reliability evaluation of bc networks reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems extra connectivity determination and faulty networks structure analysis are two important aspects for the reliability evaluation of interconnection networks an n dimensional bijective connection network in brief bc network denoted by xn is an n regular graph with 2n vertices and n2n 1 edges the hypercubes mobius cubes crossed cubes and twisted cubes are some examples of the bc networks by exploring the boundary problem of the bc networks we prove that when n 4 and 0 h n 4 the h extra connectivity of an n dimensional bc network xn is kh xn n h 1 1 2h h 3 furthermore there exists a large connected component and the remaining small components have at most h vertices in total if the total number of faulty vertices is strictly less its h extra connectivity as an application the results on the h extra connectivity and structure of faulty networks on hypercubes mobius cubes crossed cubes and twisted cubes are obtained

a characterization of markov equivalence classes for acyclic digraphs undirected graphs and acyclic digraphs adgs as well as their mutual extension to chain graphs are widely used to describe dependencies among variables in multivariate distributions in particular the likelihood functions of adg models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building bayesian networks for expert systems whereas the undirected graph associated with a dependence model is uniquely determined there may however be many adgs that determine the same dependence markov model thus the family of all adgs with a given set of vertices is naturally partitioned into markov equivalence classes each class being associated with a unique statistical model statistical procedures such as model selection or model averaging that fail to take into account these equivalence classes may incur substantial computational or other inefficiencies here it is shown that each markov equivalence class is uniquely determined by a single chain graph the essential graph that is itself simultaneously markov equivalent to all adgs in the equivalence class essential graphs are characterized a polynomial time algorithm for their construction is given and their applications to model selection and other statistical questions are described

propagation of probabilities means and variances in mixed graphical association models abstract a scheme is presented for modeling and local computation of exact probabilities means and variances for mixed qualitative and quantitative variables the models assume that the conditional distribution of the quantitative variables given the qualitative is multivariate gaussian the computational architecture is set up by forming a tree of belief universes and the calculations are then performed by local message passing between universes the asymmetry between the quantitative and qualitative variables sets some additional limitations for the specification and propagation structure approximate methods when these are not appropriately fulfilled are sketched it has earlier been shown how to exploit the local structure in the specification of a discrete probability model for fast and efficient computation thereby paving the way for exploiting probability based models as parts of realistic systems for planning and decision support the purpose of this article is to extend this computational s

distance between populations using mixed continuous and categorical variables summary a general form of the location model is considered for mixed continuous and categorical variables observed in a number of different populations and some special cases of practical interest are cited the distance between any two populations is derived for each of these models estimation of parameters in these distance measures is discussed and the methods are illustrated by application to previously published data

chain graph models and their causal interpretations chain graphs are a natural generalization of directed acyclic graphs and undirected graphs however the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent there are many simple and apparently plausible but ultimately fallacious interpretations of chain graphs that are often invoked implicitly or explicitly these interpretations also lead to flawed methods for applying background knowledge to model selection we present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from the equilibrium distributions of dynamic models with feed back these dynamic interpretations lead to a simple theory of intervention extending the theory developed for directed acyclic graphs finally we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feed back in econometrics

characterizing markov equivalence classes for amp chain graph models chain graphs cg adicyclic graphs use undirected and directed edges to represent both structural and associative dependences like acyclic directed graphs adgs the cg associated with a statistical markov model may not be unique so cgs fall into markov equivalence classes which may be superexponentially large leading to unidentifiability and computational inefficiency in model search and selection it is shown here that under the andersson madigan perlman amp interpretation of a cg each markov equivalence class can be uniquely represented by a single distinguished cg the amp essential graph that is itself simultaneously markov equivalent to all cgs in the amp markov equivalence class a complete characterization of amp essential graphs is obtained like the essential graph previously introduced for adgs the amp essential graph will play a fundamental role for inference and model search and selection for amp cg models

the t k diagnosability of the bc graphs processor fault diagnosis takes an important role in fault tolerant computing on multiprocessor systems there are two classical diagnosis strategies the precise strategy and the pessimistic strategy both of which are based on the well known pmc diagnostic model nevertheless the degree of diagnosability of the system is limited under these two strategies a better method called the t k diagnosis strategy is proposed by somani and peleg in which the identified fault set is allowed to contain at most k fault free processors using this diagnosis strategy the degree of diagnosability of the hypercube increases greatly as the number of the fault free processors in the fault set increases we study the t k diagnosability of so called bc graphs that include hypercubes crossed cubes mobius cubes and twisted cubes etc we show that any n dimensional bc graph is t n k k diagnosable when n spl ges 4 and 0 spl les k spl les n where t n k k 1 n 1 2 k 1 k 2 1 therefore the crossed cube the mobius cube and the twisted cube all have the same t k diagnosability as the hypercube as a result the algorithms developed for diagnosis on the hypercube may also be used to diagnose multiprocessor systems whose network topologies are based on bc graphs

edge pancyclicity and path embeddability of bijective connection graphs an n dimensional bijective connection graph in brief bc graph is a regular graph with 2 n nodes and n2 n 1 edges the n dimensional hypercube crossed cube mobius cube etc are some examples of the n dimensional bc graphs in this paper we propose a general method to study the edge pancyclicity and path embeddability of the bc graphs first we prove that a path of length l with dist x n x y 2 y in x n where x n n 4 is a n dimensional bc graph satisfying the three specific conditions and v x n is the node set of x n furthermore by this result we can claim that x n is edge pancyclic lastly we show that these results can be applied to not only crossed cubes and mobius cubes but also other bc graphs except crossed cubes and mobius cubes so far the research on edge pancyclicity and path embeddability has been limited in some specific interconnection architectures such as crossed cubes mobius cubes

markov properties of nonrecursive causal models this paper aims to solve an often noted incompatibility between graphical chain models which elucidate the conditional independence structure of a set of random variables and simultaneous equations systems which focus on direct linear interactions and correlations between random variables various authors have argued that the incompatibility arises mainly from the fact that in a simultaneous equations system e g a lisrel model reciprocal causality is possible whereas this is not so in the case of graphical chain models in this article it is shown that this view is not correct in fact the definition of the markov property embodied in a graph can be generalized to a wider class of graphs which includes certain nonrecursive graphs the resulting class of reciprocal graph probability models strictly includes the class of chain graph probability models the class of lattice conditional independence probability models is also strictly included it is shown that the resulting methodology is directly applicable to quite general simultaneous equations systems that are subject to mild restrictions only provided some adjustments are made general simultaneous equations systems can be handled as well in all cases consistency with the lisrel methodology is maintained

response models for mixed binary and quantitative variables summary a number of special representations are considered for the joint distribution of qualitative mostly binary and quantitative variables in addition to the conditional gaussian models and to conditional gaussian regression chain models some emphasis is placed on models derived from an underlying multivariate normal distribution and on models in which discrete probabilities are specified linearly in terms of unknown parameters the possibilities for choosing between the models empirically are examined as well as the testing of independence and conditional independence and the estimation of parameters often the testing of independence is exactly or nearly the same for a number of different models

marginalization and conditioning for lwf chain graphs supported by grant fa9550 12 1 0392 from the u s air force office of scientific research afosr and the defense advanced research projects agency darpa

marginalization and collapsibility in graphical interaction models the behaviour of a graphical interaction model under marginalization is discussed a graphical interaction model is called collapsible onto a set of variables if the class of marginal distributions is the same as that implied by the related subgraph the necessary and sufficient condition for collapsibility is found and it is shown that collapsibility is equivalent to a range of other important statistical properties of the model

ideal parent structure learning for continuous variable bayesian networks bayesian networks in general and continuous variable networks in particular have become increasingly popular in recent years largely due to advances in methods that facilitate automatic learning from data yet despite these advances the key task of learning the structure of such models remains a computationally intensive procedure which limits most applications to parameter learning this problem is even more acute when learning networks in the presence of missing values or hidden variables a scenario that is part of many real life problems in this work we present a general method for speeding structure search for continuous variable networks with common parametric distributions we efficiently evaluate the approximate merit of candidate structure modifications and apply time consuming exact computations only to the most promising ones thereby achieving significant improvement in the running time of the search algorithm our method also naturally and efficiently facilitates the addition of useful new hidden variables into the network structure a task that is typically considered both conceptually difficult and computationally prohibitive we demonstrate our method on synthetic and real life data sets both for learning structure on fully and partially observable data and for introducing new hidden variables during structure search

