stable weights that balance covariates for estimation with incomplete outcome data weighting methods that adjust for observed covariates such as inverse probability weighting are widely used for causal inference and estimation with incomplete outcome data part of the appeal of such methods is that one set of weights can be used to estimate a range of treatment effects based on different outcomes or a variety of population means for several variables however this appeal can be diminished in practice by the instability of the estimated weights and by the difficulty of adequately adjusting for observed covariates in some settings to address these limitations this article presents a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher this method allows the researcher to balance very precisely the means of the observed covariates and other features of their marginal and joint distributions such as variances and correlations and also for example the

randomization inference for treatment effect variation summary applied researchers are increasingly interested in whether and how treatment effects vary in randomized evaluations especially variation that is not explained by observed covariates we propose a model free approach for testing for the presence of such unexplained variation to use this randomization based approach we must address the fact that the average treatment effect which is generally the object of interest in randomized experiments actually acts as a nuisance parameter in this setting we explore potential solutions and advocate for a method that guarantees valid tests in finite samples despite this nuisance we also show how this method readily extends to testing for heterogeneity beyond a given model which can be useful for assessing the sufficiency of a given scientific theory we finally apply our method to the national head start impact study which is a large scale randomized evaluation of a federal preschool programme finding that there is indeed significant unexplained treatment effect variation

the hanna neumann conjecture for demushkin groups abstract we confirm the hanna neumann conjecture for topologically finitely generated closed subgroups u and w of a nonsolvable demushkin group g namely we show that g u g w d u g w g 1 d u d w where d k max d k 1 0 and d k is the least cardinality of a topological generating set for the group k

causal mediation analysis in the multilevel intervention and multicomponent mediator case summary mediation analysis is an important tool in social and medical sciences as it helps to understand why an intervention works the commonly used approach given by baron and kenny requires the strong assumption sequential ignorability to yield causal interpretation ten have and his colleagues proposed a rank preserving model to relax this assumption however the rank preserving model is restricted to the case with binary intervention and single mediator and needs another strong assumption rank preserving we propose a new model that can relax this assumption and can handle both multilevel intervention and multicomponent mediators as an estimating equation based method our model can handle both correlated data with the generalized estimating equation and missing data with inverse probability weighting finally our method can also be used in many other research settings using mathematical models similar to mediation analysis such as treatment compliance and post randomized treatment component analysis for the causal mediation model proposed we first show identifiability for the parameters in the model we then propose a semiparametric method for estimating the model parameters and derive asymptotic results for the estimators proposed simulation shows good performance for the proposed estimators in finite sample sizes finally we apply the method proposed to two real world clinical studies the college student drinking study and the improving mood promoting access to collaborative treatment for late life depression study

fast rcs computation over a frequency band using method of moments in conjunction with asymptotic waveform evaluation technique the method of moments mom in conjunction with the asymptotic waveform evaluation awe technique is applied to obtain the radar cross section rcs of an arbitrarily shaped three dimensional 3 d perfect electric conductor pec body over a frequency band the electric field integral equation efie is solved using the mom to obtain the equivalent surface current on the pec body in the awe technique the equivalent surface current is expanded in a taylor s series around a frequency in the desired frequency band the taylor series coefficients are then matched via the pade approximation to a rational function using the rational function the surface current is obtained at any frequency within the frequency range which is in turn used to calculate the rcs of the 3 d pec body a rational function approximation is also obtained using the model based parameter estimation mbpe method and compared with the pade approximation numerical results for a square plate a cube and a sphere are presented over a frequency bandwidth good agreement between the awe and the exact solution over the bandwidth is observed

causal inference in paired two arm experimental studies under noncompliance with application to prognosis of myocardial infarction motivated by a study about prompt coronary angiography in myocardial infarction we propose a method to estimate the causal effect of a treatment in two arm experimental studies with possible noncompliance in both treatment and control arms we base the method on a causal model for repeated binary outcomes before and after the treatment which includes individual covariates and latent variables for the unobserved heterogeneity between subjects moreover given the type of noncompliance the model assumes the existence of three subpopulations of subjects compliers never takers and always takers we estimate the model using a two step estimator at the first step we estimate the probability that a subject belongs to one of the three subpopulations on the basis of the available covariates at the second step we estimate the causal effects through a conditional logistic method the implementation of which depends on the results from the first step the estimator is approximately consistent and under certain circumstances exactly consistent we provide evidence that the bias is negligible in relevant situations we compute standard errors on the basis of a sandwich formula the application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next 2 years with a log odds of about 2 given that noncompliance is significant for patients being given the treatment because of high risk conditions classical estimators fail to detect or at least underestimate this effect copyright 2013 john wiley sons ltd

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

causal inference by using invariant prediction identification and confidence intervals summary what is the difference between a prediction that is made with a causal model and that with a non causal model suppose that we intervene on the predictor variables or change the whole environment the predictions from a causal model will in general work as well under interventions as for observational data in contrast predictions from a non causal model can potentially be very wrong if we actively intervene on variables here we propose to exploit this invariance of a prediction under a causal model for causal inference given different experimental settings e g various interventions we collect all models that do show invariance in their predictive accuracy across settings and interventions the causal model will be a member of this set of models with high probability this approach yields valid confidence intervals for the causal relationships in quite general scenarios we examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable we further investigate robustness properties of our approach under model misspecification and discuss possible extensions the empirical properties are studied for various data sets including large scale gene perturbation experiments

toward causal inference with interference a fundamental assumption usually made in causal inference is that of no interference between individuals or units that is the potential outcomes of one individual are assumed to be unaffected by the treatment assignment of other individuals however in many settings this assumption obviously does not hold for example in the dependent happenings of infectious diseases whether one person becomes infected depends on who else in the population is vaccinated in this article we consider a population of groups of individuals where interference is possible between individuals within the same group we propose estimands for direct indirect total and overall causal effects of treatment strategies in this setting relations among the estimands are established for example the total causal effect is shown to equal the sum of direct and indirect causal effects using an experimental design with a two stage randomization procedure first at the group level then at the individual level within groups unbiased estimators of the proposed estimands are presented variances of the estimators are also developed the methodology is illustrated in two different settings where interference is likely assessing causal effects of housing vouchers and of vaccines

nonuniform frequency sampling with active learning application to wide band frequency domain modeling and design one must employ many frequency points to synthesize a wide band time domain signal scattered or radiated from a given linear device if the structure is large relative to wavelengths of interest the large number of required frequency domain computations may require significant computational resources an active learning framework is introduced to reduce the number of frequencies needed for frequency domain numerical computations or measurements this method is used to optimally select frequency points at which a computation of measurement should be performed resulting in nonuniform frequency sampling and often a reduced number of total frequency points vis a spl grave vis uniform sampling in this paper we focus on wide band frequency domain numerical modeling demonstrating a reduction in the required number of computations the method consists of two basic steps tied to fitting the frequency domain data to a simple parametric model one step involves estimation of model parameters using a least square ls algorithm this process is based on data from frequency points computed thus far by the rigorous numerical model the next step is to optimally choose the next frequency point for analysis by the numerical model this new frequency point is selected with the goal of reducing uncertainty in the simplified parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations are performed each at the most informative frequency for learning the parameters of the associated simpler parametric model after demonstrating this technique with scattering problems the idea is employed for design of an ultrawide band antenna in this design a genetic algorithm ga is employed to optimize the geometry and the resistive loading of an antenna with the number of required frequency domain numerical computations reduced by the parametric model and active learning

posterior predictive p values extending work of rubin this paper explores a bayesian counterpart of the classical p value namely a tail area probability of a test statistic under a null hypothesis the bayesian formulation using posterior predictive replications of the data allows a test statistic to depend on both data and unknown nuisance parameters and thus permits a direct measure of the discrepancy between sample and population quantities the tail area probability for a test statistic is then found under the joint posterior distribution of replicate data and the nuisance parameters both conditional on the null hypothesis this posterior predictive p value can also be viewed as the posterior mean of a classical p value averaging over the posterior distribution of nuisance parameters under the null hypothesis and thus it provides one general method for dealing with nuisance parameters two classical examples including the behrens fisher problem are used to illustrate the posterior predictive p value and some of its interesting properties which also reveal a new bayesian interpretation for some classical p values an application to multiple imputation inference is also presented a frequency evaluation shows that in general if the replication is defined by new nuisance parameters and new data then the type i frequentist error of an level posterior predictive test is often close to but less than and will never exceed 2

valid randomization based p values for partially post hoc subgroup analyses by partially post hoc subgroup analyses we mean analyses that compare existing data from a randomized experiment from which a subgroup specification is derived to new subgroup only experimental data we describe a motivating example in which partially post hoc subgroup analyses instigated statistical debate about a medical device s efficacy we clarify the source of such analyses invalidity and then propose a randomization based approach for generating valid posterior predictive p values for such partially post hoc subgroups lastly we investigate the approach s operating characteristics in a simple illustrative setting through a series of simulations showing that it can have desirable properties under both null and alternative hypotheses

on the nature and discovery of structure abstract extending principles of experimentation we discuss conditions under which nonexperimental data allow consistent estimation of effects of the kind revealed by experimentation and relevant to decisions we show how implications of these conditions are often overlooked and how failure to distinguish between factors and concomitants makes almost anything said about a model ambiguous if not wrong the effects to be estimated dictate the factors to be included consistency and efficiency determine the concomitants whose effects are not to be estimated concomitants may affect but must not be affected by the factors effects of excluded variables on an included variable may cause inconsistency if the included variable is a factor can only reduce inconsistency if the included variable is a concomitant exclusion of a variable because it is highly correlated with another may sometimes be legitimate if both variables are concomitants never if either is a factor a condition for consistent estimatio

on the conditional logistic estimator in two arm experimental studies with non compliance and before after binary outcomes the behavior of the conditional logistic estimator is analyzed under a causal model for two arm experimental studies with possible non compliance in which the effect of the treatment is measured by a binary response variable we show that when non compliance may only be observed in the treatment arm the effect measured on the logit scale of the treatment on compliers and that of the control on non compliers can be identified and consistently estimated under mild conditions the same does not happen for the effect of the control on compliers a simple correction of the conditional logistic estimator is then proposed which allows us to considerably reduce the bias in estimating this quantity and the causal effect of the treatment over control on compliers a two step estimator results on the basis of which we can also set up a wald test for the hypothesis of absence of a causal effect of the treatment the asymptotic properties of the estimator are studied by exploiting the general theory on maximum likelihood estimation of misspecified models finite sample properties of the estimator and of the related wald test are studied by simulation the extension of the approach to the case of missing responses is also outlined the approach is illustrated by an application to a dataset deriving from a study on the efficacy of a training course on the breast self examination practice copyright 2010 john wiley sons ltd

semiparametric models for longitudinal data with application to cd4 cell numbers in hiv seroconverters summary the paper describes a semiparametric model for longitudinal data which is illustrated by its application to data on the time evolution of cd4 cell numbers in hiv seroconverters the essential ingredients of the model are a parametric linear model for covariate adjustment a nonparametric estimation of a smooth time trend serial correlation between measurements on an individual subject and random measurement error a back fitting algorithm is used in conjunction with a cross validation prescription to fit the model a notable feature in the application is that the onset of hiv infection is associated with a sudden drop in cd4 cells followed by a longer term slower decay the model is also used to estimate an individual s curve by combining his data with the population curve shrinkage toward the population mean trajectory is controlled in a natural way by the estimated covariance structure of the data

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

facilitating score and causal inference trees for large observational studies assessing treatment effects in observational studies is a multifaceted problem that not only involves heterogeneous mechanisms of how the treatment or cause is exposed to subjects known as propensity but also differential causal effects across sub populations we introduce a concept termed the facilitating score to account for both the confounding and interacting impacts of covariates on the treatment effect several approaches for estimating the facilitating score are discussed in particular we put forward a machine learning method called causal inference tree cit to provide a piecewise constant approximation of the facilitating score with interpretable rules cit splits data in such a way that both the propensity and the treatment effect become more homogeneous within each resultant partition causal inference at different levels can be made on the basis of cit together with an aggregated grouping procedure cit stratifies data into strata where causal effects can be conveniently assessed within each besides a feasible way of predicting individual causal effects ice is made available by aggregating ensemble cit models both the stratified results and the estimated ice provide an assessment of heterogeneity of causal effects and can be integrated for estimating the average causal effect ace mean square consistency of cit is also established we evaluate the performance of proposed methods with simulations and illustrate their use with the nsw data in dehejia and wahba 1999 where the objective is to assess the impact of a labor training program the national supportedwork nsw demonstration on post intervention earnings

new g formula for the sequential causal effect and blip effect of treatment in sequential causal inference in sequential causal inference two types of causal effects are of practical interest namely the causal effect of the treatment regime called the sequential causal effect and the blip effect of

demuskin fields with valuations we study the arithmetic structure of fields f of characteristic neq p containing a primitive pth root of unity for which the maximal pro p galois group of f is a finitely generated demuskin group

