the fisher neyman pearson theories of testing hypotheses one theory or two abstract the fisher and neyman pearson approaches to testing statistical hypotheses are compared with respect to their attitudes to the interpretation of the outcome to power to conditioning and to the use of fixed significance levels it is argued that despite basic philosophical differences in their main practical aspects the two theories are complementary rather than contradictory and that a unified approach is possible that combines the best features of both as applications the controversies about the behrens fisher problem and the comparison of two binomials 2 2 tables are considered from the present point of view

combining information from independent sources through confidence distributions this paper develops new methodology together with related theories for combining information from independent studies through confidence distributions a formal definition of a confidence distribution and its asymptotic counterpart i e asymptotic confidence distribution are given and illustrated in the context of combining information two general combination methods are developed the first along the lines of combining p values with some notable differences in regard to optimality of bahadur type efficiency the second by multiplying and normalizing confidence densities the latter approach is inspired by the common approach of multiplying likelihood functions for combining parametric information the paper also develops adaptive combining methods with supporting asymptotic theory which should be of practical interest the key point of the adaptive development is that the methods attempt to combine only the correct information downweighting or excluding studies containing little or wrong information about the true parameter of interest the combination methodologies are illustrated in simulated and real data examples with a variety of applications

p value functions an underused method to present research results and to promote quantitative reasoning null hypothesis significance testing has received a great amount of attention in recent years in the light of the reproducibility crisis of science recently there have been calls to retire the dichotomization of study results into significant or not significant depending on whether the p value crosses some threshold or not ways of improving the interpretation of p values and confidence intervals are therefore needed we illustrate the use of p value functions which display confidence limits and p values for any confidence level for a parameter p value functions accessibly display a wealth of information point estimate for the parameter one sided and two sided confidence limits at any level and one sided and two sided p values for any null and non null value and the counternull value presenting several recent examples from the literature we show how p value functions can be applied to present evidence and to make informed statistical inferences without resorting to dichotomization we argue that p value functions are more informative than commonly used summaries of study results such as single p values or confidence intervals p value functions require minimal retraining are easily interpreted and show potential to fix many of the common misinterpretation of p values and confidence intervals to facilitate the adoption of p value functions we released an r package for creating p value functions for several commonly used estimates

comparison of meta analysis versus analysis of variance of individual patient data meta analysis is a method of synthesizing the results of independent studies we consider the case in which there are multiple treatments and a control with the goal of estimating the relative effect of each treatment based on continuous outcomes even when all data are available rather than only summary data it has become common to use meta analytic estimators of treatment contrasts alternatively we could use a two way analysis of variance model with no interaction in which one factor is study and one factor is treatment for the unbalanced case we obtain the surprising result that the standard meta analysis estimates of treatment contrasts are identical to the least squares estimators of treatment contrasts in the linear model because a meta analysis of individual patient data can be considerably more costly in terms of data retrieval than a meta analysis of summary data this equivalence provides for cost efficient analysis

spectral super elements for wave propagation in structures with local non uniformities the spectral element method for the analysis of wave propagation in structures is extended by the introduction of a super element concept to handle local regions of non uniformity the region of interest is meshed with conventional finite elements and its stiffness and mass matrices dynamically condensed leaving only the connection degrees of freedom these are further condensed to just waveguide connectivities thus making the element suitable for assembly with other spectral elements the formulation is verified by comparison with 2 d finite element solutions examples of its use in waveguides with cracks holes and extended joints are demonstrated

inferential models a framework for prior free posterior probabilistic inference posterior probabilistic statistical inference without priors is an important but so far elusive goal fisher s fiducial inference dempster shafer theory of belief functions and bayesian inference with default priors are attempts to achieve this goal but to date none has given a completely satisfactory picture this article presents a new framework for probabilistic inference based on inferential models ims which not only provides data dependent probabilistic measures of uncertainty about the unknown parameter but also does so with an automatic long run frequency calibration property the key to this new approach is the identification of an unobservable auxiliary variable associated with observable data and unknown parameter and the prediction of this auxiliary variable with a random set before conditioning on data here we present a three step im construction and prove a frequency calibration property of the im s belief function under mild conditions a corresponding optimality theory is develo

