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Among Judea Pearls many contributions to Causality and Statistics, the graphical d-separation} criterion, the do-calculus and the mediation formula stand out. In this chapter we show that d-separation} provides direct insight into an earlier causal model originally described in terms of potential outcomes and event trees. In turn, the resulting synthesis leads to a simplification of the do-calculus that clarifies and separates the underlying concepts, and a simple counterfactual formulation of a complete identification algorithm in causal models with hidden variables.
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional independence b
Modern RNA sequencing technologies provide gene expression measurements from single cells that promise refined insights on regulatory relationships among genes. Directed graphical models are well-suited to explore such (cause-effect) relationships. H
A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the systems response under interventions. The class of structural causal models provides a language that allows us to model the beh
We consider modeling, inference, and computation for analyzing multivariate binary data. We propose a new model that consists of a low dimensional latent variable component and a sparse graphical component. Our study is motivated by analysis of item
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious