Marginalized Importance Sampling (MIS)

Implementation: crl.estimators.mis.MarginalizedImportanceSamplingEstimator

Assumptions

• Sequential ignorability
• Overlap/positivity
• Markov property

Requires

• TrajectoryDataset with state_space_n

Diagnostics to check

• overlap.support_violations
• ess.ess_ratio

Formula

MIS replaces cumulative importance ratios with marginal state-action ratios computed from counts.

Uncertainty

• Normal-approximation CI by default.
• Bootstrap CI available via bootstrap=True.

Failure modes

• Requires discrete state space; sparse counts can inflate variance.

Minimal example

from crl.estimators.mis import MarginalizedImportanceSamplingEstimator

report = MarginalizedImportanceSamplingEstimator(estimand).estimate(dataset)

References

• Xie et al. (2019)