marginal inferential models prior free probabilistic inference on interest parameters the inferential models im framework provides prior free frequency calibrated and posterior probabilistic inference the key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown parameters when nuisance parameters are present a marginalization step can reduce the dimension of the auxiliary variable which in turn leads to more efficient inference for regular problems exact marginalization can be achieved and we give conditions for marginal im validity we show that our approach provides exact and efficient marginal inference in several challenging problems including a many normal means problem in nonregular problems we propose a generalized marginalization technique and prove its validity details are given for two benchmark examples namely the behrens fisher and gamma mean problems

on the equivalence of meta analysis using literature and using individual patient data summary when data come from several independent studies for the purpose of estimating treatment control differences meta analysis can be carried out either on the best linear unbiased estimators computed from each study or on the pooled individual patient data modelled as a two way model without interaction where the two factors represent the different studies and the different treatments assuming that observations within and between studies are independent having a common variance olkin and sampson 1998 have obtained the surprising result that the two meta analytic procedures are equivalent i e they both produce the same estimator in this article the same equivalence is established for the two way fixed effects model without interaction with the only assumption that the observations across studies be independent a consequence of the equivalence result is that regardless of the covariance structure it is possible to get an explicit representation for the best linear unbiased estimator of any vector of treatment contrasts in a two way fixed effects model without interaction as long as the studies are independent another interesting consequence is that for the purpose of best linear unbiased estimation an unbalanced two way fixed effects model without interaction can be treated as several independent unbalanced one way models regardless of the covariance structure when the studies are independent

exact meta analysis approach for discrete data and its application to 2 2 tables with rare events this article proposes a general exact meta analysis approach for synthesizing inferences from multiple studies of discrete data the approach combines the p value functions also known as significance functions associated with the exact tests from individual studies it encompasses a broad class of exact meta analysis methods as it permits broad choices for the combining elements such as tests used in individual studies and any parameter of interest the approach yields statements that explicitly account for the impact of individual studies on the overall inference in terms of efficiency power and the type i error rate those statements also give rises to empirical methods for further enhancing the combined inference although the proposed approach is for general discrete settings for convenience it is illustrated throughout using the setting of meta analysis of multiple 2 2 tables in the context of rare events data such as observing few zero or zero total i e zero events in both arms out

how conservative is fisher s exact test a quantitative evaluation of the two sample comparative binomial trial the debate as to which statistical methodology is most appropriate for the analysis of the two sample comparative binomial trial has persisted for decades practitioners who favor the conditional methods of fisher fisher s exact test fet claim that only experimental outcomes containing the same amount of information should be considered when performing analyses hence the total number of successes should be fixed at its observed level in hypothetical repetitions of the experiment using conditional methods in clinical settings can pose interpretation difficulties since results are derived using conditional sample spaces rather than the set of all possible outcomes perhaps more importantly from a clinical trial design perspective this test can be too conservative resulting in greater resource requirements and more subjects exposed to an experimental treatment the actual significance level attained by fet the size of the test has not been reported in the statistical literature berger j r statist soc d the statistician 2001 50 79 85 proposed assessing the conservativeness of conditional methods using p value confidence intervals in this paper we develop a numerical algorithm that calculates the size of fet for sample sizes n up to 125 per group at the two sided significance level alpha 0 05 additionally this numerical method is used to define new significance levels alpha alpha epsilon where epsilon is a small positive number for each n such that the size of the test is as close as possible to the pre specified alpha 0 05 for the current work without exceeding it lastly a sample size and power calculation example are presented which demonstrates the statistical advantages of implementing the adjustment to fet using alpha instead of alpha in the two sample comparative binomial trial

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

recommended tests for association in 2 2 tables summary the asymptotic pearson s chi squared test and fisher s exact test have long been the most used for testing association in 2 2 tables unconditional tests preserve the significance level and generally are more powerful than fisher s exact test for moderate to small samples but previously were disadvantaged by being computationally demanding this disadvantage is now moot as software to facilitate unconditional tests has been available for years moreover fisher s exact test with mid p adjustment gives about the same results as an unconditional test consequently several better tests are available and the choice of a test should depend only on its merits for the application involved unconditional tests and the mid p approach ought to be used more than they now are the traditional fisher s exact test should practically never be used copyright q 2009 john wiley sons ltd

cauchy combination test a powerful test with analytic p value calculation under arbitrary dependency structures abstract combining individual p values to aggregate multiple small effects has a long standing interest in statistics dating back to the classic fisher s combination test in modern large scale da

bayes and likelihood calculations from confidence intervals recently there has been considerable progress on setting good approximate confidence intervals for a single parameter in a multi parameter family here we use these frequentist results as a convenient device for making bayes empirical bayes and likelihood inferences about a simple formula is given that produces an approximate likelihood function l x for with all nuisance parameters eliminated based on any system of approximate confidence intervals the statistician can then modify l x with bayes or empirical bayes information for without worrying about nuisance parameters

