tables chapter 8 describes a study to estimate ecological amplitudes of plant species with respect to ellenberg s moisture scale from species data alone the question that is addressed as well is how consequent ellenberg s moisture indicator values are finally chapter 9 cross tabulates various gradient analysis techniques by the type of problem regression calibration ordination etc and the response model linear or unimodal furthermore improvements are proposed for detrended correspondence analysis a computer program named mom is written which can perform most of the methods discussed

standardized estimates from categorical regression models we consider the problem of interpreting categorical regression models such as the polytomous logistic model the continuation ratio model the stereotype model and the cumulative odds model we present a method to convert categorical regression coefficients into estimates of standardized fitted probabilities probability differences and probability ratios we use a delta method approach to estimate standard errors we then present a small simulation study to compare different transforms for setting confidence limits and provide an illustration of our approach in an observational study of drug therapy of polymyositis

surface critical phenomena in three dimensional percolation using monte carlo methods and finite size scaling we investigate surface critical phenomena in the bondpercolation model on the simple cubic lattice with two open surfaces in one direction we decompose the whole lattice into percolation clusters and sample the surface and bulk dimensionless ratios q1 and qb defined on the basis of the moments of the cluster size distribution these ratios are used to determine critical points at the bulk percolation threshold pbc we determine the surface bond occupation probability at the special transition as p 1c ssd 0 418 17s2d and further obtain the corresponding surface thermal and magnetic exponents as y t1 ssd 0 5387s2d and y h1 ssd 1 8014s6d respectively next from the pair correlation function on the surfaces we determine y h1 sod 1 0246s4d and y h1 sed 1 25s6d for the ordinary and the extraordinary transition respectively of which the former is consistent with the existing result y h1 sod 1 024s4d we also numerically derive the line of surface phase transitions occurring at pb pbc and determine the pertinent asymptotic values of the universal ratios q1 and qb

verification of ising phase transitions in the three dimensional ashkin teller model using monte carlo simulations monte carlo simulations in the three dimensional 3d ashkin teller model on a cubic lattice are performed in the regions of the two parameter space diagram where ising type phase transitions are expected the scaling behavior of the binder cumulant q and the magnetic susceptibility in the critical region are exploited in simulations the periodic boundary conditions and the metropolis algorithm are used starting from ising critical exponents and applying the finite size scaling analysis of the cumulant q with nonlinear corrections the accurate positions of the critical couplings on the continuous phase transition lines are calculated for these couplings the critical exponent y h is calculated analyzing the magnetic susceptibility in the framework of the finite size scaling with corrections the values of y h agree with the 3d ising model value along two lines determined by the order parameter ssigma

critical energy distribution function of the baxter wu model abstract in this work we examine the critical finite size scaling behavior of the energy probability distribution function and its corresponding binder cumulant at critical point based on the results of monte carlo simulations at zero external magnetic field using the recently developed triangle cluster algorithm we calculate the energy distribution function s exponents and we derive the scaling relations for the energy binder cumulant finally we predict the exact form of the scaled energy distribution function most of our conclusions seem applicable not only to the baxter wu model but also to other ising like models

classification efficiency of multinomial logistic regression relative to ordinal logistic regression abstract classification procedures are useful for the prediction of a response or outcome as a result of knowledge of the levels of one or more independent or predictor variables the procedure is said to classify the possibly multivariate observation to a level of the response variable an example might be the prediction of whether an individual will be well suffer a nonfatal heart attack or suffer a fatal heart attack this prediction might be made on the basis of the levels of various independent variables such as weight blood pressure and serum cholesterol to name a few the three response categories of the aforementioned example are ordinal an example of three nonordered response categories might be as follows well death from heart attack and death from cancer there is some recent interest in ordinal classification procedures it is reasonable to assume that when the response variable is ordinal inclusion of ordinality in the classification model to be estimated should improve mode

a note on regression analysis of ordinal data with variability of classification summary the effect of observation variability in the classification of an ordinal response is examined within the framework of the proportional hazards regression model for ordinal data a model is proposed which incorporates this type of variability and the behaviour of the proportional hazards model when this new model is appropriate is examined four data sets are used to illustrate the practical application of the model

