Interaction Models

Abstract

The articles in this bundle are all associated with the notion of interaction and represent the genesis of the subject of graphical models in its modern form, the origins of these being traceable back to Gibbs [11] and Wright [30] and earlier.Around 1976, Terry was fascinated by the notion of conditional independence, along the lines later published in Dawid [6,7]. In 1976, Terry invited me to Perth and we were running a daily research seminar with the theme of studying similarities and differences between Statistics and Statistical Mechanics. In particular, we wondered what the relations were between notions of interaction as represented in linear models, in multi-dimensional contingency tables, and in stochastic models for particle systems; in addition, the purpose was also to understand what was the relation between these concepts and conditional independence.As we discovered that these were all essentially the same concepts, the similarity being obscured by very different traditions of notation, the term graphical model was coined. Our findings, also obtained in collaboration with John Darroch, were collected in Darroch et al. Of these articles, Darroch et al.[5] rather quickly had a seminal impact and a small community of researchers in the area of graphical models gradually emerged. In a certain sense, the article does not contain much formally new material (if any at all), but for the first time a simple, visual description and interpretation of the class of log-linear models [12,13], which otherwise could seem obscure, was available. The interpretation of a subclass of the models in terms of conditional independence had an immediate intuitive appeal. In addition, the article identified and emphasized models represented by chordal or triangulated graphs as those where estimation

Interactions and computer experiments

“…The analysis of interactions has a long tradition in Statistics. Interaction quantification emerges in the study of contingency tables (e.g., Højsgaard, 2003; Lauritzen, 2012), in the analysis of variance (ANOVA) of multifactor experiments (Gelman, 2005; Landsheer & van den Wittenboer, 2015) and in the design and analysis of computer experiments (Box et al, 2005; Lewis & Dean, 2001; Wang, 2007; Wu, 2015). A full coverage of the subject is outside the reach of this section, limiting the attention to works more closely related to ours.…”

Bayesian inference for latent chain graphs

“…Chain graphs [17,19,35] provide an elegant unifying point of view on Markov and Bayesian networks. These models allow for edges that are both directed and undirected and do not contain any semi-directed cycles.…”