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

generalized fiducial inference for ultrahigh dimensional regression in recent years the ultrahigh dimensional linear regression problem has attracted enormous attention from the research community under the sparsity assumption most of the published work is devoted to the selection and estimation of the predictor variables with nonzero coefficients this article studies a different but fundamentally important aspect of this problem uncertainty quantification for parameter estimates and model choices to be more specific this article proposes methods for deriving a probability density function on the set of all possible models and also for constructing confidence intervals for the corresponding parameters these proposed methods are developed using the generalized fiducial methodology which is a variant of fisher s controversial fiducial idea theoretical properties of the proposed methods are studied and in particular it is shown that statistical inference based on the proposed methods will have correct asymptotic frequentist property in terms of empirical perform

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

meta analysis with fixed unknown study specific parameters meta analysis is a valuable tool for combining information from independent studies however most common meta analysis techniques rely on distributional assumptions that are difficult if not impossible to verify for instance in the commonly used fixed effects and random effects models we take for granted that the underlying study level parameters are either exactly the same across individual studies or that they are realizations of a random sample from a population often under a parametric distributional assumption in this article we present a new framework for summarizing information obtained from multiple studies and make inference that is not dependent on any distributional assumption for the study level parameters specifically we assume the study level parameters are unknown fixed parameters and draw inferences about for example the quantiles of this set of parameters using study specific summary statistics this type of problem is known to be quite challenging see hall and miller we

confidence distributions and a unifying framework for meta analysis this article develops a unifying framework as well as robust meta analysis approaches for combining studies from independent sources the device used in this combination is a confidence distribution cd which uses a distribution function instead of a point point estimator or an interval confidence interval to estimate a parameter of interest a cd function contains a wealth of information for inferences and it is a useful device for combining studies from different sources the proposed combining framework not only unifies most existing meta analysis approaches but also leads to development of new approaches we illustrate in this article that this combining framework can include both the classical methods of combining p values and modern model based meta analysis approaches we also develop under the unifying framework two new robust meta analysis approaches with supporting asymptotic theory in one approach each study size goes to infinity and in the other approach the number of studies

frequentist prediction intervals and predictive distributions summary we consider parametric frameworks for the prediction of future values of a random variable y based on previously observed data x simple pivotal methods for obtaining calibrated prediction intervals are presented and illustrated frequentist predictive distri butions are defined as confidence distributions and their utility is demonstrated a simple pivotal based approach that produces prediction intervals and predictive distributions with well calibrated frequentist probability interpretations is introduced and efficient simulation methods for producing predictive distributions are considered properties related to an average kullback leibler measure of goodness for predictive or estimated distributions are given the predictive distributions here are shown to be optimal in certain settings with invariance structure and to dominate plug in distributions under certain conditions

high order dynamic modeling and parameter identification of structural discontinuities in timoshenko beams by using reflection coefficients abstract properties of discontinuities such as bolt joints and cracks in the waveguide structures are difficult to evaluate by either analytical or numerical methods due to the complexity and uncertainty of the discontinuities in this paper the discontinuity in a timoshenko beam is modeled with high order parameters and then these parameters are identified by using reflection coefficients at the discontinuity the high order model is composed of several one order sub models in series and each sub model consists of inertia stiffness and damping components in parallel the order of the discontinuity model is determined based on the characteristics of the reflection coefficient curve and the accuracy requirement of the dynamic modeling the model parameters are identified through the least square fitting iteration method of which the undetermined model parameters are updated in iteration to fit the dynamic reflection coefficient curve with the wave based one by using the spectral super element method ssem simulation cases including one order discontinuities on infinite and finite beams and a two order discontinuity on an infinite beam were employed to evaluate both the accuracy of the discontinuity model and the effectiveness of the identification method for practical considerations effects of measurement noise on the discontinuity parameter identification are investigated by adding different levels of noise to the simulated data the simulation results were then validated by the corresponding experiments both the simulation and experimental results show that 1 the one order discontinuities can be identified accurately with the maximum errors of 6 8 and 8 7 respectively 2 and the high order discontinuities can be identified with the maximum errors of 15 8 and 16 2 respectively and 3 the high order model can predict the complex discontinuity much more accurately than the one order discontinuity model

