I'd like to formalize Hammersley–Clifford theorem which corresponds to Section 11.1.3 in high dimensional statistics.
I'm planning to use a proof technique based on the Möbius function, and to prove the result for both undirected and directed graphical models. When defining graphical models, I intend to use a definition that can also be applied to causal inference, and I'm considering using Patrick Forré's Transitional Conditional Independence as a reference.
I'd like to formalize Hammersley–Clifford theorem which corresponds to Section 11.1.3 in high dimensional statistics.
I'm planning to use a proof technique based on the Möbius function, and to prove the result for both undirected and directed graphical models. When defining graphical models, I intend to use a definition that can also be applied to causal inference, and I'm considering using Patrick Forré's Transitional Conditional Independence as a reference.