Many missiles can carry either kind of warhead. James Acton calls the resulting uncertainty warhead ambiguity, and adds two relatives: destination ambiguity, when the observer cannot tell where a maneuvering weapon is headed and may wrongly conclude it is headed for its own territory, and target ambiguity, when a strike on conventional forces looks like a strike on nuclear ones because the two are entangled. China’s DF-26 intermediate-range ballistic missile is one example of a missile that can carry either warhead. This tool puts you in the seat of the state that detects the launch.
Three hypotheses: no attack (F), a conventional launch (C), a nuclear launch (N). Priors: Pr(real) and Pr(nuclear | real), so the prior is F = 1 − Pr(real), C = Pr(real)(1 − Pr(nuclear | real)), N = Pr(real) Pr(nuclear | real).
A second, independent sensor divides the weight on F by its likelihood ratio. Launch site and trajectory are treated as independent given the true state, and each multiplies the weights by Pr(evidence | state). The posterior is the normalized product. The multipliers shown are the nuclear-to-conventional likelihood ratios.
Entanglement. With entanglement e, a share of conventional launches comes from mixed sites (0.8e + 0.05) and heads for dual-use targets (0.05 + 0.45e) or for co-located forces that also serve your nuclear mission (0.02 + 0.25e); nuclear launches also shift to mixed sites. As e rises, site and target say less about the warhead. The observer computes likelihoods at its assumed e; outcomes are generated at the actual e.
Each response has a cost in each state (editable in the panel). The expected cost of a response is the belief-weighted sum; the model picks the lowest. In the nuclear state, waiting and conventional retaliation add a deterrent loss scaled by one minus survivability: forces that would be destroyed before they could respond. Launch on warning avoids that loss but is catastrophic if the attack was conventional or not an attack at all.
Campaign map. For each cell the model enumerates every site and trajectory, weights them by how often a conventional launch produces them at the actual entanglement, and sums the probability that the chosen response is launch on warning. The campaign figure is 1 − (1 − r)K for K conventional launches, assuming independence.
The model is this tool’s own stylized construction. Acton’s work describes the ambiguities in words; it contains no Bayesian or decision-theoretic model, and none of the formulas above come from the sources. Every number is notional: priors, likelihoods, costs, the sensor weight and the campaign size. They were chosen so the model behaves as the sources describe, not estimated from data, and no public data exist to estimate them. The model is a teaching device about how beliefs and entanglement interact. It does not describe any real warning system or decision procedure.
What it leaves out. Time pressure and staged decisions; Acton’s central concern, pre-launch ambiguity, which can last for days (the two pre-launch cases show it); signaling and statements that could clarify a launch; and the adversary’s reaction to your response. Acton notes that post-launch ambiguity could spark a nuclear response only for states able to launch before weapons detonate, which the posture switch represents.