Observation-Regime-Aware Bayesian Updates for Closed-Loop Scientific Agents

Closed-loop scientific agents that iteratively select experiments and update beliefs must handle outcomes that are not always fully observed. Measurements may fall below instrument detection limits (censored), experiments may be infeasible, or execution may fail. We formalize three observation regimes (full, censored, and absent), each requiring a distinct Bayesian likelihood, connecting this taxonomy to Rubin (1976)’s missing-data classification. In a controlled simulator with discrete hypotheses and Gaussian outcomes, we demonstrate that the most common real- world practice of substituting constants for censored non-detects and applying a standard density likelihood causes iterative Bayesian agents to converge to wrong hypotheses, not merely slower, regardless of experiment selection strategy. When the true hypothesis produces 96% censored outcomes, a regime-aware agent using the cumulative-distribution-function likelihood identifies it correctly in 96% of trials, while substitution-based agents identify it in 0%, always converging to the hypothesis whose mean is closest to the substitution constant.