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

fault free hamiltonian cycles in crossed cubes with conditional link faults the crossed cube which is a variation of the hypercube possesses some properties superior to the hypercube in this paper assuming that each node is incident with at least two fault free links we show that an n dimensional crossed cube contains a fault free hamiltonian cycle even if there are up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated we also verify that the assumption is practically meaningful by evaluating its occurrence probability which is very close to 1

possibility theory conditional independence the subtle notion of conditioning is controversial in several contexts for example in possibility theory where in fact different definitions have been introduced we refer to a general axiomatic definition of conditional possibility and then we deal with partial assessments on not necessarily structured domains containing only elements of interest we study a notion of coherence which assures the extendability of an assessment as a conditional possibility and we introduce a procedure for checking coherence moreover we propose a definition of independence for conditional possibility which avoids some counterintuitive situations and we study its main properties in order to compare it with other definitions introduced in literature then we check which properties among the graphoid ones are satisfied this allows to compare our definition with other independence notions given in the context of other uncertainty formalisms this analysis is relevant for graphical models in order to single out and visualize dependence relations among random variables

hierarchical interaction models lauritzen and wermuth have proposed a class of models for mixed qualitative and continuous data defined by two properties that the continuous variables are normally distributed given the qualitative variables and that a set of conditional independence relations hold between specified pairs of variables the present paper examines an extension to this class called hierarchical interaction models a compact form for model representation is described and an estimation algorithm is given some properties of the models a compact form for model representation is described and an estimation algorithm is given some properties of the models concerning marginalization and conditioning are examined the class includes and generalizes hierarchical log linear models standard fixed effect anova multivariate anova and multivariate regression models

the t k diagnosability for regular networks the t k diagnosis strategy can significantly enhance the system s self diagnosing capability at the expense of no more than k fault free processors vertices being mistakenly diagnosed as faulty under the pmc model it is a generalization of the precise and pessimistic diagnosis strategies of system level diagnosis on multiprocessor systems it can detect up to t faulty processors vertices which might include at most k misdiagnosed processors vertices where k is typically a small number in the case k ge 1 to our knowledge there is no known t k diagnosis algorithm for general regular networks in this paper we first propose a general t k diagnosis k ge 1 algorithm for some m regular networks these m regular networks satisfying some conditions could establish the t k diagnosis algorithm say t k g diag to determine the t k diagnosability the complexity of this algorithm is only o n log n when n ge 2 m or o nm when n where n is the number of vertices in the network second we present a complete proof that the network g is actually t k diagnosable finally we establish the t k diagnosability 1 le k le 3 of some regular networks including an n dimensional alternating group graph an n dimensional split star network a l n hypermesh and an n l star graph which are well known interconnection networks proposed for multiprocessor systems

simple linear time algorithms to test chordality of graphs test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs chordal graphs arise naturally in the study of gaussian elimination on sparse symmetric matrices acyclic hypergraphs arise in the study of relational data bases rose tarjan and lueker siam j c

the extra connectivity extra conditional diagnosability and t k diagnosability of the data center network dcell abstract connectivity and diagnosability are two important metrics in evaluating the fault tolerability of a network the g extra connectivity and the g extra conditional diagnosability are both defined under the restraint that every component of the network removing a faulty vertex set has at least g 1 fault free vertices the t k diagnosability is an outstanding diagnosis strategy in which the identified faulty vertex set is allowed to contain at most k fault free vertices as a well known model for a large scale data center network dcn with a server centric structure the m dimensional dcell with n port switches and t m n servers d m n has many desirable properties in this paper we first investigate the g extra connectivity of d m n for 0 g n 1 based on this we establish the g extra conditional diagnosability of d m n under the pmc model for 0 g n 1 finally we evaluate the t k diagnosability of d m n under the pmc model for 1 k n 1

