optimization for training neural nets various techniques of optimizing criterion functions to train neural net classifiers are investigated these techniques include three standard deterministic techniques variable metric conjugate gradient and steepest descent and a new stochastic technique it is found that the stochastic technique is preferable on problems with large training sets and that the convergence rates of the variable metric and conjugate gradient techniques are similar

sample size considerations for gee analyses of three level cluster randomized trials cluster randomized trials in health care may involve three instead of two levels for instance in trials where different interventions to improve quality of care are compared in such trials the intervention is implemented in health care units clusters and aims at changing the behavior of health care professionals working in this unit subjects while the effects are measured at the patient level evaluations within the generalized estimating equations approach we derive a sample size formula that accounts for two levels of clustering that of subjects within clusters and that of evaluations within subjects the formula reveals that sample size is inflated relative to a design with completely independent evaluations by a multiplicative term that can be expressed as a product of two variance inflation factors one that quantifies the impact of within subject correlation of evaluations on the variance of subject level means and the other that quantifies the impact of the correlation between subject level means on the variance of the cluster means power levels as predicted by the sample size formula agreed well with the simulated power for more than 10 clusters in total when data were analyzed using bias corrected estimating equations for the correlation parameters in combination with the model based covariance estimator or the sandwich estimator with a finite sample correction

finite sample adjustments in estimating equations and covariance estimators for intracluster correlations bias corrected covariance estimators are introduced in the context of an estimating equations approach for intracluster correlations among binary outcomes simulation study results show that the bias corrected covariance estimators perform better than uncorrected sandwich estimators in terms of bias and coverage probabilities additionally introduction of a matrix based bias correction into the estimating equations considerably improves point and interval estimation for the intracluster correlations the methods are illustrated using data from a nested cross sectional cluster trial on reducing underage drinking

updating beliefs about variables given new information on how those variables relate bayesian techniques specify how to update beliefs about a variable given information on that variable or related variables in many cases statistical analyses also provide information about the relationship between variables but the borel paradox prohibits many natural ways of updating beliefs conditioned on information about a relationship this paper presents a method by which beliefs can be updated without violating the borel paradox under certain circumstances we apply our approach to relationships specified by a statistical model i e regression and relationships described by statistical simulation

nonlinear parameter estimation via the genetic algorithm a modified genetic algorithm is used to solve the parameter identification problem for linear and nonlinear iir digital filters under suitable hypotheses the estimation error is shown to converge in probability to zero the scheme is also applied to feedforward and recurrent neural networks

conditioning on the propensity score can result in biased estimation of common measures of treatment effect a monte carlo study propensity score methods are increasingly being used to estimate causal treatment effects in the medical literature conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments the degree to which conditioning on the propensity score introduces bias into the estimation of the conditional odds ratio or conditional hazard ratio which are frequently used as measures of treatment effect in observational studies has not been extensively studied we conducted monte carlo simulations to determine the degree to which propensity score matching stratification on the quintiles of the propensity score and covariate adjustment using the propensity score result in biased estimation of conditional odds ratios hazard ratios and rate ratios we found that conditioning on the propensity score resulted in biased estimation of the true conditional odds ratio and the true conditional hazard ratio in all scenarios examined treatment effects were biased towards the null treatment effect however conditioning on the propensity score did not result in biased estimation of the true conditional rate ratio in contrast conventional regression methods allowed unbiased estimation of the true conditional treatment effect when all variables associated with the outcome were included in the regression model the observed bias in propensity score methods is due to the fact that regression models allow one to estimate conditional treatment effects whereas propensity score methods allow one to estimate marginal treatment effects in several settings with non linear treatment effects marginal and conditional treatment effects do not coincide

bias reduction in effectiveness analyses of longitudinal ordinal doses with a mixed effects propensity adjustment a mixed effects propensity adjustment is described that can reduce bias in longitudinal studies involving non equivalent comparison groups there are two stages in this data analytic strategy first a model of propensity for treatment intensity examines variables that distinguish among subjects who receive various ordered doses of treatment across time using mixed effects ordinal logistic regression second the effectiveness model examines multiple times until recurrence to compare the ordered doses using a mixed effects grouped time survival model effectiveness analyses are initially stratified by propensity quintile then the quintile specific results are pooled assuming that there is not a propensity x treatment interaction a monte carlo simulation study compares bias reduction in fully specified propensity model relative to misspecified models in addition type i error rate and statistical power are examined the approach is illustrated by applying it to a longitudinal observational study of maintenance treatment of major depression

