Results 1  10
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11
Algebraic Algorithms for Sampling from Conditional Distributions
 Annals of Statistics
, 1995
"... We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so a ..."
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Cited by 192 (16 self)
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We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.
On the toric algebra of graphical models
, 2006
"... We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a loglinear model, or other more general exponential models. For decomposable graphical models these conditions are equivalent to a set of con ..."
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Cited by 36 (6 self)
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We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a loglinear model, or other more general exponential models. For decomposable graphical models these conditions are equivalent to a set of conditional independence statements similar to the Hammersley–Clifford theorem; however, we show that for nondecomposable graphical models they are not. We also show that nondecomposable models can have nonrational maximum likelihood estimates. These results are used to give several novel characterizations of decomposable graphical models.
Binary models for marginal independence
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B
, 2005
"... A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a versi ..."
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Cited by 16 (2 self)
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A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. The approach is illustrated on a simple example. Relations to multivariate logistic and dependence ratio models are discussed.
The mode oriented stochastic search (MOSS) algorithm for loglinear models with conjugate priors
, 2008
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HIERARCHICAL MODELS, MARGINAL POLYTOPES, AND LINEAR CODES
"... Abstract. In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with ..."
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Cited by 3 (3 self)
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Abstract. In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them. 1.
Evaluation of PerRecord Identification Risk By Additive Modeling of Interaction for Contingency Table Cell Probabilities
, 2001
"... We propose to fit a Lancastertype additive model of interaction terms for cell probabilities of contingency tables to evaluate the conditional probability of population uniqueness of sample unique records in microdata sets. Moment estimation of the Lancastertype additive model is straightforwar ..."
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Cited by 2 (1 self)
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We propose to fit a Lancastertype additive model of interaction terms for cell probabilities of contingency tables to evaluate the conditional probability of population uniqueness of sample unique records in microdata sets. Moment estimation of the Lancastertype additive model is straightforward and the proposed estimation procedure is intuitively appealing from the viewpoint of disclosure risk assessment.
A conjugate prior for discrete hierarchical loglinear models
, 2009
"... In Bayesian analysis of multiway contingency tables, the selection of a prior distribution for either the loglinear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of conjugate priors for the wide class of discrete hierarchical logl ..."
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Cited by 2 (1 self)
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In Bayesian analysis of multiway contingency tables, the selection of a prior distribution for either the loglinear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of conjugate priors for the wide class of discrete hierarchical loglinear models, which includes the class of graphical models. These priors are defined as the Diaconis–Ylvisaker conjugate priors on the loglinear parameters subject to “baseline constraints” under multinomial sampling. We also derive the induced prior on the cell probabilities and show that the induced prior is a generalization of the hyper Dirichlet prior. We show that this prior has several desirable properties and illustrate its usefulness by identifying the most probable decomposable, graphical and hierarchical loglinear models for a sixway contingency table.
Computing Maximum Likelihood Estimates . . .
"... We develop computational strategies for extended maximum likelihood estimation, as defined in Rinaldo (2006), for general classes of loglinear models of widespred use, under Poisson and productmultinomial sampling schemes. We derive numerically efficient procedures for generating and manipulating ..."
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We develop computational strategies for extended maximum likelihood estimation, as defined in Rinaldo (2006), for general classes of loglinear models of widespred use, under Poisson and productmultinomial sampling schemes. We derive numerically efficient procedures for generating and manipulating design matrices and we propose various algorithms for computing the extended maximum likelihood estimates of the expectations of the cell counts. These algorithms allow to identify the set of estimable cell means for any given observable table and can be used for modifying traditional goodnessoffit tests to accommodate for a nonexistent MLE. We describe and take advantage of the connections between extended maximum likelihood
Computing Maximum Likelihood . . .
, 2006
"... We develop computational strategies for extended maximum likelihood estimation, as defined in Rinaldo (2006), for general classes of loglinear models of widespred use, under Poisson and productmultinomial sampling schemes. We derive numerically efficient procedures for generating and manipulating ..."
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We develop computational strategies for extended maximum likelihood estimation, as defined in Rinaldo (2006), for general classes of loglinear models of widespred use, under Poisson and productmultinomial sampling schemes. We derive numerically efficient procedures for generating and manipulating design matrices and we propose various algorithms for computing the extended maximum likelihood estimates of the expectations of the cell counts. These algorithms allow to identify the set of estimable cell means for any given observable table and can be used for modifying traditional goodnessoffit tests to accommodate for a nonexistent MLE. We describe and take advantage of the connections between extended maximum likelihood
Reviewed by:
, 2010
"... doi: 10.3389/fncom.2010.00016 Higherorder correlations in nonstationary parallel spike trains: statistical modeling and inference ..."
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doi: 10.3389/fncom.2010.00016 Higherorder correlations in nonstationary parallel spike trains: statistical modeling and inference