identification of joint properties of a structure using frf data abstract the connections between structural components i e joints are extremely difficult to model accurately by using a pure analytical approach alternatively joint properties can be extracted from experimental data a method for identifying extracting joint properties from the measured frequency response function frf data is presented in this paper one of the major difficulties in accurate identification of joint properties is that the identification results can be significantly affected by various errors in the measured data even if errors in the measured data are at an insignificantly low level say 5 in frfs their effects on the identification can be severe enough so that in some cases the predicted joint properties can be completely irrelevant to the true properties of joints apart from the accuracy of the data used for the identification the accuracy of the identification also significantly depends upon the mathematical formulae used for the identification even with the same experimental data the accuracies of the identification by different methods can be significantly different therefore developing methods that are insensitive to measurement errors is of utmost importance for the identification of joint properties from experimental data in this paper techniques for improving the accuracy of joint identification are discussed it is demonstrated that by using all available information effectively the accuracy of the identification can be much improved both numerical and experimental examples are presented

discontinuity location on a timoshenko beam by using a novel wave reflection technique abstract based on the physical phenomenon that some propagating waves are partially reflected by discontinuities in waveguide structures this paper proposes a novel discontinuity locating method which is potentially able to detect both the added and embedded discontinuities such as supports and cracks in this method the reflection coefficients of a discontinuity can be obtained experimentally by using a generalized discontinuity approach without the information of the discontinuity position on the other hand these reflection coefficients can be derived from a reflection coefficient prediction model in terms of the discontinuity position by minimizing the error between the reflection coefficients from measurements and those from the prediction model in the frequency bands in which the guided waves are sensitive to the discontinuity and can propagate with low decay rate the discontinuity position parameter in the prediction model can then be identified two numerical cases of locating an added discontinuity and an embedded discontinuity on a beam are proposed to introduce the effectiveness of the method simulation results show that these two discontinuities can be located accurately with zero error in practice the accuracy of discontinuity locating may be influenced by some factors 1 boundary conditions of the beam 2 sizes and locations of the discontinuity and 3 measurement noise the investigation of these factors in simulation shows that this locating method is insensitive to the boundary conditions of the beam effective to small size of the discontinuity and robust to the measurement noise finally three experiments were developed to locate an added discontinuity on a finite beam a crack in an infinite beam with depth ratio of 1 2 and a crack in an infinite beam with depth ratio of 1 6 respectively the corresponding locating errors of these three experiments are 0 percent 0 077 percet and 0 154 percent

generalized fiducial inference a review and new results abstractr a fisher the father of modern statistics proposed the idea of fiducial inference during the first half of the 20th century while his proposal led to interesting methods for quantifying uncertainty other prominent statisticians of the time did not accept fisher s approach as it became apparent that some of fisher s bold claims about the properties of fiducial distribution did not hold up for multi parameter problems beginning around the year 2000 the authors and collaborators started to reinvestigate the idea of fiducial inference and discovered that fisher s approach when properly generalized would open doors to solve many important and difficult inference problems they termed their generalization of fisher s idea as generalized fiducial inference gfi the main idea of gfi is to carefully transfer randomness from the data to the parameter space using an inverse of a data generating equation without the use of bayes theorem the resulting generalized fiducial distribution gfd can

identification techniques of structure connection parameters using frequency response functions the identification method for stiffness constant parameters and damping coefficient parameters of connections using test data is derived when a structure is attached to another structure via connections because of the inherent difficulties of deriving spatial models from test data the frequency response function frf is used as a response model the identification method using the frfs works for each discrete frequency so that the connection properties can be found for each frequency and can be averaged using statistical methods for an accurate identification if highly sensitive regions are excluded this identification method for connection using frfs gives accurate estimations and can be applied to a general structure in an easier manner than the modal model methods which require a mathematical model of the mass damping and stiffness matrices or natural frequencies and mode shapes

the highest confidence density region and its usage for joint inferences about constrained parameters suppose that we are interested in making joint inferences about a set of constrained parameters confidence regions for these parameters are often constructed via a normal approximation of the distribution of a consistent estimator for a transformation of the parameters in this article we utilize the confidence distribution a frequentist counterpart to the posterior distribution in bayesian statistics to obtain optimal confidence regions for the parameters members of such a region can be generated efficiently via a standard markov chain monte carlo algorithm we then apply this technique to draw inferences about the temporal profile of the survival function with censored observations we illustrate the new proposal with the survival data from the well known mayo primary biliary cirrhosis study and show that the volume of the new 0 95 confidence region is only one thirty fourth of that of the conventional confidence band