revision of possibility distributions a bayesian inference pattern abstract in probability theory the bayes rule of inference plays a central role as corroborated by the ever increasing number of applications in various fields the rule allows to revise a prior probability distribution when new information becomes available the posterior probability distribution takes the form of a conditional distribution although several similarities between the possibilistic and probabilistic frameworks have already been reported very few studies in possibility theory have dealt with bayesian inference the objective of this work is to thoroughly study this type of inference and to develop the counterpart of the bayes rule in the possibilistic framework with the use of conditional possibility distributions application of possibility theory wherever bayes theory has already been applied can now be envisaged as a new perspective to uncertainty modeling and processing in the last part of this paper the suitability of the proposed framework for the problem of forecast processing is discussed and an example illustrates the application of various rules of inference corresponding to different aggregation operators

analytic and geometric background of recurrence and non explosion of the brownian motion on riemannian manifolds we provide an overview of such properties of the brownian motion on complete non compact riemannian manifolds as recurrence and non explosion it is shown that both properties have various analytic characterizations in terms of the heat kernel green function liouville properties etc on the other hand we consider a number of geometric conditions such as the volume growth isoperimetric inequalities curvature bounds etc which are related to recurrence and non explosion

the performance of different propensity score methods for estimating differences in proportions risk differences or absolute risk reductions in observational studies propensity score methods are increasingly being used to estimate the effects of treatments on health outcomes using observational data there are four methods for using the propensity score to estimate treatment effects covariate adjustment using the propensity score stratification on the propensity score propensity score matching and inverse probability of treatment weighting iptw using the propensity score when outcomes are binary the effect of treatment on the outcome can be described using odds ratios relative risks risk differences or the number needed to treat several clinical commentators suggested that risk differences and numbers needed to treat are more meaningful for clinical decision making than are odds ratios or relative risks however there is a paucity of information about the relative performance of the different propensity score methods for estimating risk differences we conducted a series of monte carlo simulations to examine this issue we examined bias variance estimation coverage of confidence intervals mean squared error mse and type i error rates a doubly robust version of iptw had superior performance compared with the other propensity score methods it resulted in unbiased estimation of risk differences treatment effects with the lowest standard errors confidence intervals with the correct coverage rates and correct type i error rates stratification matching on the propensity score and covariate adjustment using the propensity score resulted in minor to modest bias in estimating risk differences estimators based on iptw had lower mse compared with other propensity score methods differences between iptw and propensity score matching may reflect that these two methods estimate the average treatment effect and the average treatment effect for the treated respectively copyright 2010 john wiley sons ltd

harnack inequality and liouville properties for l harmonic operator abstract for any complete manifold with nonnegative bakry emery s ricci curvature we prove the gradient estimate of l harmonic function as application we use this gradient estimate to deduce the localized version of the harnack inequality for l harmonic operator and some liouville properties of positive or bounded l harmonic function

time varying combinations of predictive densities using nonlinear filtering abstract we propose a bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights several specifications of multivariate time varying weights are introduced with a particular focus on weight dynamics driven by the past performance of the predictive densities and the use of learning mechanisms in the proposed approach the model set can be incomplete meaning that all models can be individually misspecified a sequential monte carlo method is proposed to approximate the filtering and predictive densities the combination approach is assessed using statistical and utility based performance measures for evaluating density forecasts of simulated data us macroeconomic time series and surveys of stock market prices simulation results indicate that for a set of linear autoregressive models the combination strategy is successful in selecting with probability close to one the true model when the model set is complete and it is able to detect parameter instability when the model set includes the true model that has generated subsamples of data also substantial uncertainty appears in the weights when predictors are similar residual uncertainty reduces when the model set is complete and learning reduces this uncertainty for the macro series we find that incompleteness of the models is relatively large in the 1970 s the beginning of the 1980 s and during the recent financial crisis and lower during the great moderation the predicted probabilities of recession accurately compare with the nber business cycle dating model weights have substantial uncertainty attached with respect to returns of the s p 500 series we find that an investment strategy using a combination of predictions from professional forecasters and from a white noise model puts more weight on the white noise model in the beginning of the 1990 s and switches to giving more weight to the professional forecasts over time information on the complete predictive distribution and not just on some moments turns out to be very important above all during turbulent times such as the recent financial crisis more generally the proposed distributional state space representation offers great flexibility in combining densities

optimal linear opinion pools consider a decision problem involving a group of m bayesians in which each member reports his her posterior distribution for some random variable the individuals all share a common prior distribution for and a common loss function but form their posterior distributions based on different data sets a single distribution of must be chosen by combining the individual posterior distributions in some type of opinion pool in this paper the optimal pool is presented when the data observed by the different members of the group are conditionally independent given when the data are not conditionally independent the optimal weights to be used in a linear opinion pool are determined for problems involving quadratic loss functions and arbitrary distributions for and the data properties of the optimal procedure are developed and some examples are discussed

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

propensity score methods for estimating relative risks in cluster randomized trials with low incidence binary outcomes and selection bias despite randomization selection bias may occur in cluster randomized trials classical multivariable regression usually allows for adjusting treatment effect estimates with unbalanced covariates however for binary outcomes with low incidence such a method may fail because of separation problems this simulation study focused on the performance of propensity score ps based methods to estimate relative risks from cluster randomized trials with binary outcomes with low incidence the results suggested that among the different approaches used multivariable regression direct adjustment on ps inverse weighting on ps and stratification on ps only direct adjustment on the ps fully corrected the bias and moreover had the best statistical properties

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

rough isometry and energy finite solutions of elliptic equations on riemannian manifolds we prove that if the s harmonic boundary of a complete riemannian manifold consists of finitely many points then the set of bounded energy finite solutions for certain nonlinear elliptic operators on the manifold is one to one corresponding to bf r l where l is the cardinality of thes harmonic boundary we also prove that the finiteness of cardinality of s harmonic boundary is a rough isometric invariant moreover in this case the cardinality is preserved under rough isometries between complete riemannian manifolds this result generalizes those of yau of donnelly of grigor yan of li and tam of kim and the present author of holopainen and of the present author but with different techniques which are demanded by the peculiarity of nonlinearity

combining probability distributions from dependent information sources inferences or decisions in the face of uncertainty should be based on all available information thus when probability distributions for an uncertain quantity are obtained from experts models or

a constrained takagi sugeno fuzzy system that allows for better interpretation and analysis abstract in this paper we present a modification of the generalized takagi sugeno gts model fiordaliso proc eufit96 conf vol 1 1996 pp 581 586 the key idea is to constrain the conclusions of each rule to perform a convex combination of the input patterns this constraint allows to interpret each rule as an input patterns mixer and therefore contributes to a better understanding of the fuzzy system inference we illustrate the functioning of the constrained system which is next applied for purposes of combining forecasts

optimal forecasting groups this paper characterizes the optimal composition of a group for making a combined forecast in the model individual forecasters have types defined according to a statistical criterion we call type coherence members of the same type have identical expected accuracy and forecasters within a type have higher covariance than forecasters of different types we derive the optimal group composition as a function of predictive accuracy between and within type covariance and group size group size plays a critical role in determining the optimal group in small groups the most accurate type should be in the majority whereas in large groups the type with the least within type covariance should dominate this paper was accepted by peter wakker decision analysis

bayesian and non bayesian approaches to statistical inference and decision making bayesian and non bayesian approaches to statistical inference and decision making are discussed and compared a pragmatic criterion success in practice as well as logical consistency are emphasized in comparing alternative approaches attention is given to learning models probability concepts prior information axiom systems and selected technical aspects of bayesian and non bayesian approaches

propensity scores used for analysis of cluster randomized trials with selection bias a simulation study cluster randomized trials crts are often prone to selection bias despite randomization using a simulation study we investigated the use of propensity score ps based methods in estimating treatment effects in crts with selection bias when the outcome is quantitative of four ps based methods adjustment on ps inverse weighting stratification and optimal full matching method three successfully corrected the bias as did an approach using classical multivariable regression however they showed poorer statistical efficiency than classical methods with higher standard error for the treatment effect and type i error much smaller than the 5 nominal level