the simple cubic lattice gas with nearest neighbour exclusion ising universality abstract the lattice gas with nearest neighbour exclusion on the simple cubic lattice is studied by means of statistically accurate monte carlo simulations with an efficient cluster algorithm our results for critical exponents are y h 2 47 1 and y t 1 60 2 these results agree well with the three dimensional ising universality class we explain the discrepancy with an earlier study the critical activity is z c 1 0559 1 the size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the monte carlo algorithm coincides with the critical point

penalized maximum likelihood estimation in logistic regression and discrimination summary maximum likelihood estimation of the parameters of the binary logistic regression model for pr h i x is discussed with separate discussion of sampling from i the conditional distribution of h given x ii the joint distribution of h and x and iii the conditional distribution of x given h difficulties associated with continuous x in the latter sampling scheme are discussed to avoid these penalized maximum likelihood estimates are introduced which give estimates of the logistic parameters and a nonparametric spline estimate of the marginal distribution of x extensions to multinomial logistic regression are outlined

renormalized four point coupling constant in the three dimensional o n model with n 0 we simulate self avoiding walks on a cubic lattice and determine the second virial coefficient for walks of different lengths this allows us to determine the critical value of the renormalized four point coupling constant in the three dimensional n vector universality class for n 0 we obtain g 1 4005 5 where g is normalized so that the three dimensional field theoretical beta function behaves as beta g g g 2 for small g as a byproduct we also obtain precise estimates of the interpenetration ratio psi psi 0 24685 11 and of the exponent nu nu 0 5876 2

properties of ideal point classification models for bivariate binary data the ideal point classification ipc model was originally proposed for analysing multinomial data in the presence of predictors in this paper we studied properties of the ipc model for analysing bivariate binary data with a specific focus on three quantities 1 the marginal probabilities 2 the association structure between the two binary responses and 3 the joint probabilities we found that the ipc model with a specific class point configuration represents either the marginal probabilities or the association structure however the ipc model is not able to represent both quantities at the same time we then derived a new parametrization of the model the bivariate ipc bipc model which is able to represent both the marginal probabilities and the association structure like the standard ipc model the results of the bipc model can be displayed in a biplot from which the effects of predictors on the binary responses and on their association can be read we will illustrate our findings with a psychological example relating personality traits to depression and anxiety disorders

bayesian model comparison for the order restricted rc association model association models constitute an attractive alternative to the usual log linear models for modeling the dependence between classification variables they impose special structure on the underlying association by assigning scores on the levels of each classification variable which can be fixed or parametric under the general row column rc association model both row and column scores are unknown parameters without any restriction concerning their ordinality however when the classification variables are ordinal order restrictions on the scores arise naturally under such restrictions we adopt an alternative parameterization and draw inferences about the equality of adjacent scores using the bayesian approach to achieve that we have constructed a reversible jump markov chain monte carlo algorithm for moving across models of different dimension and estimate accurately the posterior model probabilities which can be used either for model comparison or for model averaging the proposed methodology is evaluated through a simulation study and illustrated using actual datasets

reduction from cost sensitive ordinal ranking to weighted binary classification we present a reduction framework from ordinal ranking to binary classification the framework consists of three steps extracting extended examples from the original examples learning a binary classifier on the extended examples with any binary classification algorithm and constructing a ranker from the binary classifier based on the framework we show that a weighted 0 1 loss of the binary classifier upper bounds the mislabeling cost of the ranker both error wise and regret wise our framework allows not only the design of good ordinal ranking algorithms based on well tuned binary classification approaches but also the derivation of new generalization bounds for ordinal ranking from known bounds for binary classification in addition our framework unifies many existing ordinal ranking algorithms such as perceptron ranking and support vector ordinal regression when compared empirically on benchmark data sets some of our newly designed algorithms enjoy advantages in terms of both training speed and generalization performance over existing algorithms in addition the newly designed algorithms lead to better cost sensitive ordinal ranking performance as well as improved listwise ranking performance

prediction of ordinal outcomes when the association between predictors and outcome differs between outcome levels there are a number of regression models which are widely used to predict ordinal outcomes the commonly used models assume that all predictor variables have a similar effect at all levels of the outcome variable if this is not the case for example if some variables predict susceptibility to a disease and others predict the severity of the disease then a more complex model is required one possibility is the multinomial logistic regression model which assumes that the predictor variables have different effects at all levels of the outcome variable an alternative is to use the stereotype family of regression models a one dimensional stereotype model makes the assumption that the effect of each predictor is the same at all outcome levels however it is possible to fit stereotype models with more than one dimension up to a maximum of min k 1 p where k is the number of outcome categories and p is the number of predictor variables a stereotype model of this maximum dimension is equivalent to a multinomial logistic regression model in that it will produce the same predicted values and log likelihood if there are sufficient outcome levels and or predictor variables there may be a number of stereotype models of differing dimension the method is illustrated with an example of prediction of damage to joints in rheumatoid arthritis

critical temperatures of the d 3 s 1 2 ising model the effect of confluent corrections to scaling much attention has been paid to the d 3 s 1 2 ising model on the bcc lattice in recent years because the best high temperature series expansions were available for this lattice however in order to compare series estimates of critical exponents and temperatures with independent evaluations via the monte carlo method lattices of lower coordination number must be considered since monte carlo studies are usually made on these a study of extant susceptibility series on the fcc sc diamond and tetrahedron lattices is reported on and some comments are made on aspects of recent monte carlo analyses of the d 3 s 1 2 ising model on the sc and diamond lattices

ising universality in three dimensions a monte carlo study we investigate three ising models on the simple cubic lattice by means of monte carlo methods and finite size scaling these models are the spin 1 2 ising model with nearest neighbour interactions a spin 1 2 model with nearest neighbour and third neighbour interactions and a spin 1 model with nearest neighbour interactions the results are in accurate agreement with the hypothesis of universality analysis of the finite size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field we find that the correction to scaling amplitudes are strongly dependent on the introduction of further neighbour interactions or a third spin state in a spin 1 ising model these corrections appear to be very small this is very helpful for the determination of the universal constants of the ising model the renormalization exponents of the ising model are determined as yt 1 587 2 yh 2 4815 15 and yi 0 82 6 the universal ratio q m2 2 m4 is equal to 0 6233 4 for periodic systems with cubic symmetry the critical point of the nearest neighbour spin 1 2 model is kc 0 2216546 10

multiple group logistic discrimination among the many possible approaches suggested for statistical discrimination the logistic method can be classified midway between fully distributional solutions of which the assumption of multivariate normality is a classical example 16l and the distribution free techniques using for instance kernel or nearest neighbor methods l 32 therefore it is often called a partially parametric or partially distributional method l l this central position of the logistic model makes it one of the most attractive and widely used tools for solving regression and discrimination problems indeed since there are fewer distributional assumptions than for fully parametric models the logistic method is applicable to a larger family of multivariate distributions involving both discrete and continuous variables moreover in spite of its wide applicability and generality the method remains feasible and easy to use in contrast with nonparametric methods this paper is intended to review the basic ideas and principles of logistic discrimination 415 22 25 and also to bring additional results to some of the queries raised by professor anderson before his death we restrict our attention to discrimination between qualitatively distinct groups and do not envisage the case where groups are quantitatively distinct or ordered 3 12 14 we dedicate this paper to our friend and mentor the late professor j a anderson for his fundamental contribution to discriminant analysis and for his continuous support of our research efforts

a new model for ordinal pain data from a pharmaceutical study for the pain data analysed previously by cox and chuang this paper proposes a new model that assumes monotone scores for ordered response categories this proposed model possesses several attractive features and allows a stochastic ordering of the drugs under comparison such a model also provides insight regarding the ordinal scale used to classify response estimation of the parameters in the model is obtained by use of bmdp3r

critical behavior of the fidelity susceptibility for the d 2 transverse field ising model abstract the overlap inner product between the ground state eigenvectors with proximate interaction parameters the so called fidelity plays a significant role in the quantum information theory in this paper the critical behavior of the fidelity susceptibility is investigated for a two dimensional transverse field quantum ising model by means of the numerical diagonalization method in order to treat a variety of system sizes n 12 14 32 we adopt the screw boundary condition finite size artifacts scaling corrections of the fidelity susceptibility appear to be suppressed as compared to those of the binder parameter as a result we estimate the fidelity susceptibility critical exponent as f 0 715 20

cluster dynamics and universality of ising lattice gases abstract lattice gases with nearest neighbour exclusion are studied by means of monte carlo simulations with an efficient cluster algorithm the critical dynamics is consistent with a dynamical exponent z 0 in the case of wolff like cluster updates for square and simple cubic lattices in the studied range of lattice sizes we find the critical activity z c 0 72020 4 for the body centred cubic lattice the critical exponents y h 2 475 8 and y t 1 61 6 disagree with an earlier study but they do agree with the known values for the three dimensional ising universality class

are ordinal models useful for classification there is recent interest in classification procedures intended for use only when the response is ordinal ordinal response however is evident in the parameters estimated by either multinomial logistic or normal discriminant analyses both of which classify either ordinal or non ordinal responses further there may be harm in applying ordinal models inappropriately and ample opportunity to assume mistakenly ordinality in real data sets therefore it becomes important to ascertain whether there is benefit obtained in the appropriate application of ordinal models this paper presents the results of a simulation study designed to compare classification accuracy of various models we show that ordinal models classify less accurately than the multinomial logistic and normal discriminant procedures under a variety of circumstances until further studies become available we presently conclude that ordinal models confer no advantage when the main purpose of the analysis is classification

discriminant analysis when all variables are ordered determination of the equation that relates an ordered dependent variable to ordered independent variables is sought one solution non parametric discriminant analysis npd involves obtaining the best monotonic step function by means of a computer search procedure although one can use alternative selection criteria in obtaining the equation the illustrative examples use absolute distance this paper compares the prediction procedures obtained from npd with those from linear discriminant analysis linear regression with and without transformed variables and logistic regression we show that npd is analogous to regression tree analysis with incorporation of ordered variables and monotonicity we use various prediction functions to predict the example data the data using the leave one out technique and a verification set consistently non parametric discriminant analysis performs as good as or better than the tested alternatives

percolation between vacancies in the two dimensional blume capel model using suitable monte carlo methods and finite size scaling we investigate the blume capel model on the square lattice we construct percolation clusters by placing nearest neighbor bonds between vacancies with a variable bond probability pb at the tricritical point we locate the percolation threshold of these vacancy clusters at pbc 0 706 336 at this point we determine the fractal dimension of the vacancy clusters as xf 0 13085 21 160 and the exponent governing the renormalization flow in the pb direction as yp 0 4262 17 40 for bond probability pbpbc the vacancy clusters maintain strong critical correlations the fractal dimension is xf 0 07502 3 40 and the leading correction exponent is yp 0 452 19 40 the above values fit well in the kac table for the tricritical ising model these vacancy clusters have much analogy with those consisting of ising spins of the same sign although the associated quantities and magnetization m are energylike and magnetic quantities respectively however along the critical line of the blume capel model the vacancies are more or less uniformly distributed over the whole lattice in this case no critical percolation correlations are observed in the vacancy clusters at least in the physical region pb 1

confluent singularities in 3d continuum φ4 theory resolving critical point discrepancies a new analysis of the three dimensional 4 continuum model series for critical exponents and amplitude ratios is presented by explicitly allowing for a second correction to scaling term with exponent 2 and 2 1 2 0 a revision is found of previous critical point estimates that are all in the direction of resolving the remaining discrepancies between the 3d and 4 analyses the new estimates are also consistent with those obtained from high temperature series analyses of 3d lattice ising models for example the exponents 1 238 0 630 0 0355 and correction to scaling amplitude ratio 0 77 are easily accommodated and possibly even preferred detailed verification will require further terms both in the low order perturbation theory and the high order asymptotic expansions

lifted worm algorithm for the ising model we design an irreversible worm algorithm for the zero field ferromagnetic ising model by using the lifting technique we study the dynamic critical behavior of an energylike observable on both the complete graph and toroidal grids and compare our findings with reversible algorithms such as the prokof ev svistunov worm algorithm our results show that the lifted worm algorithm improves the dynamic exponent of the energylike observable on the complete graph and leads to a significant constant improvement on toroidal grids

gaussian estimation for correlated binomial data summary the mean variance structure of correlated binomial data is discussed and whittle s 1961 gaussian estimation is suggested as a useful general method in this context comparisons are made with other monrent methods in current use

admissibility of the usual confidence set for the mean of a univariate or bivariate normal population the unknown variance case summary in the gaussian linear regression model with unknown mean and variance we show that the standard confidence set for one or two regression coefficients is admissible in the sense of joshi this solves a long standing open problem in mathematical statistics and this has important implications on the performance of modern inference procedures post model selection or post shrinkage particularly in situations where the number of parameters is larger than the sample size as a technical contribution of independent interest we introduce a new class of conjugate priors for the gaussian location scale model