graphical regression models for polytomous variables when modeling the relationship between two nominal categorical variables it is often desirable to include covariates to understand how individuals differ in their response behavior typically however not all the relevant covariates are available with the result that the measured variables cannot fully account for the associations between the nominal variables under the assumption that the observed and unobserved variables follow a homogeneous conditional gaussian distribution this paper proposesrc m regression models to decompose the residual associations between the polytomous variables based on goodman s 1979 1985 rc m association model a distinctive feature ofrc m regression models is that they facilitate the joint estimation of effects due to manifest and omitted continuous variables without requiring numerical integration therc m regression models are illustrated using data from the high school and beyond study tatsuoka lohnes 1988

regression models for a bivariate discrete and continuous outcome with clustering abstract developmental toxicity studies of laboratory animals play a crucial role in the testing and regulation of chemicals and pharmaceutical compounds exposure to developmental toxicants typically causes a variety of adverse effects such as fetal malformations and reduced fetal weight at term in this article we discuss regression methods for jointly analyzing bivariate discrete and continuous outcomes that are motivated by the statistical problems that arise in analyzing data from developmental toxicity studies we focus on marginal regression models that is models in which the marginal expectation of the bivariate response vector is related to a set of covariates by some known link functions in these models the regression parameters for the marginal expectation are of primary scientific interest whereas the association between the binary and continuous response is considered to be a nuisance characteristic of the data we describe a likelihood based approach based on the general location mode

an algorithm for reading dependencies from the minimal undirected independence map of a graphoid that satisfies weak transitivity we present a sound and complete graphical criterion for reading dependencies from the minimal undirected independence map g of a graphoid m that satisfies weak transitivity here complete means that it is able to read all the dependencies in m that can be derived by applying the graphoid properties and weak transitivity to the dependencies used in the construction of g and the independencies obtained from g by vertex separation we argue that assuming weak transitivity is not too restrictive as an intermediate step in the derivation of the graphical criterion we prove that for any undirected graph g there exists a strictly positive discrete probability distribution with the prescribed sample spaces that is faithful to g we also report an algorithm that implements the graphical criterion and whose running time is considered to be at most o n2 e n for n nodes and e edges finally we illustrate how the graphical criterion can be used within bioinformatics to identify biologically meaningful gene dependencies

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

dag representation of asymmetric independence models arising in coherent conditional possibility theory in this paper we study the representation by means of an acyclic directed graph dag of the independence model induced by a coherent t conditional possibility where t stands for the minimum or a strict t norm such models are in general not closed under symmetric property so we must rely on a proper asymmetric notion of vertex separation which produces structures closed under all graphoid properties and their reverses except for symmetry namely asymmetric graphoids focusing on this kind of models we present an efficient procedure to generate and represent them symbolically we then introduce asymmetric markov properties and prove their equivalence providing in this way a method to extract the model encoded in a dag finally an algorithm to build a minimal i map given an ordering of the random variables is drawn

a fast fault identification algorithm for bijective connection graphs using the pmc model diagnosis of reliability is an important topic for interconnection networks under the classical pmc model dahura and masson 5 proposed a polynomial time algorithm with time complexity o n 2 5 to identify all faulty nodes in an n node network this paper addresses the fault diagnosis of so called bijective connection bc graphs including hypercubes twisted cubes locally twisted cubes crossed cubes and mobius cubes utilizing a helpful structure proposed by hsu and tan 20 that was called the extending star by lin et al 24 and noting the existence of a structured hamiltonian path within any bc graph we present a fast diagnostic algorithm to identify all faulty nodes in o n time where n 2 n n 4 stands for the total number of nodes in the n dimensional bc graph as a result this algorithm is significantly superior to dahura masson s algorithm when applied to bc graphs