propensity score methods for bias reduction in the comparison of a treatment to a non randomized control group in observational studies investigators have no control over the treatment assignment the treated and non treated that is control groups may have large differences on their observed covariates and these differences can lead to biased estimates of treatment effects even traditional covariance analysis adjustments may be inadequate to eliminate this bias the propensity score defined as the conditional probability of being treated given the covariates can be used to balance the covariates in the two groups and therefore reduce this bias in order to estimate the propensity score one must model the distribution of the treatment indicator variable given the observed covariates once estimated the propensity score can be used to reduce bias through matching stratification subclassification regression adjustment or some combination of all three in this tutorial we discuss the uses of propensity score methods for bias reduction give references to the literature and illustrate the uses through applied examples

intra cluster correlation selection for cluster randomized trials in this paper we give focus to cluster randomized trials also known as group randomized trials which randomize clusters or groups of subjects to different trial arms such as intervention or control outcomes from subjects within the same cluster tend to exhibit an exchangeable correlation measured by the intra cluster correlation coefficient icc our primary interest is to test if the intervention has an impact on the marginal mean of an outcome using recently developed methods we propose how to select a working icc structure with the goal of choosing the structure that results in the smallest standard errors for regression parameter estimates and thus the greatest power for this test specifically we utilize small sample corrections for the estimation of the covariance matrix of regression parameter estimates this matrix is incorporated within correlation selection criteria proposed in the generalized estimating equations literature to choose one of multiple working icc structures under consideration we demonstrate the potential power and utility of this approach when used in cluster randomized trial settings via a simulation study and application example and we discuss practical considerations for its use in practice copyright 2016 john wiley sons ltd

fuzzy versus nonfuzzy in combining classifiers designed by boosting boosting is recognized as one of the most successful techniques for generating classifier ensembles typically the classifier outputs are combined by the weighted majority vote the purpose of this study is to demonstrate the advantages of some fuzzy combination methods for ensembles of classifiers designed by boosting we ran two fold cross validation experiments on six benchmark data sets to compare the fuzzy and nonfuzzy combination methods on the fuzzy side we used the fuzzy integral and the decision templates with different similarity measures on the nonfuzzy side we tried the weighted majority vote as well as simple combiners such as the majority vote minimum maximum average product and the naive bayes combination in our experiments the fuzzy combination methods performed consistently better than the nonfuzzy methods the weighted majority vote showed a stable performance though slightly inferior to the performance of the fuzzy combiners

stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure a more traditional alternative technique is the direct adjustment for confounding in regression models this paper discusses fundamental differences between the two approaches with a focus on linear regression and propensity score stratification and identifies points to be considered for an adequate comparison the treatment estimators are examined for unbiasedness and efficiency this is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models we demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model even if it is built on coarser covariate strata than the linear model as a consequence the coarsening property of the propensity score adjustment for a one dimensional confounder instead of a high dimensional covariate may be viewed as a way to implement a pre specified richly parametrized linear model we conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome

modeling expert judgments for bayesian updating this paper examines how a bayesian decision maker would update his her probability p for the occurrence of an event a in the light of a number of expert opinions expressed as probabilities q 1 cdots q n of a it is seen among other things that the linear opinion pool lambda 0p sum n i 1 lambda iq i corresponds to an application of bayes theorem when the decision maker has specified only the mean of the marginal distribution for q 1 cdots q n and requires his her formula for the posterior probability of a to satisfy a certain consistency condition a product formula similar to that of bordley 1982 is also derived in the case where the experts are deemed to be conditionally independent given a and given its complement

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

maximum entropy aggregation of expert predictions this paper presents a maximum entropy framework for the aggregation of expert opinions where the expert opinions concern the prediction of the outcome of an uncertain event the event to be predicted and individual predictions rendered are assumed to be discrete random variables a measure of expert competence is defined using a distance metric between the actual outcome of the event and each expert s predicted outcome following levy and delic levy w b h delic 1994 maximum entropy aggregation of individual opinions ieee trans sys man cybernetics 24 606 613 we use shannon s information measure shannon shannon c e 1948 a mathematical theory of communication bell syst tech j 27 379 423 jaynes jaynes e t 1957 information theory and statistical mechanics phys rev 106 part i 620 630 108 part ii 171 190 to derive aggregation rules for combining two or more expert predictions into a single aggregated prediction that appropriately calibrates different degrees of expert c

why are experts correlated decomposing correlations between judges we derive an analytic model of the inter judge correlation as a function of five underlying parameters inter cue correlation and the number of cues capture our assumptions about the environment while differentiations between cues the weights attached to the cues and un reliability describe assumptions about the judges we study the relative importance of and interrelations between these five factors with respect to inter judge correlation results highlight the centrality of the inter cue correlation we test the model s predictions with empirical data and illustrate its relevance for example we show that typically additional judges increase efficacy at a greater rate than additional cues

a simulation study of odds ratio estimation for binary outcomes from cluster randomized trials we used simulation to compare accuracy of estimation and confidence interval coverage of several methods for analysing binary outcomes from cluster randomized trials the following methods were used to estimate the population averaged intervention effect on the log odds scale marginal logistic regression models using generalized estimating equations with information sandwich estimates of standard error gee unweighted cluster level mean difference cl u weighted cluster level mean difference cl w and cluster level random effects linear regression cl re methods were compared across trials simulated with different numbers of clusters per trial arm numbers of subjects per cluster intraclass correlation coefficients rho and intervention versus control arm proportions two thousand data sets were generated for each combination of design parameter values the results showed that the gee method has generally acceptable properties including close to nominal levels of confidence interval coverage when a simple adjustment is made for data with relatively few clusters cl u and cl w have good properties for trials where the number of subjects per cluster is sufficiently large and rho is sufficiently small cl re also has good properties in this situation provided a t distribution multiplier is used for confidence interval calculation in studies with small numbers of clusters for studies where the number of subjects per cluster is small and rho is large all cluster level methods may perform poorly for studies with between 10 and 50 clusters per trial arm

a probabilistic approach to martin boundaries for manifolds with ends we use martingale methods and coupling arguments to prove results of li and tam 1987 and donnelly 1986 characterizing positive and bounded harmonic functions respectively on certain manifolds with ends

a covariance estimator for gee with improved small sample properties summary in this paper we propose an alternative covariance estimator to the robust covariance estimator of generalized estimating equations gee hypothesis tests using the robust covariance estimator can have inflated size when the number of independent clusters is small resampling methods such as the jackknife and bootstrap have been suggested for covariance estimation when the number of clusters is small a drawback of the resampling methods when the response is binary is that the methods can break down when the number of subjects is small due to zero or near zero cell counts caused by resampling we propose a bias corrected covariance estimator that avoids this problem in a small simulation study we compare the bias corrected covariance estimator to the robust and jackknife covariance estimators for binary responses for situations involving 10 40 subjects with equal and unequal cluster sizes of 16 64 observations the bias corrected covariance estimator gave tests with sizes close to the nominal level even when the number of subjects was 10 and cluster sizes were unequal whereas the robust and jackknife covariance estimators gave tests with sizes that could be 2 3 times the nominal level the methods are illustrated using data from a randomized clinical trial on treatment for bone loss in subjects with periodontal disease

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

reconciliation of probability distributions several people each express their opinion of an uncertain quantity by providing their mean and standard deviation of it in this paper we discuss the problem of incorporating all these opinions into a single reconciled probability distribution for the quantity the usual procedure is least squares based on normality the paper illustrates the advantages of using t distributions instead and clarifies the role of the information provided by the standard deviations suitable approximations are provided for many cases

dichotomizing a continuous outcome in cluster randomized trials impact on power in cluster randomized trials crts clusters of individuals are randomized rather than the individuals themselves for such trials power depends in part on the degree of similarity among responses within a cluster which is quantified by the intaclass correlation coefficient icc thus for a fixed sample size power decreases with increasing icc in reliability studies with two observers dichotomizing a continuous outcome variable has been shown to reduce the icc we checked by a simulation study that this property still applies to crts in which cluster sizes are variable and usually greater than in reliability studies and observations within clusters are exchangeable then in a crt dichotomizing a continuous outcome actually induces two antagonistic effects decreased power because of loss of information and increased power induced by attenuation of the icc therefore we aimed to assess the impact of dichotomizing a continuous outcome on power in a crt we derived an analytical formula for power based on a generalized estimating equation approach after dichotomizing a continuous outcome this theoretical result was obtained by considering equal cluster sizes and we then assessed its accuracy by a simulation study in the more realistic situation of varying cluster sizes we showed that dichotomization is associated with decreased power attenuation of the icc does not compensate for the loss of power induced by loss of information loss of power is reduced with increased initial continuous outcome icc and or prevalence of success for the dichotomized outcome approaching 50

