inference for mixtures of finite polya tree models mixtures of polya tree models provide a flexible alternative when a parametric model may only hold approximately i provide computational strategies for obtaining full semiparametric inference for mixtures of finite polya tree models given a standard parameterization including models that would be troublesome to fit using dirichlet process mixtures recommendations are put forth on choosing the level of a finite polya tree and model comparison is discussed several examples demonstrate the utility of finite polya tree modeling including data fit to generalized linear mixed models and several survival models

marginal likelihood from the metropolis hastings output this article provides a framework for estimating the marginal likelihood for the purpose of bayesian model comparisons the approach extends and completes the method presented in chib 1995 by overcoming the problems associated with the presence of intractable full conditional densities the proposed method is developed in the context of mcmc chains produced by the metropolis hastings algorithm whose building blocks are used both for sampling and marginal likelihood estimation thus economizing on prerun tuning effort and programming experiments involving the logit model for binary data hierarchical random effects model for clustered gaussian data poisson regression model for clustered count data and the multivariate probit model for correlated binary data are used to illustrate the performance and implementation of the method these examples demonstrate that the method is practical and widely applicable

objective bayesian survival analysis using shape mixtures of log normal distributions survival models such as the weibull or log normal lead to inference that is not robust to the presence of outliers they also assume that all heterogeneity between individuals can be modeled through covariates this article considers the use of infinite mixtures of lifetime distributions as a solution for these two issues this can be interpreted as the introduction of a random effect in the survival distribution we introduce the family of shape mixtures of log normal distributions which covers a wide range of density and hazard functions bayesian inference under nonsubjective priors based on the jeffreys rule is examined and conditions for posterior propriety are established the existence of the posterior distribution on the basis of a sample of point observations is not always guaranteed and a solution through set observations is implemented in addition we propose a method for outlier detection based on the mixture structure a simulation study illustrates the performance of our methods under dif

computing bayes factors using a generalization of the savage dickey density ratio abstract we present a simple method for computing bayes factors the method derives from observing that in general a bayes factor can be written as the product of a quantity called the savage dickey density ratio and a correction factor both terms are easily estimated from posterior simulation in some cases it is possible to do these computations without ever evaluating the likelihood

multivariate student t regression models pitfalls and inference we consider likelihood based inference from multivariate regression models with independent student t errors some very intruiging pitfalls of both bayesian and classical methods on the basis of point observations are uncovered bayesian inference may be precluded as a consequence of the coarse nature of the data global maximization of the likelihood function is a vacuous exercise since the likelihood function is unbounded as we tend to the boundary of the parameter space a bayesian analysis on the basis of set observations is proposed and illustrated by several examples

bayesian case influence diagnostics for survival models we propose bayesian case influence diagnostics for complex survival models we develop case deletion influence diagnostics for both the joint and marginal posterior distributions based on the kullback leibler divergence k l divergence we present a simplified expression for computing the k l divergence between the posterior with the full data and the posterior based on single case deletion as well as investigate its relationships to the conditional predictive ordinate all the computations for the proposed diagnostic measures can be easily done using markov chain monte carlo samples from the full data posterior distribution we consider the cox model with a gamma process prior on the cumulative baseline hazard we also present a theoretical relationship between our case deletion diagnostics and diagnostics based on cox s partial likelihood a simulated data example and two real data examples are given to demonstrate the methodology

local model influence abstract this article develops a general method for assessing the influence of model assumptions in a bayesian analysis we assume that model choices are indexed by a hyperparameter with some given initial choice we use the term model to encompass both the sampling model and the prior distribution we wish to assess the effect of changing the hyperparameter away from the initial choice we are performing a sensitivity analysis with the hyperparameter defining our perturbations we use the kullback leibler divergence to measure the difference between posteriors corresponding to different choices of the hyperparameter we also measure the change in priors if small changes in the priors lead to large changes in posteriors the choice of hyperparameter is influential the second order difference in the kullback leibler divergence is expressed by fisher information matrices the relative change in posteriors compared with priors may be summarized by the relative eigenvalue of the posterior and prior fishe