meta analysis of quantile intervals from different studies with an application to a pulmonary tuberculosis data after the completion of many studies experimental results are reported in terms of distribution free confidence intervals that may involve pairs of order statistics this article considers a meta analysis procedure to combine these confidence intervals from independent studies to estimate or construct a confidence interval for the true quantile of the population distribution data synthesis is made under both fixed effect and random effect meta analysis models we show that mean square error mse of the combined quantile estimator is considerably smaller than that of the best individual quantile estimator we also show that the coverage probability of the meta analysis confidence interval is quite close to the nominal confidence level the random effect meta analysis model yields a better coverage probability and smaller mse than the fixed effect meta analysis model the meta analysis method is then used to synthesize medians of patient delays in pulmonary tuberculosis diagnosis in china to provide an illustration of the proposed methodology

on the relative efficiency of using summary statistics versus individual level data in meta analysis meta analysis is widely used to synthesize the results of multiple studies although meta analysis is traditionally carried out by combining the summary statistics of relevant studies advances in technologies and communications have made it increasingly feasible to access the original data on individual participants in the present paper we investigate the relative efficiency of analyzing original data versus combining summary statistics we show that for all commonly used parametric and semiparametric models there is no asymptotic efficiency gain by analyzing original data if the parameter of main interest has a common value across studies the nuisance parameters have distinct values among studies and the summary statistics are based on maximum likelihood we also assess the relative efficiency of the two methods when the parameter of main interest has different values among studies or when there are common nuisance parameters across studies we conduct simulation studies to confirm the theoretical results and provide empirical comparisons from a genetic association study

prediction of dynamic characteristics using updated finite element models abstract model updating techniques are used to update a finite element model of a structure so that an updated model predicts the dynamics of a structure more accurately the application of such an updated model in dynamic design demands that it also predict the effects of structural modifications with a reasonable accuracy this paper deals with updating of a finite element model of a structure and its subsequent use for predicting the effects of structural modifications updated models have been obtained by a direct model updating method and by an iterative method of model updating based on the frequency response function frf data the suitability of updated models for predicting the effect of structural modifications is evaluated by some computer and laboratory experiments first a study is performed using a simulated fixed fixed beam cases of complete incomplete and noisy data are considered updated models are obtained by the direct and the frf based method in each of these cases these models are then used for predicting the changes in the dynamic characteristics brought about due to a mass and a beam modification the simulated study is followed by a study involving actual measured data for the case of an f shape test structure the updated finite element models for this structure are obtained again by the direct and the frf based method structural modifications in terms of mass and beam modifications are then introduced to evaluate the updated model for its usefulness in dynamic design it is found that the predictions based on the iterative method based updated model are reasonably accurate and therefore this updated model can be used with reasonable accuracy to perform dynamic design the predictions on the basis of the direct method based updated model are found to be reasonably accurate in the lower portion of the updating frequency range but the predictions are in a significant error in the remaining portion of the updating frequency range it is concluded that the updated models that are closer to the structure physically are likely to perform better in predicting the effects of structural modification

a multiple quadrature eight node hexahedral finite element for large deformation elastoplastic analysis abstract a multiple quadrature underintegrated hexahedral finite element which is free of volumetric and shear locking and has no spurious singular modes is described and implemented for nonlinear analysis finite element formulations are derived in the corotational coordinate system the use of consistent tangent operators for large deformation elastoplasticity with nonlinear isotropic kinematic hardening rules preserves the quadratic rate of convergence of the newton s iteration method in static analysis test problems studied demonstrate the efficiency and effectiveness of this element in solving a wide variety of problems including sheet metal forming processes

asymptotic distribution of p values in composite null models abstract we investigate the compatibility of a null model h 0 with the data by calculating a p value that is the probability under h 0 that a given test statistic t exceeds its observed value when the null model consists of a single distribution the p value is readily obtained and it has a uniform distribution under h 0 on the other hand when the null model depends on an unknown nuisance parameter one must somehow get rid of e g by estimating it to calculate a p value various proposals have been suggested to remove each yielding a different candidate p value but unlike the simple case these p values typically are not uniformly distributed under the null model in this article we investigate their asymptotic distribution under h 0 we show that when the asymptotic mean of the test statistic t depends on the posterior predictive p value of guttman and rubin and the plug in p value are conservative i e their asymptotic distributions are more concentrated around 1 2 than a uni