brief paper algebraic and topological aspects of the regulator problem for lumped linear systems the regulator problem with robustness is solved for systems modelled by rational transfer matrices a topology for possibly unstable plants is presented a necessary and sufficient condition is derived for the existence of a proper controller which provides internal stability and output regulation throughout an open neighbourhood of the plant a characterization of all such controllers is determined

on diagnosability of large fault sets in regular topology based computer systems the classical diagnosability approach has its limitation when dealing with large fault sets in large multiprocessor systems this is due to limited diagnosability of large multiprocessor systems connected using regular interconnection structures we propose an alternative approach to system diagnosis by allowing a few upper bounded number of units to be diagnosed incorrectly this measure is called t k diagnosability using this new measure it is possible to increase the degree of diagnosability of large system considerably the t k diagnosis guarantees that all the faulty units processors in a system are detected provided the number of faulty units does not exceed t while at most k units are incorrectly diagnosed we provide necessary and sufficient conditions for t k diagnosability and discuss their implication to demonstrate the power of this approach we analyze the diagnosability of large systems connected as hypercube star graph and meshes it is shown that a substantial increase in the degree of diagnosability of these structures is achieved compared with the degree of diagnosability achieved using the classic diagnosability approach at the cost of a comparably small number of incorrectly diagnosed units

a lower bound on the size of k neighborhood in generalized cubes abstract the determination of the minimum size of a k neighborhood i e a neighborhood of a set of k nodes in a given graph is essential in the analysis of diagnosability and fault tolerance of multicomputer systems the generalized cubes include the hypercube and most hypercube variants as special cases in this paper we present a lower bound on the size of a k neighborhood in n dimensional generalized cubes where 2 n 1 k 3 n 2 this lower bound is tight in that it is met by the n dimensional hypercube our result is an extension of two previously known results

joint response graphs and separation induced by triangular systems summary we consider joint probability distributions generated recursively in terms of univariate conditional distributions satisfying conditional independence restrictions the independences are captured by missing edges in a directed graph a matrix form of such a graph called the generating edge matrix is triangular so the distributions that are generated over such graphs are called triangular systems we study consequences of triangular systems after grouping or reordering of the variables for analyses as chain graph models i e for alternative recursive factorizations of the given density using joint conditional distributions for this we introduce families of linear triangular equations which do not require assumptions of distributional form the strength of the associations that are implied by such linear families for chain graph models is derived the edge matrices of chain graphs that are implied by any triangular system are obtained by appropriately transforming the generating edge matrix it is shown how induced independences and dependences can be studied by graphs by edge matrix calculations and via the properties of densities some ways of using the results are illustrated

minimal sufficient causation and directed acyclic graphs notions of minimal sufficient causation are incorporated within the directed acyclic graph causal framework doing so allows for the graphical representation of sufficient causes and minimal sufficient causes on causal directed acyclic graphs while maintaining all of the properties of causal directed acyclic graphs this in turn provides a clear theoretical link between two major conceptualizations of causality one counterfactual based and the other based on a more mechanistic understanding of causation the theory developed can be used to draw conclusions about the sign of the conditional covariances among variables

graphical and recursive models for contingency tables summary we discuss two classes of models for contingency tables graphical and recursive models both of which arise from restrictions that are expressible as conditional independencies of variable pairs the first of these is a subclass of hierarchical log linear models each of its models can be represented by an undirected graph in the second class each model corresponds to a particular kind of a directed graph instead and can be characterized by a nontrivial factorization of the joint distribution in terms of response variables we derive decomposable or multiplicative models as the intersecting class this result has useful consequences for exploratory types of analysis as well as for the model interpretation we can give an aid for detecting well fitting decomposable models in a transformation of the observed contingency table and each decomposable model may be interpreted with the help of an undirected or directed graph

on chain graph models for description of conditional independence structures a chain graph cg is a graph admitting both directed and undirected edges with partially directed cycles forbidden it generalizes both the concept of undirected graph ug and the concept of directed acyclic graph dag a chain graph can be used to describe efficiently the conditional independence structure of a multidimensional discrete probability distribution in the form of a graphoid that is in the form of a list of statements x is independent of y given z obeying a set of five properties axioms an input list of independency statements for every cg is defined and it is shown that the classic moralization criterion for cgs embraces exactly the graphoid closure of the input list a new direct separation criterion for reading independency statements from a cg is introduced and shown to be equivalent to the moralization criterion using this new criterion it is proved that for every cg there exists a strictly positive discrete probability distribution that embodies exactly the independency statements displayed by the graph thus both criteria are shown to be complete and the use of cgs as tools for description of conditional independence structures is justified

h optimal feedback controllers for linear multivariable systems this paper treats the problem of designing for a linear multivariable plant a feedback controller which minimizes the h infty norm of a weighted sensitivity matrix there exists a family of optimal improper feedbacks this family is determined by application of a theory of ball and helton a method for computing optimal feedbacks is described in detail and a numerical example is included it is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices

separation and completeness properties for amp chain graph markov models pearl s well known d separation criterion for an acyclic directed graph adg is a pathwise separation criterion that can be used to efficiently identify all valid conditional independence relations in the markov model determined by the graph this paper introduces p separation a pathwise separation criterion that efficiently identifies all valid conditional independences under the andersson madigan perlman amp alternative markov property for chain graphs adicyclic graphs which include both adgs and undirected graphs as special cases the equivalence of p separation to the augmentation criterion occurring in the amp global markov property is established and p separation is applied to prove completeness of the global markov property for amp chain graph models strong completeness of the amp markov property is established that is the existence of markov perfect distributions that satisfy those and only those conditional independences implied by the amp property equivalently by p separation a linear time algorithm for determining p separation is presented

on the t k diagnosability of bc networks to increase the degree of the diagnosability of a system under system level diagnosis strategies somani and peleg introduced a measure so called t k diagnosis strategy in which the identified fault set is allowed to contain at most k fault free processors using this diagnosis strategy the degree of diagnosability of the bc graphs include hypercubes crossed cubes mobius cubes and twisted cubes etc as the subfamily increases greatly as the number of the fault free processors in the fault set increases for 1 5 and n 1

bayesian network based multiagent system application in e marketplace abstract the concept of e marketplace has been touted through the extensive use of the internet however the task of filtering the potential supplier base in the e marketplace is tedious while evaluating all the necessary qualitative and quantitative decision factors since the buyers have to evaluate and select suppliers by conveying necessary contingent information among potential suppliers a superior structure of a multiagent system is constructed in this study to present the characteristics of the e marketplace the illustrative examples results prevail to show that after communicating among the virtual e marketplace the suppliers did know how to adapt their strategies to accommodate buyers demand on the other hand the buyers also know which supplier is the most appropriate for short term as well as long term

collapsibility and response variables in contingency tables summary various definitions of the collapsibility of a hierarchical log linear model for a multidimensional contingency table are considered and shown to be equivalent necessary and sufficient conditions for collapsibility are found in terms of the generating class it is shown that log linear models are appropriate for tables with response and explanatory variables if and only if they are collapsible onto the explanatory variables some key word8 collapsibility contingency table graphical model interaction graph log linear model response variable s sufficiency shown to be closely related some models have the property that relations between a set of the classifying factors may be studied by examination of the table of marginal totals formed by summing over the remaining factors such models are said to be collapsible onto the given set of factors collapsibility has important consequences for hypothesis testing and model selection and can be useful in data reduction we consider various definitions of collapsibility and show their equivalence furthermore necessary and sufficient conditions for collapsi bility are found in terms of the generating class many tables analysed in practice involve response variables simple examples one of which is given in 3 suffice to show the importance of distinguishing between response and explanatory variables first that inappropriate models may be avoided and second that natural and relevant models that are not log linear may be considered this paper characterizes appropriate and inappropriate log linear models for tables with response variables and some alternative approaches for the analysis of such tables are briefly considered we consider a multidimensional contingency table n based on a set of classifying factors f for a given subset a of f we are interested in the table of marginal totals na that is to say the table of cell counts summed over the remaining factors ac that is the complement of a in f we identify a hierarchical log linear model l that is the set of probabilities p e l with its generating class whose elements generators are given in square brackets thus for example the model ab bcd for a 4 way table corresponds

maximum likelihood estimation for mixed continuous and categorical data with missing values summary maximum likelihood procedures for analysing mixed continuous and categorical data with missing values are presented the general location model of olkin tate 1961 and extensions introduced by krzanowski 1980 1982 form the basis for our methods maximum likelihood estimation with incomplete data is achieved by an application of the em algorithm dempster laird rubin 1977 special cases of the algorithm include orchard woodbury s 1972 algorithm for incomplete normal samples fuchs s 1982 algorithms for log linear modelling of partially classified contingency tables and day s 1969 algorithm for multivariate normal mixtures applications include a imputation of missing values b logistic regression and discriminant analysis with missing predictors and unclassified observations c linear regression with missing continuous and categorical predictors and d parametric cluster analysis with incomplete data methods are illustrated using data from the st louis risk research project some key word8 cluster analysis discriminant analysis em algorithm incomplete data linear regression logistic regression log linear model mixture model

efficient unicast in bijective connection networks with the restricted faulty node set the connectivity is an important criteria to measure the fault tolerant performance of a graph however the connectivity based on the condition of the set of arbitrary faulty nodes is generally lower in this paper in order to heighten this measure we introduce the restricted connectivity into bijective connection networks first we prove that the probability that all the neighbors of an arbitrary node becomes faulty in any n dimensional bijective connection network x n is very low when n becomes sufficient large then we give a constructive proof that under the condition that each node of an n dimensional bijective connection network x n has at least one fault free neighbor its restricted connectivity is 2n 2 about half of the connectivity of x n finally by our constructive proof we give an o n algorithm to get a reliable path of length at most n 3 log 2 f 1 between any two fault free nodes in an n dimensional bijective connection network in particular since the family of bc networks contains hypercubes crossed cubes mobius cubes etc our algorithm is appropriate for these cubes

the g extra connectivity and diagnosability of crossed cubes abstract connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network g in 1996 fabrega and fiol proposed the g extra connectivity of g in 2016 zhang et al proposed the g extra diagnosability of g that requires every component of g s has at least g 1 vertices the g extra connectivity of g is necessary for g extra diagnosability of g in this paper we show that the g extra connectivity of the crossed cube cq n is n g 1 1 2 g g 3 for n 5 0 g n 2 and the g extra diagnosability of cq n is n 1 2 g g 1 under the pmc model for n 5 0 g n 2 and the mm model for n 7 0 g n 2

ancestral graph markov models this paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all dag independence models this class of graphs called maximal ancestral graphs has two attractive features there is at most one edge between each pair of vertices every missing edge corresponds to an independence relation these features lead to a simple parameterization of the corresponding set of distributions in the gaussian case

gaussian markov distributions over finite graphs on s interesse aux modeles de selection de covariance introduites par dempster 1972 et etudies par wermuth 1976

an efficient fault tolerant routing algorithm in bijective connection networks with restricted faulty edges in this paper we study fault tolerant routing in bijective connection networks with restricted faulty edges first we prove that the probability that all the incident edges of an arbitrary node become faulty in an n dimensional bijective connection network denoted by x n is extremely low when n becomes sufficient large then we give an o n algorithm to find a fault free path of length at most email protected log 2 f 1 between any two different nodes in x n if each node of x n has at least one fault free incident edge and the number of faulty edges is not more than 2n 3 in fact we also for the first time provide an upper bound of the fault diameter of all the bijective connection networks with the restricted faulty edges since the family of bc networks contains hypercubes crossed cubes mobius cubes etc all the results are appropriate for these cubes

on substantive research hypotheses conditional independence graphs and graphical chain models summary graphs consisting of points and lines or arrows as connections between selected pairs of points are used to formulate hypotheses about relations between variables points stand for variables connections represent associations when a missing connection is interpreted as a conditional independence the graph characterizes a conditional independence structure as well statistical models called graphical chain models correspond to special types of graphs which are interpreted in this fashion examples are used to illustrate how conditional independences are reflected in summary statistics derived from the models and how the graphs help to identify analogies and equivalences between different models graphical chain models are shown to provide a unifying concept for many statistical techniques that in the past have proven to be useful in analyses of data they also provide tools for new types of analysis

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

an approximation to maximum likelihood estimates in reduced models summary an approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model i e a model with additional parameters the approximation is close provided that the data are consistent with the first model applications are described to log linear models for discrete data to models for multivariate normal distributions with special covariance matrices and to mixed discrete continuous models

improved likelihood ratio statistics for covariance selection models summary the expected value of the likelihood ratio statistic for covariance selection models when this statistic has a closed form is derived correct to terms of order n 2 n being the sample size then a bartlett type correction factor is available for such statistics by simulation the practical use of such a correction factor is illustrated and is compared with an alternative correction factor in a special case the null density of the corrected statistic is also considered

reliability evaluation of bc networks in terms of the extra vertex and edge connectivity reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems the extra connectivity and the extra edge connectivity are two important parameters for the reliability evaluation of interconnection networks the mbi n dimensional bijective connection network in brief bc network includes several well known network models such as hypercubes mobius cubes crossed cubes and twisted cubes in this paper we explore the extra connectivity and the extra edge connectivity of bc networks and discuss the structure of bc networks with many faults we obtain a sharp lower bound of g extra edge connectivity of an mbi n dimensional bc network for n geq 4 and 1 leq g leq 2 n over 2 we also obtain a sharp lower bound of g extra connectivity of an n dimensional bc network for n geq 4 and 1 leq g leq 2 n which improves the result in reliability evaluation of bc networks ieee trans computers doi 10 1109 tc 2012 106 for 1 leq g leq n 3 furthermore we give a remark about exploring the g extra edge connectivity of bc networks for the more general mbi g and we also characterize the structure of bc networks with many faulty nodes or links as an application we obtain several results on the mbi g extra edge connectivity and the structure of faulty networks on hypercubes mobius cubes crossed cubes and twisted cubes

maximum likelihood estimation in graphical models with missing values in this paper we discuss maximum likelihood estimation when some observations are missing in mixed graphical interaction models assuming a conditional gaussian distribution as introduced by lauritzen wermuth 1989 for the saturated case ml estimation with missing values via the em algorithm has been proposed by little schluchter 1985 we expand their results to the special restrictions in graphical models and indicate a more efficient way to compute the e step the main purpose of the paper is to show that for certain missing patterns the computational effort can considerably be reduced

h optimal solutions of robust regulator problem for linear mimo systems the robust regulator problem for linear mimo systems in the frequency domain is considered the stability robustness of the overall system is analysed with respect to additive perturbations in the mathematical model of the plant and a controller that has been designed to solve the regulator problem for the nominal plant po s it is shown that in the special case where the reference signal or the disturbance has a pole at s j k the robustness can be upper bounded by the minimum singular value of po j k this upper bound can be achieved in the case of a stable plant and step reference and disturbance a design procedure for obtaining h optimal solutions is given

propagating imprecise probabilities in bayesian networks abstract often experts are incapable of providing exact probabilities likewise samples on which the probabilities in networks are based must often be small and preliminary in such cases the probabilities in the networks are imprecise the imprecision can be handled by second order probability distributions it is convenient to use beta or dirichlet distributions to express the uncertainty about probabilities the problem of how to propagate point probabilities in a bayesian network now is transformed into the problem of how to propagate dirichlet distributions in bayesian networks it is shown that the propagation of dirichlet distributions in bayesian networks with incomplete data results in a system of probability mixtures of beta binomial and dirichlet distributions approximate first order probabilities and their second order probability density functions are obtained by stochastic simulation a number of properties of the propagation of imprecise probabilities are discussed by the use of examples an important property is that the imprecision of inferences increases rapidly as new premises are added to an argument the imprecision can be used as a pruning criterion in a network to keep the number of variables involved in an inferential argument small thus imprecision may be used as an ockam s razor in bayesian networks