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

linear matrix inequality formulation of spectral mask constraints with applications to fir filter design the design of a finite impulse response fir filter often involves a spectral mask that the magnitude spectrum must satisfy the mask specifies upper and lower bounds at each frequency and hence yields an infinite number of constraints in current practice spectral masks are often approximated by discretization but in this paper we derive a result that allows us to precisely enforce piecewise constant and piecewise trigonometric polynomial masks in a finite and convex manner via linear matrix inequalities while this result is theoretically satisfying in that it allows us to avoid the heuristic approximations involved in discretization techniques it is also of practical interest because it generates competitive design algorithms based on interior point methods for a diverse class of fir filtering and narrowband beamforming problems the examples we provide include the design of standard linear and nonlinear phase fir filters robust chip waveforms for wireless communications and narrowband beamformers for linear antenna arrays our main result also provides a contribution to system theory as it is an extension of the well known positive real and bounded real lemmas

objective bayesian analysis for the student t regression model we develop a bayesian analysis based on two different jeffreys priors for the student t regression model with unknown degrees of freedom it is typically difficult to estimate the number of degrees of freedom improper prior distributions may lead to improper posterior distributions whereas proper prior distributions may dominate the analysis we show that bayesian analysis with either of the two considered jeffreys priors provides a proper posterior distribution finally we show that bayesian estimators based on jeffreys analysis compare favourably to other bayesian estimators based on priors previously proposed in the literature

on the evaluation of argumentation formalisms argumentation theory has become an important topic in the field of ai the basic idea is to construct arguments in favor and against a statement to select the acceptable ones and finally to determine whether the original statement can be accepted or not several argumentation systems have been proposed in the literature some of them the so called rule based systems use a particular logical language with strict and defeasible rules while these systems are useful in different domains e g legal reasoning they unfortunately lead to very unintuitive results as is discussed in this paper in order to avoid such anomalies in this paper we are interested in defining principles called rationality postulates that can be used to judge the quality of a rule based argumentation system in particular we define two important rationality postulates that should be satisfied the consistency and the closure of the results returned by that system we then provide a relatively easy way in which these rationality postulates can be warranted for a particular rule based argumentation system developed within a european project on argumentation

mixtures of exponential distributions arbitrary nonparametric mixtures of exponential and weibull fixed shape distributions are considered as possible models for a lifetime distribution a characterization of such distributions is given by the well known characterization of laplace transforms the maximum likelihood estimate of the mixing distribution is investigated and found to be supported on a finite number of points it is shown to be unique and weakly convergent to the true mixing measure with probability one a practical algorithm for computing the maximum likelihood estimate is described its performance is briefly discussed and some illustrative examples given

far field multicast beamforming for uniform linear antenna arrays the problem of transmit beamforming to multiple cochannel multicast groups is considered for the important special case when the channel vectors are vandermonde this arises when a uniform linear antenna antenna ula array is used at the transmitter under far field line of sight propagation conditions as provisioned in 802 16e and related wireless backhaul scenarios two design approaches are pursued i minimizing the total transmitted power subject to providing at least a prescribed received signal to interference plus noise ratio sinr to each intended receiver and ii maximizing the minimum received sinr under a total transmit power budget whereas these problems have been recently shown to be np hard in general it is proven here that for vandermonde channel vectors it is possible to recast the optimization in terms of the autocorrelation sequences of the sought beam vectors yielding an equivalent convex reformulation this affords efficient optimal solution using modern interior point methods the optimal beam vectors can then be recovered using spectral factorization robust extensions for the case of partial channel state information where the direction of each receiver is known to lie in an interval are also developed interestingly these also admit convex reformulation the various optimal designs are illustrated and contrasted in a suite of pertinent numerical experiments

convex optimization problems involving finite autocorrelation sequences we discuss convex optimization problems in which some of the variables are constrained to be finite autocorrelation sequences problems of this form arise in signal processing and communications and we describe applications in filter design and system identification autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density which results in a set of linear inequalities they can also be cast as linear matrix inequalities via the kalman yakubovich popov lemma the linear matrix inequality formulation is exact and results in convex optimization problems that can be solved using interior point methods for semidefinite programming however it has an important drawback to represent an autocorrelation sequence of length n it requires the introduction of a large number n n 1 2 of auxiliary variables this results in a high computational cost when general purpose semidefinite programming solvers are used we present a more efficient implementation based on duality and on interior point methods for convex problems with generalized linear inequalities