three dimensional corotational framework for elasto plastic analysis of multilayered composite shells acontinuum basedlayerwiseshear deformablee niteelementformulationispresentedforelasto plasticanalysis oflayered compositesshells theproposed formulationiscast in a corotationalcone guration for e nitedeformation analysis the elasto plastic constitutive equations that are based on rate independent deviatoric plasticity are also written in the corotational kinematic framework issues of covariance and spatial invariance are addressed and an appropriate stress updating strategy is proposed numerical examples are presented to demonstrate the range of applicability of the proposed framework for bending dominated response of elasto plastic layered composite shells nomenclature b body force vector c e fourth order elastic modulus tensor c i n 1 tangent modului consistent with the radial return algorithm d p plastic strain rate tensor e deviatoric strain tensor e p equivalent plastic strain fn 1 incremental deformation gradient ft x deformation gradient f ae q von mises pressure insensitive yield condition a e p hardening rule for back stress i identity matrix

selecting likelihood weights by cross validation the relevance weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision unlike its classical counterpart the weighted likelihood combines all relevant information while inheriting many of its desirable features including good asymptotic properties however in order to be effective the weights involved in its construction need to be judiciously chosen choosing those weights is the subject of this article in which we demonstrate the use of cross validation we prove the resulting weighted likelihood estimator wle to be weakly consistent and asymptotically normal an application to disease mapping data is demonstrated

conditional inferential models combining information for prior free probabilistic inference summary the inferential model im framework provides valid prior free probabilistic inference by focusing on predicting unobserved auxiliary variables but efficient im based inference can be challenging when the auxiliary variable is of higher dimension than the parameter here we show that features of the auxiliary variable are often fully observed and in such cases a simultaneous dimension reduction and information aggregation can be achieved by conditioning this proposed conditioning strategy leads to efficient im inference and casts new light on fisher s notions of sufficiency conditioning and also bayesian inference a differential equation driven selection of a conditional association is developed and validity of the conditional im is proved under some conditions for problems that do not admit a conditional im of the standard form we propose a more flexible class of conditional ims based on localization examples of local conditional ims in a bivariate normal model and a normal variance components model are also given

empirical bayes methods for combining likelihoods abstract suppose that several independent experiments are observed each one yielding a likelihood l k k for a real valued parameter of interest k for example k might be the log odds ratio for a 2 2 table relating to the kth population in a series of medical experiments this article concerns the following empirical bayes question how can we combine all of the likelihoods l k to get an interval estimate for any one of the k s say 1 the results are presented in the form of a realistic computational scheme that allows model building and model checking in the spirit of a regression analysis no special mathematical forms are required for the priors or the likelihoods this scheme is designed to take advantage of recent methods that produce approximate numerical likelihoods l k k even in very complicated situations with all nuisance parameters eliminated the empirical bayes likelihood theory is extended to situations where the k s have a regression structure as well as an empiri

meta analysis framework for exact inferences with application to the analysis of rare events the usefulness of meta analysis has been recognized in the evaluation of drug safety as a single trial usually yields few adverse events and offers limited information for rare events conventional meta analysis methods may yield an invalid inference as they often rely on large sample theories and require empirical corrections for zero events these problems motivate research in developing exact methods including tian et al s method of combining confidence intervals 2009 biostatistics 10 275 281 and liu et al s method of combining p value functions 2014 jasa 109 1450 1465 this article shows that these two exact methods can be unified under the framework of combining confidence distributions cds furthermore we show that the cd method generalizes tian et al s method in several aspects given that the cd framework also subsumes the mantel haenszel and peto methods we conclude that the cd method offers a general framework for meta analysis of rare events we illustrate the cd framework using two real data sets collected for the safety analysis of diabetes drugs

statistical inference likelihood to significance abstract the concepts of likelihood and significance were defined and initially developed by r a fisher but followed almost separate and distinct routes we suggest that a central function of statistical inference is in fact the conversion of the first likelihood into the second significance a linking of the fisher concepts a first order asymptotic route for this is incorporated into most statistical packages it uses the standardized maximum likelihood estimate the standardized score or the signed square root of the likelihood ratio statistic as arguments for the standard normal distribution function thus giving approximate tail probabilities or observed levels of significance recent third order asymptotic methods provide a substantial increase in accuracy but need the first derivative dependence of likelihood on the data value as an additional input this can be envisaged as the effect on the likelihood function of dithering the data point extensions to the multivariate multiparameter cont

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation