11,692 research outputs found
Concepts and a case study for a flexible class of graphical Markov models
With graphical Markov models, one can investigate complex dependences,
summarize some results of statistical analyses with graphs and use these graphs
to understand implications of well-fitting models. The models have a rich
history and form an area that has been intensively studied and developed in
recent years. We give a brief review of the main concepts and describe in more
detail a flexible subclass of models, called traceable regressions. These are
sequences of joint response regressions for which regression graphs permit one
to trace and thereby understand pathways of dependence. We use these methods to
reanalyze and interpret data from a prospective study of child development, now
known as the Mannheim Study of Children at Risk. The two related primary
features concern cognitive and motor development, at the age of 4.5 and 8 years
of a child. Deficits in these features form a sequence of joint responses.
Several possible risks are assessed at birth of the child and when the child
reached age 3 months and 2 years.Comment: 21 pages, 7 figures, 7 tables; invited, refereed chapter in a boo
Modeling heterogeneity in random graphs through latent space models: a selective review
We present a selective review on probabilistic modeling of heterogeneity in
random graphs. We focus on latent space models and more particularly on
stochastic block models and their extensions that have undergone major
developments in the last five years
Graphical Markov models: overview
We describe how graphical Markov models started to emerge in the last 40
years, based on three essential concepts that had been developed independently
more than a century ago. Sequences of joint or single regressions and their
regression graphs are singled out as being best suited for analyzing
longitudinal data and for tracing developmental pathways. Interpretations are
illustrated using two sets of data and some of the more recent, important
results for sequences of regressions are summarized.Comment: 22 pages, 9 figure
Modeling dependent gene expression
In this paper we propose a Bayesian approach for inference about dependence
of high throughput gene expression. Our goals are to use prior knowledge about
pathways to anchor inference about dependence among genes; to account for this
dependence while making inferences about differences in mean expression across
phenotypes; and to explore differences in the dependence itself across
phenotypes. Useful features of the proposed approach are a model-based
parsimonious representation of expression as an ordinal outcome, a novel and
flexible representation of prior information on the nature of dependencies, and
the use of a coherent probability model over both the structure and strength of
the dependencies of interest. We evaluate our approach through simulations and
in the analysis of data on expression of genes in the Complement and
Coagulation Cascade pathway in ovarian cancer.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS525 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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