Intervening on time derivatives

Area of Science:

• Causal Inference
• Philosophy of Science
• Statistical Modeling

Background:

• Interventionism defines causal influence via correlations under interventions.
• The link between correlated changes and actual causal influence is often unclear.
• Standard interventionist criteria struggle with variables like time derivatives and integrals.

Purpose of the Study:

• To examine the plausibility of interventionism with a case involving velocity and position.
• To identify limitations of current interventionist criteria in specific scenarios.
• To propose a modification to interventionist criteria for improved causal analysis.

Main Methods:

• Analyzing a problem-case with time derivative (velocity) and integral (position) variables.
• Evaluating orthodox interventionist criteria against this case.
• Exploring alternative criteria including stochastic interventions and model restrictions.
• Developing a modified interventionist criterion allowing interventions to affect off-target variables.

Main Results:

• Orthodox interventionist criteria prove inadequate for the velocity-position case without added dependencies.
• Tested alternatives like stochasticity and model restrictions do not resolve the issue.
• A proposed modification allows interventions to influence variables beyond their direct targets.
• This modification, with introduced dependencies, aligns with practical causal analysis.

Conclusions:

• The correspondence between correlated changes and causal influence requires careful handling of intervention dependencies.
• A modified interventionist framework can accommodate complex variable relationships, like those involving derivatives and integrals.
• The proposed modification offers a more robust approach to causal inference in challenging cases.