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.

Traditionally, multivariate discrete data are analyzed by means of log-linear models. In this paper we show how an algebraic approach leads naturally to alternative models, parametrized in terms of the moments of the distribution. Moreover we derive a complete characterization of all meaningful transformations of the components and show how transformations affect the moments of a distribution. It turns out that our models provide the necessary formal description of longitudinal data; moreover in the classical case, they can be considered as an analysis tool, complementary to log-linear models. 1 Introduction We start with a given multivariate discrete nominal variable X. Questions of interest about X can be roughly divided into two groups. One group is related to conditional characteristics such as conditional independencies or questions concerning the sign and/or magnitude of log-odds ratios. The other group focuses on marginal characteristics such as marginal independencies or multiv...

We describe a method for aligning multiple unlabeled configurations simultaneously. Specifically, we extend the two-configuration matching approach of Green and Mardia (2006) to the multiple configuration setting. Our approach is based on the introduction of a set of hidden locations underlying the observed configuration points. A Poisson process prior is assigned to these locations, resulting in a simplified formulation of the model. We make use of a structure containing the relevant information on the matches, of which there are different types to take into account. Bayesian inference can be made simultaneously on the matching and the relative transformations between the configurations. We focus on the particular case of rigid-body transformations and Gaussian observation errors. We apply our method to a problem in chemoinformatics: the alignment of steroid molecules. Supplementary materials are available online.

hierarchical models

Likelihood method Profile likelihood function Profile likelihood-based confidence interval Application to repeated categorical dataSIPSlideshow Foulum 7_6_2007b.nb 3

Neurons can transmit information about the characteristics of a stimulus via the spike rate of neurons and via synchronization of the neurons. To describe how ‘synchronous ’ two spike trains are, a variety of association measures can be used. We propose a new measure of synchrony, the conditional synchrony measure, which is the probability of firing together given that at least one of the two neurons is active. Focus is on the specification of a flexible marginal model for multivariate correlated binary data together with a pseudo-likelihood estimation approach, to adequately and directly describe the measures of interest. A joint model must allow different time- and covariatedepending firing rates for each neuron, and must account for the association between them. The association between neurons might depend on covariates as well.