Marginalization and Conditioning for LWF Chain Graphs
In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs after marginalization and conditioning for a given CMG or a given LWF CG. We then define and study the class of anterial graphs, which is also stable under marginalization and conditioning and contains LWF CGs, but has a simpler structure than CMGs.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Marginal AMP Chain Graphs
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to so…
Selection biasError AMP Chain Graphs
Any regular Gaussian probability distribution that can be represented by an AMP chain graph (CG) can be expressed as a system of linear equations with correlated errors whose structure depends on the CG. However, the CG …
Selection biasModeling Latent Selection with Structural Causal Models
Selection bias is ubiquitous in real-world data, and can lead to misleading results if not dealt with properly. We introduce a conditioning operation on Structural Causal Models (SCMs) to model latent selection from a ca…
Causal InferenceSelection biasProbabilistic Inference Using Generators - The Statues Algorithm
We present here a new probabilistic inference algorithm that gives exact results in the domain of discrete probability distributions. This algorithm, named the Statues algorithm, calculates the marginal probability distr…
Every LWF and AMP chain graph originates from a set of causal models
This paper aims at justifying LWF and AMP chain graphs by showing that they do not represent arbitrary independence models. Specifically, we show that every chain graph is inclusion optimal wrt the intersection of the in…
Selection bias