GraphicalModels : Table of Contents

• GraphicalModels -- a package for discrete and Gaussian statistical graphical models
• bidirectedEdgesMatrix -- matrix corresponding to the bidirected edges of a bigraph or a mixed graph
• Coefficients -- optional input to choose the base field
• compU -- key in hash table gaussianRingData: component of undirected edges in vertex set of a mixed graph
• compW -- key in hash table gaussianRingData: component of bidirected edges in vertex set of a mixed graph
• conditionalIndependenceIdeal -- ideal of a list of conditional independent statements
• covarianceMatrix -- covariance matrix of a Gaussian graphical model
• directedEdgesMatrix -- matrix corresponding to the directed edges of a digraph or a mixed graph
• discreteVanishingIdeal -- vanishing ideal of a discrete graphical model
• gaussianMatrices -- matrices whose minors generate the Gaussian conditional independence ideal
• gaussianParametrization -- parametrization of the covariance matrix in terms of treks
• gaussianParametrization(...,SimpleTreks=>...) -- optional input for gaussianParametrization
• gaussianRing -- ring of Gaussian correlations on n random variables or a graphical model
• gaussianRing(...,kVariableName=>...) -- symbol used for indeterminates in a ring of Gaussian joint probability distributions
• gaussianRing(...,lVariableName=>...) -- symbol used for indeterminates in a ring of Gaussian joint probability distributions
• gaussianRing(...,pVariableName=>...) -- symbol used for indeterminates in a ring of Gaussian joint probability distributions
• gaussianRing(...,sVariableName=>...) -- symbol used for indeterminates in a ring of Gaussian joint probability distributions
• gaussianRing(Bigraph) -- ring of Gaussian correlations of a graphical model coming from a bigraph
• gaussianRing(Digraph) -- ring of Gaussian correlations of a graphical model coming from a digraph
• gaussianRing(Graph) -- ring of Gaussian correlations of a graphical model coming from an undirected graph
• gaussianRing(MixedGraph) -- ring of Gaussian correlations of a graphical model coming from a mixed graph
• gaussianRing(ZZ) -- ring of Gaussian correlations on n random variables
• gaussianRingData -- hash table with main parameters of a gaussian ring
• gaussianVanishingIdeal -- vanishing ideal of a Gaussian graphical model
• gaussianVanishingIdeal(...,OldVersion=>...) -- optional argument in gaussianVanishingIdeal to use old method for gaussianRings coming from directed graphs
• globalMarkov -- global Markov statements for a graph or a directed graph
• graphType -- class of graph used to generate a gaussian ring
• hiddenMap -- linear map between the ring of a model with one hidden variable and the ring of the corresponding fully observed model
• identifyParameters -- solve the identifiability problem for Gaussian graphical models
• inverseMarginMap -- inverse of the marginMap
• kVar -- key in hash table gaussianRingData: labels of k variables
• kVariableName -- optional input to choose the variable names for concentration matrix in gaussianRing
• localMarkov -- local Markov statements for a graph or a directed graph
• lVar -- key in hash table gaussianRingData: labels of l variables
• lVariableName -- optional input to choose the variable names for the regression matrix
• marginMap -- linear map on joint distributions for discrete random variables replacing marginals for indeterminates
• markovMatrices -- matrices whose minors form the ideal of a list of independence statements
• markovRing -- ring of joint probability distributions on several discrete random variables
• markovRing(...,Coefficients=>...) -- optional input to choose the base field in markovRing or gaussianRing
• markovRing(...,VariableName=>...) -- symbol used for indeterminates in a ring of discrete joint probability distributions
• nn -- key in hash table gaussianRingData: total number of variables
• OldVersion -- optional argument in gaussianVanishingIdeal to use old method for gaussianRings coming from directed graphs
• pairMarkov -- pairwise Markov statements for a graph or a directed graph
• pVar -- key in hash table gaussianRingData: labels of p variables
• pVariableName -- optional input to choose the variable names for the covariance matrix of the error terms
• SimpleTreks -- optional input for gaussianParametrization
• sVar -- key in hash table gaussianRingData: labels of s variables
• sVariableName -- optional input to choose the variable names for the covariance matrix
• trekIdeal -- trek separation ideal of a mixed graph
• trekSeparation -- trek separation statements of a mixed graph
• undirectedEdgesMatrix -- matrix corresponding to the edges of an undirected graph
• VariableName -- optional input to choose indeterminate name in markovRing