a gtd based parametric model for radar scattering this paper presents a new approach to scattering center extraction based on a scattering model derived from the geometrical theory of diffraction gtd for stepped frequency measurements at high frequencies the model is better matched to the physical scattering process than the damped exponential model and conventional fourier analysis in addition to determining downrange distance energy and polarization the gtd based model extracts frequency dependent scattering information allowing partial identification of scattering center geometry we derive expressions for the cramer rao bound of this model using these expressions we analyze the behavior of the new model as a function of scatterer separation bandwidth number of data points and noise level additionally a maximum likelihood algorithm is developed for estimation of the model parameters we present estimation results using data measured on a compact range to validate the proposed modeling procedure

causal inference without counterfactuals abstract a popular approach to the framing and answering of causal questions relies on the idea of counterfactuals outcomes that would have been observed had the world developed differently for example if the patient had received a different treatment by definition one can never observe such quantities nor assess empirically the validity of any modeling assumptions made about them even though one s conclusions may be sensitive to these assumptions here i argue that for making inference about the likely effects of applied causes counterfactual arguments are unnecessary and potentially misleading an alternative approach based on bayesian decision analysis is presented properties of counterfactuals are relevant to inference about the likely causes of observed effects but close attention then must be given to the nature and context of the query as well as to what conclusions can and cannot be supported empirically in particular even in the absence of statistical uncertainty such inferences m

demuskin groups galois modules and the elementary type conjecture abstract let p be a prime and f p the maximal p extension of a field f containing a primitive pth root of unity we give a new characterization of demuskin groups among galois groups gal f p f when p 2 and assuming the elementary type conjecture when p 2 as well this characterization is in terms of the structure as galois modules of the galois cohomology of index p subgroups of gal f p f

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

a recursive description of pro p galois groups abstract in this note we study a modified version of the elementary type conjecture for pro p galois groups to be precise let g p f be the galois group of the maximal galois p extension of a field f containing a primitive p th root of unity under some natural assumptions concerning valuation rings of f and also orderings of f when p 2 we prove that g p f can be obtained from suitable closed subgroups using a finite number of free pro p products and semidirect products

causal inference using potential outcomes design modeling decisions causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units observed values of the potential outcomes are revealed by the assignment mechanism a probabilistic model for the treatment each unit receives as a function of covariates and potential outcomes fisher made tremendous contributions to causal inference through his work on the design of randomized experiments but the potential outcomes perspective applies to other complex experiments and nonrandomized studies as well as noted by kempthorne in his 1976 discussion of savage s fisher lecture fisher never bridged his work on experimental design and his work on parametric modeling a bridge that appears nearly automatic with an appropriate view of the potential outcomes framework where the potential outcomes and covariates are given a bayesian distribution to complete the model specification also this framework crisply separates scientific inference for causal effects and decisions based on s

bias in estimating the causal hazard ratio when using two stage instrumental variable methods two stage instrumental variable methods are commonly used to estimate the causal effects of treatments on survival in the presence of measured and unmeasured confounding two stage residual inclusion 2sri has been the method of choice over two stage predictor substitution 2sps in clinical studies we directly compare the bias in the causal hazard ratio estimated by these two methods under a principal stratification framework we derive a closed form solution for asymptotic bias of the causal hazard ratio among compliers for both the 2sps and 2sri methods when survival time follows the weibull distribution with random censoring when there is no unmeasured confounding and no always takers our analytic results show that 2sri is generally asymptotically unbiased but 2sps is not however when there is substantial unmeasured confounding 2sps performs better than 2sri with respect to bias under certain scenarios we use extensive simulation studies to confirm the analytic results from our closed form solutions we apply these two methods to prostate cancer treatment data from surveillance epidemiology and end results medicare and compare these 2sri and 2sps estimates with results from two published randomized trials copyright 2015 john wiley sons ltd

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

combining an extrapolation technique with the method of moments for solving large scattering problems involving bodies of revolution the purpose of this work is to combine an extrapolation technique with the method of moments mom to solve scattering problems involving large bodies it has been shown in a previous work that the current induced on the smooth parts of large scatterers may be represented as a series of complex exponential functions with a few terms based on this concept a hybrid set of basis functions is constructed using entire domain functions of complex exponential type on the smooth portion of the scatterer complemented by subdomain basis functions near edges and discontinuities an extrapolation procedure is developed in which the scattering problem is first solved for a portion of the scatterer using the conventional mom next a set of entire domain basis functions whose behaviour could be extrapolated with an increase in the size of the scatterer is extracted from this original solution the procedure outlined has the very desirable feature that the total number of basis functions remains unchanged even as the scatterer size is increased allowing for large scatterers to be handled with a relatively small number of unknowns the extrapolation technique is applied to scattering problems from bodies of revolution bors and numerical results for an open cylinder and a barrel shaped bor are presented

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

compensation and amplification of attenuation bias in causal effect estimates covariate adjusted treatment effects are commonly estimated in non randomized studies it has been shown that measurement error in covariates can bias treatment effect estimates when not appropriately accounted for so far these delineations primarily assumed a true data generating model that included just one single covariate it is however more plausible that the true model consists of more than one covariate we evaluate when a further covariate may reduce bias due to measurement error in another covariate and in which cases it is not recommended to include a further covariate we analytically derive the amount of bias related to the fallible covariate s reliability and systematically disentangle bias compensation and amplification due to an additional covariate with a fallible covariate it is not always beneficial to include an additional covariate for adjustment as the additional covariate can extensively increase the bias the mechanisms for an increased bias due to an additional covariate can be complex even in a simple setting of just two covariates a high reliability of the fallible covariate or a high correlation between the covariates cannot in general prevent from substantial bias we show distorting effects of a fallible covariate in an empirical example and discuss adjustment for latent covariates as a possible solution

bayesianly justifiable and relevant frequency calculations for the applied statistician a common reaction among applied statisticians is that the bayesian statistician s energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying bayes s theorem to calculate conditional distributions of unknowns given knowns i feel however that the applied bayesian statistician s tool kit should be more extensive and include tools that may be usefully labeled frequency calculations three types of bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician

doubly robust type estimation for covariate adjustment in latent variable modeling due to the difficulty in achieving a random assignment a quasi experimental or observational study design is frequently used in the behavioral and social sciences if a nonrandom assignment depends on the covariates multiple group structural equation modeling that includes the regression function of the dependent variables on the covariates that determine the assignment can provide reasonable estimates under the condition of correct specification of the regression function however it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large therefore the propensity score adjustment methods have been proposed since they do not require the specification of the regression function and have been applied to several applied studies however these methods produce biased estimates if the assignment mechanism is incorrectly specified in order to make a more robust inference it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology in this study we propose a doubly robust type estimation method for marginal multiple group structural equation modeling this method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified a simulation study indicates that the proposed estimation method is more robust than the existing methods

positive association among three binary variables and cross product ratios we show that when the three way association level among the three binary variables x u 1 and u 2 is fixed dp pr x 1 u 1 1 pr x 11 u 1 0 increases as the cross product ratio of u 1 and u 2 increases under the assumption that x is positively associated with u 1 and u 2 we then discuss some implications of this property

on the optimal sampling strategy for model based parameter estimation using rational functions we investigate several sampling strategies in performing model based parameter estimation based on the rational function model they are i uniform like sampling ii random sampling and iii sampling based on the fisher information theory the sampling strategies are implemented for the calculation of the input impedance of an antenna over a broad frequency range the model parameters of the rational functions are found by the cauchy method the results are evaluated against the optimal sampling solution obtained by a genetic algorithm search

modeling partial compliance through copulas in a principal stratification framework within the principal stratification framework for causal inference modeling partial compliance is challenging because the continuous nature of the principal strata raises subtle specification issues in this context we propose an approach based on the assumption that the joint distribution of the degree of compliance to the treatment and the degree of compliance to the control follows a plackett copula so that their association is modeled in a flexible way through a single parameter moreover given the two compliances the distribution of the outcomes is parameterized in a flexible way through a regression model which may include interaction and quadratic terms and may also be heteroscedastic in order to estimate the parameters of the resulting model and then the causal effect of the treatment we adopt a maximum likelihood approach via the em algorithm in applying this approach the marginal distributions of the two compliances are estimated by their empirical distribution functions so that no co

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

efficient radar signature prediction using a frequency aspect interpolation technique based on adaptive feature extraction a radar cross section rcs interpolation technique in both frequency and aspect is proposed for the efficient prediction of radar signatures from computational electromagnetics data our approach is based on a multiple arrival model for the induced current on the target the model parameters are determined by an adaptive feature extraction afe algorithm which uses an iterative search and extract procedure to find the individual model features random frequency and aspect sampling is used to circumvent the ambiguity in selecting the features numerical examples are presented to test the interpolation algorithm it is found that sufficient accuracy in the predicted radar features can be achieved even when the original computed data is sampled at 5 1 below the nyquist criterion in either frequency or aspect the algorithm is also applied to efficiently predict the radar images of the benchmark vfy218 airplane at uhf band with good results