harmonic maps from noncompact riemannian manifolds with non negative ricci curvature outside a compact set in this paper we prove the uniqueness and existence of harmonic maps of finite energy from a complete noncompact riemannian manifold m g with sobolev constant s2 m 0 and ricci curvature ric m 0 outside some compact subset into a complete manifold of nonpositive curvature or a regular ball in particular we prove the uniqueness and existence of bounded harmonic functions on m g

confidence interval estimation of the intraclass correlation coefficient for binary outcome data we obtain closed form asymptotic variance formulae for three point estimators of the intraclass correlation coefficient that may be applied to binary outcome data arising in clusters of variable size our results include as special cases those that have previously appeared in the literature fleiss and cuzick 1979 applied psychological measurement 3 537 542 bloch and kraemer 1989 biometrics 45 269 287 altaye donner and klar 2001 biometrics 57 584 588 simulation results indicate that confidence intervals based on the estimator proposed by fleiss and cuzick provide coverage levels close to nominal over a wide range of parameter combinations two examples are presented

large scale behavior of kernels of schrodinger operators in this paper we study the asymptotic behavior of solutions to schrodinger equations on manifolds with nonnegative ricci curvature and euclidean volume growth as a first application we get a sharp asymptotic estimate on the green s function for the laplacian which sharpens results of li and yau next we establish a definite gap in the possible rates of decay of exterior harmonic functions on these manifolds when the manifold also has quadratic curvature decay we get supremum estimates on the c 2 norm of the green s function this has function theoretic implications for these manifolds we then give a generalization to manifolds with nonnegative ricci curvature outside a compact set finally we study schrodinger operators where the potential decays quadratically at infinity in this setting we obtain a geometric version at infinity of a classical theorem of bers

copula models for aggregating expert opinions this paper discusses the use of multivariate distributions that are functions of their marginals for aggregating information from various sources the function that links the marginals is called a copula the information to be aggregated can be point estimates of an unknown quantity i or with suitable modeling assumptions probability distributions for i this approach allows the bayesian decision maker performing the aggregation to separate two difficult aspects of the model construction procedure qualities of the individual sources such as bias and precision are incorporated into the marginal distributions dependence among sources is encoded into the copula which serves as a dependence function and joins the marginal distributions into a single multivariate distribution the procedure is designed to be suitable for situations in which the decision maker must use subjective judgments as a basis for constructing the aggregation model we review properties of copulas pertinent to the information aggregation problem a subjectively assessable measure of dependence is developed that allows the decision maker to choose from a one parameter family of copulas a specific member that is appropriate for the level of dependence among the information sources the discussion then focuses on the class of archimedean copulas and frank s family of copulas in particular showing the specific relationship between the family and our measure of dependence a realistic example demonstrates the approach

the bias due to incomplete matching observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group in practice there is a trade off between the desires to find matches for all treated units and to obtain matched treated control pairs that are extremely similar to each other we derive expressions for the bias in the average matched pair difference due to the failure to match all treated units incomplete matching and the failure to obtain exact matches inexact matching a practical example shows that the bias due to incomplete matching can be severe and moreover can be avoided entirely by using an appropriate multivariate nearest available matching algorithm which in the example leaves only a small residual bias due to inexact matching

decision templates for multiple classifier fusion an experimental comparison abstract multiple classifier fusion may generate more accurate classification than each of the constituent classifiers fusion is often based on fixed combination rules like the product and average only under strict probabilistic conditions can these rules be justified we present here a simple rule for adapting the class combiner to the application c decision templates one per class are estimated with the same training set that is used for the set of classifiers these templates are then matched to the decision profile of new incoming objects by some similarity measure we compare 11 versions of our model with 14 other techniques for classifier fusion on the satimage and phoneme datasets from the database elena our results show that decision templates based on integral type measures of similarity are superior to the other schemes on both data sets