PreprintCC BY 4.0arXiv
Backtracking Direct, Indirect and Total Effects
Abstract
Natural direct and indirect effects are defined through cross-world interventional counterfactuals. We propose an alternative construction based on backtracking counterfactuals. Rather than intervening on the treatment or mediator, we use a backtracking conditional distribution to construct an alternative exogenous state satisfying a desired treatment-mediator constraint. This yields the backtracking direct and indirect effects, and also the backtracking total effect. Likewise, we adapt the population intervention effects.
Related
- Direct and Indirect Competition in a Two-Prey-One-Predator System : Global Dynamics, Chaos, and the Paine Conjecture
- Direct and Indirect Physics-Informed Neural Networks for Dirichlet Boundary Control of Semilinear Parabolic Equations: A Conditional Error Analysis
- Direct and indirect impacts of COVID-19 vaccination in Slovenia in 2021: a retrospective modelling study
- Direct and indirect operator learning strategies for parametric optimal control problems
- Non-backtracking Laplacian for hypergraphs
BibTeX
@misc{pena2026backtracking,
title = {{Backtracking Direct, Indirect and Total Effects}},
author = {Jose M. Peña},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28910},
eprint = {2610.28910},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28910},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Backtracking Direct, Indirect and Total Effects
AU - Jose M. Peña
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28910
UR - https://arxiv.org/abs/2610.28910
AB - Natural direct and indirect effects are defined through cross-world interventional counterfactuals. We propose an alternative construction based on backtracking counterfactuals. Rather than intervening on the treatment or mediator, we use a backtracking conditional distribution to construct an alternative exogenous state satisfying a desired treatment-mediator constraint. This yields the backtracking direct and indirect effects, and also the backtracking total effect. Likewise, we adapt the population intervention effects.
ER -