Causal Bayesian networks via probability trees

1 Connection to Pearlian structural causal models

The relationship to Structural Causal Models (SCMs) is

• Graphical representation: Like Judea Pearl’s DAG-based SCMs, probability trees encode causal dependencies through directed structures, though trees explicitly model sequential decision points rather than general networks.
• Interventional logic: Both frameworks support counterfactual reasoning, but probability trees implement interventions through branch modifications (e.g., fixing node values) rather than graph surgery via Pearl’s do-operator.

The tree structure imposes natural identifiability through:

1. Temporal ordering of nodes
2. Restricted parent sets at each branching point This avoids needing external tools like do-calculus for many identification problems.

There is a deepmind demonstration notebook (Genewein et al. 2020).

2 Connection to mechanised causal graphs

Another obvious formalism in this domain is mechanised causal graphs.

Once again, I got an LLM to attempt to summarise the relationship between these two formalisms:

Both methodologies: 1. Extend traditional causal models by adding hierarchical elements to Pearlian SCMs 2. Enable policy-aware reasoning about decision-making agents 3. Support intervention analysis through modified graph operations

3 References