outlier models and prior distributions in bayesian linear regression summary bayesian inference in regression models is considered using heavy tailed error distri butions to accommodate outliers the particular class of distributions that can be con structed as scale mixtures of normal distributions are examined and use is made of them as both error models and prior distributions in bayesian linear modelling includ ing simple regression and more complex hierarchical models with structured priors depending on unknown hyperprior parameters the modelling of outliers in nominally normal linear regression models using alternative error distributions which are heavy tailed relative to the normal provides an automatic means of both detecting and accommodating possibly aberrant observations such realistic models do however often lead to analytically intractable analyses with complex posterior distributions in several dimensions that are difficult to summarize and understand in this paper we consider a special yet rather wide class of heavy tailed unimodal and symmetric error distributions for which the analyses though apparently intractable can be examined in some depth by exploiting certain properties of the assumed error form the distributions concerned are those that can be con structed as scale mixtures of normal distributions in his paper concerning location parameters de finetti 1961 discusses such distributions and suggests the hypothetical interpretation that each observation is taken using an instrument with normal error but each time chosen at random from a collection of instruments of different precisions the distribution of the

multigroup multicast beamformer design for miso ofdm with antenna selection we study the problem of designing transmit beamformers for a multigroup multicasting by considering a multiple input single output orthogonal frequency division multiplexing framework the design objective involves either minimizing the total transmit power for certain guaranteed quality of service or maximizing the minimum achievable rate among the users for a given transmit power budget the problem of interest can be formulated as a nonconvex quadratically constrained quadratic programming qcqp for which the prevailing semidefinite relaxation sdr technique is inefficient for at least two reasons at first the relaxed problem cannot be reformulated as a semidefinite programming second even if the relaxed problem is solved the so called randomization procedure should be used to generate a feasible solution to the original qcqp which is difficult to derive for the considered problem to overcome these shortcomings we adopt successive convex approximation framework to find multicast beamformers directly the proposed method not only avoids the need of randomization search but also incurs less computational complexity compared to an sdr approach in addition we also extend multicasting beamformer design problem with an additional constraint on the number of active elements which is particularly relevant when the number of antennas is larger than that of radio frequency chains numerical results are used to demonstrate the superior performance of our proposed methods over the existing solutions

robust statistical modeling using the t distribution abstract the t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer than normal tails an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems including linear and nonlinear regression robust estimation of the mean and covariance matrix with missing data unbalanced multivariate repeated measures data multivariate modeling of pedigree data and multivariate nonlinear regression the degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference with moderate increases in computational complexity for many models estimation of precision from asymptotic theory and the bootstrap is discussed and graphical methods for checking the appropriateness of the t distribution are presented

bayesian linear regression with skew symmetric error distributions with applications to survival analysis we study bayesian linear regression models with skew symmetric scale mixtures of normal error distributions these kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy tails and asymmetry we propose a general noninformative prior structure for these regression models and show that the corresponding posterior distribution is proper under mild conditions we extend these propriety results to cases where the response variables are censored the latter scenario is of interest in the context of accelerated failure time models which are relevant in survival analysis we present a simulation study that demonstrates good frequentist properties of the posterior credible intervals associated with the proposed priors this study also sheds some light on the trade off between increased model flexibility and the risk of over fitting we illustrate the performance of the proposed models with real data although we focus on models with univariate response variables we also present some extensions to the multivariate case in the supporting information copyright 2016 john wiley sons ltd

optimal and successive approaches to signal design for multiple antenna physical layer multicasting in modern wireless communications systems that send a common information stream called multicasting systems are widely needed for distributing content such as television or radio in this paper the multiple antenna physical layer multicasting channel is considered in which a common message is simultaneously transmitted to multiple single antenna users to achieve the capacity of this multicasting set up the covariance matrix of the transmit signal vector needs to be determined to maximize the smallest maximum achievable rate among all the users in this paper we develop a simple successive algorithm to determine the covariance matrix of the signal vector under the assumption that channel state information csi is perfectly available at the transmitter we first characterize properties of the capacity achieving covariance matrix and derive a closed form expression for the matrix in the two user case we then derive a closed form expression for the rate maximizing beamformer in the case of two users and propose a successive beamforming algorithm that generates the beamforming vector with low computational complexity in the proposed precoding design scheme the covariance matrix is successively constructed by orthogonalizing the subspace spanned by each user s channel vector until the maximum number of recursions which is the same as the minimum of the number of transmit antennas and the number of users is reached the achievable rate of the proposed scheme is compared with the capacity of optimal transmission transmit beamforming antenna subset selection and open loop transmission which does not require csi at the transmitter as the number of users and or antennas grows large it is shown that the average achievable rate of the proposed scheme achieves the same average achievable rate scaling as the true capacity while reducing the computational complexity

randomized algorithms for optimal solutions of double sided qcqp with applications in signal processing quadratically constrained quadratic programming qcqp with double sided constraints has plenty of applications in signal processing as have been addressed in recent years qcqp problems are hard to solve in general and they are typically approached by solving a semidefinite programming sdp relaxation followed by a postprocessing procedure existing postprocessing schemes include gaussian randomization to generate an approximate solution rank reduction procedure the so called purification and some specific rank one matrix decomposition techniques to yield a globally optimal solution in this paper we propose several randomized postprocessing methods to output not an approximate solution but a globally optimal solution for some solvable instances of the double sided qcqp i e instances with a small number of constraints we illustrate their applicability in robust receive beamforming radar optimal code design and broadcast beamforming for multiuser communications as a byproduct we derive an alternative shorter proof for the sturm zhang rank one matrix decomposition theorem

capacity limits of multi antenna multicasting under correlated fading channels physical layer multicasting in wireless networks has been proposed to efficiently send an identical message to multiple users simultaneously in this paper we consider multiple antenna multicasting where the transmitter is equipped with mt antennas and data is transmitted to k single antenna users when the downlink channels are assumed to follow an uncorrelated rayleigh distribution the multicasting capacity scaling for the large k asymptote is known on the other hand the effect of channel spatial correlation on the capacity performance has not been well addressed therefore we investigate the effect of correlation using the channel correlation information at the transmitter using extreme value theory it is shown that signaling using uniformly allocated transmit powers on the spatial channel correlation matrix s eigenvectors with non zero eigenvalues approaches the multicasting capacity for the large k asymptote compared to the performance of uncorrelated fading channels with a constraint on the trace of the spatial correlation matrix it is shown that the channel correlation degrades the performance specifically if the correlation matrix is full rank the asymptotic outage average capacity ratio which is defined as the ratio of the outage average capacities of the correlated fading channel and the uncorrelated fading channel as k goes to infinity is equivalent to the geometric mean of the eigenvalues of the transmit channel correlation matrix of the correlated channel on the other hand if the correlation matrix is not full rank the capacity ratios become zero to assess the value of knowledge of the channel correlation information at the transmitter we compare the asymptotic performances with and without knowledge of the channel correlation information specifically the asymptotic performance improvement due to this correlation knowledge becomes mt m 1 m for the large k asymptote where m is the rank of the transmit channel correlation matrix in addition we discuss the issues of nonidentical transmit channel correlations among the users and correlation between users channels

parallel and distributed methods for constrained nonconvex optimization part ii applications in communications and machine learning in part i of this paper we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex objective function subject to nonconvex constraints based on inner convex approximations this part ii is devoted to the nontrivial application of the framework to the following relevant large scale problems ranging from communications to machine learning 1 generalizations of the rate profile maximization in mimo interference broadcast networks 2 the max min fair multicast multigroup beamforming problem in a multicell environment and 3 a general nonconvex constrained bi criteria formulation for k sparse variable selection in statistical learning the two criteria are a nonconvex loss objective function measuring the fitness of the model to data and the latter is a nonconvex sparsity inducing constraint in the general form of difference of convex dc functions which allows to accomodate in a unified fashion convex and nonconvex surrogates of the ell 0 function the proposed algorithms outperform current state of the art schemes for 1 3 both theoretically and numerically for instance they are the first distributed schemes for the class of problems 1 and 2 and they also lead to subproblems enjoying closed form solutions

marginal likelihood from the gibbs output abstract in the context of bayes estimation via gibbs sampling with or without data augmentation a simple approach is developed for computing the marginal density of the sample data marginal likelihood given parameter draws from the posterior distribution consequently bayes factors for model comparisons can be routinely computed as a by product of the simulation hitherto this calculation has proved extremely challenging our approach exploits the fact that the marginal density can be expressed as the prior times the likelihood function over the posterior density this simple identity holds for any parameter value an estimate of the posterior density is shown to be available if all complete conditional densities used in the gibbs sampler have closed form expressions to improve accuracy the posterior density is estimated at a high density point and the numerical standard error of resulting estimate is derived the ideas are applied to probit regression and finite mixture models

approximation bounds for semidefinite relaxation of max min fair multicast transmit beamforming problem consider a downlink multicast scenario where a base station equipped with multiple antennas wishes to simultaneously broadcast a number of signals to some given groups of users over a common bandwidth the goal of the base station is to select appropriate beamforming vectors so as to maximize the minimum signal to interference plus noise ratio sinr among all users under a power budget constraint since this max min fair transmit beamforming problem is np hard in general a randomized polynomial time approximation approach based on semidefinite relaxation sdr has been proposed recently where excellent performance in both simulated and measured wireless channels has been reported this paper shows that the sdr based approach can provide at least an o 1 m approximation to the optimum solution where m is the total number of users this estimate implies that the sdr solution achieves an sinr that is at most logm o 1 db away from the highest possible value the existence of such a data independent bound certifies the worst case approximation quality of the sdr algorithm for any problem instance and any number of transmit antennas for real valued problems the corresponding approximation ratio is shown to be o 1 m2 while the sinr loss due to sdr approximation is at most 2logm o 1 db

