On statistical models associated with acyclic directed mixed graphs

Add to your list(s) Download to your calendar using vCal

• Qingyuan Zhao (Statistical Laboratory)
• Friday 01 November 2024, 15:30-17:00
• MR12, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Martina Scauda.

Causal models in statistics are often described by acyclic directed mixed graphs (ADMGs), which contain directed and bidirected edges and no directed cycles. This article surveys various interpretations of ADM Gs, discusses their relations in different sub-classes of ADM Gs, and argues that one of them—nonparametric equation system (the E model below)—should be used as the default interpretation. The E model is closely related to but different from the interpretation of ADM Gs as directed acyclic graphs (DAGs) with latent variables that is commonly found in the literature. Our endorsement of the E model is based on two observations. First, in a subclass of ADM Gs called unconfounded graphs (which retain most of the good properties of directed acyclic graphs and bidirected graphs), the E model is equivalent to many other interpretations including the global Markov and nested Markov models. Second, the E model for an arbitrary ADMG is exactly the union of that for all unconfounded expansions of that graph. This property is referred to as completeness, as it shows that the model does not commit to any specific latent variable explanation. In proving that the E model is nested Markov, we also develop an ADMG -based theory for causality that may be of independent interest.

Preprint available at: https://www.statslab.cam.ac.uk/~qz280/publication/admg-model/paper.pdf

This talk is part of the Causal Inference Reading Group series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• Causal Inference Reading Group
• DPMMS Lists
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR12, Centre for Mathematical Sciences, Wilberforce Road, Cambridge
• School of Physical Sciences
• Statistical Laboratory info aggregator
• bld31

Note that ex-directory lists are not shown.