discussion to bayesian measures of model complexity and fit by spiegelhalter d j best n g carlin b p and van der linde a

an abstract argumentation theoretic approach to default reasoning abstract we present an abstract framework for default reasoning which includes theorist default logic logic programming autoepistemic logic non monotonic modal logics and certain instances of circumscription as special cases the framework can be understood as a generalisation of theorist the generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions an assumption can be defeated or attacked if its contrary can be proved possibly with the aid of other conflicting assumptions we show that given such a framework the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions as an extension of a given theory if and only if the set of assumptions is conflict free in the sense that it does not attack itself and it attacks every assumption not in the set we propose a more liberal argumentation theoretic semantics based upon the notion of admissible extension in logic programming we regard a set of assumptions in general as admissible if and only if it is conflict free and defends itself by attacking every set of assumptions which attacks it we identify conditions for the existence of extensions and for the equivalence of different semantics

rank constrained separable semidefinite programming with applications to optimal beamforming consider a downlink communication system where multiantenna base stations transmit independent data streams to decentralized single antenna users over a common frequency band the goal of the base stations is to jointly adjust the beamforming vectors to minimize the transmission powers while ensuring the signal to interference noise ratio requirement of each user within the system at the same time it may be necessary to keep the interference generated on other coexisting systems under a certain tolerable level in addition one may want to include general individual shaping constraints on the beamforming vectors this beamforming problem is a separable homogeneous quadratically constrained quadratic program and it is difficult to solve in general in this paper we give conditions under which strong duality holds and propose efficient algorithms for the optimal beamforming problem first we study rank constrained solutions of general separable semidefinite programs sdps and propose rank reduction procedures to achieve a lower rank solution then we show that the sdp relaxation of three classes of optimal beamforming problem always has a rank one solution which can be obtained by invoking the rank reduction procedures

a logic based theory of deductive arguments abstract we explore a framework for argumentation based on classical logic in which an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item which is a formula we provide some basic definitions for arguments and various kinds of counter arguments defeaters this leads us to the definition of canonical undercuts which we argue are the only defeaters that we need to take into account we then motivate and formalise the notion of argument trees and argument structures which provide a way of exhaustively collating arguments and counter arguments we use argument structures as the basis of our general proposal for argument aggregation there are a number of frameworks for modelling argumentation in logic they incorporate formal representation of individual arguments and techniques for comparing conflicting arguments in these frameworks if there are a number of arguments for and against a particular conclusion an aggregation function determines whether the conclusion is taken to hold we propose a generalisation of these frameworks in particular our new framework makes it possible to define aggregation functions that are sensitive to the number of arguments for or against we compare our framework with a number of other types of argument systems and finally discuss an application in reasoning with structured news reports

on the estimation of long tailed skewed distributions with actuarial applications abstract very long tailed skewed distributions often arise in practice in particular we find that size of loss distributions in casualty insurance are mainly of this type compounding explains why many of these losses have approximate pareto generalized pareto burr and log t distributions an adaptation of the empirical mean residual life function helps the statistician select the correct model to fit in these cases it is then discovered that minimum distance estimates in particular that of cramer von mises and minimum chi square estimates are extremely valuable and easy to use in the case of grouped data two substantial examples are given one involving hurricane losses and the other dealing with malpractice claims

weighted fair multicast multigroup beamforming under per antenna power constraints a multiantenna transmitter that conveys independent sets of common data to distinct groups of users is considered this model is known as physical layer multicasting to multiple cochannel groups in this context the practical constraint of a maximum permitted power level radiated by each antenna is addressed the per antenna power constrained system is optimized in a maximum fairness sense with respect to predetermined quality of service weights in other words the worst scaled user is boosted by maximizing its weighted signal to interference plus noise ratio a detailed solution to tackle the weighted max min fair multigroup multicast problem under per antenna power constraints is therefore derived the implications of the novel constraints are investigated via prominent applications and paradigms what is more robust per antenna constrained multigroup multicast beamforming solutions are proposed finally an extensive performance evaluation quantifies the gains of the proposed algorithm over existing solutions and exhibits its accuracy over per antenna power constrained systems

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea