Known Variable, Unexplained Cause: When the Absence of an Expected Event Signals a Change of State

People routinely wait for events that follow a known pattern: a bus, a reply, a child coming home from school. Intuition says that the longer one waits, the sooner the event should occur. This paper argues that this intuition holds only within the range of the known pattern. Beyond it, continued absence of the event stops being a delay and becomes evidence that the underlying system has changed state, even when the cause of that change is unknown. We propose the Known Variable, Unexplained Cause (KVUC) model, which formalizes this shift as a Bayesian competition between a normal state, in which the event follows its usual timing distribution, and an altered state, in which the event does not occur. The model yields a break-even threshold at which the altered state becomes more probable than the normal one, and shows that this threshold arrives earlier when the known pattern is narrower and when alterations are more frequent. Its central claim is that a reliable conclusion that "something happened" can be reached without identifying what happened, and that this conclusion should trigger a change of decision. We relate the model to cure models in survival analysis, statistical process control, change-point detection and the psychology of waiting, and outline applications in B2B sales, asset monitoring, logistics, project management and personal safety.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-03
DOI
https://doi.org/10.5281/zenodo.23922868
Primary Topic
Advanced Statistical Process Monitoring
Type
preprint
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preprint

Known Variable, Unexplained Cause: When the Absence of an Expected Event Signals a Change of State

José Pablo Mujica
Zenodo (CERN European Organization for Nuclear Research)
Advanced Statistical Process Monitoring
preprint

Known Variable, Unexplained Cause: When the Absence of an Expected Event Signals a Change of State

José Pablo Mujica
preprint en

Abstract

People routinely wait for events that follow a known pattern: a bus, a reply, a child coming home from school. Intuition says that the longer one waits, the sooner the event should occur. This paper argues that this intuition holds only within the range of the known pattern. Beyond it, continued absence of the event stops being a delay and becomes evidence that the underlying system has changed state, even when the cause of that change is unknown. We propose the Known Variable, Unexplained Cause (KVUC) model, which formalizes this shift as a Bayesian competition between a normal state, in which the event follows its usual timing distribution, and an altered state, in which the event does not occur. The model yields a break-even threshold at which the altered state becomes more probable than the normal one, and shows that this threshold arrives earlier when the known pattern is narrower and when alterations are more frequent. Its central claim is that a reliable conclusion that "something happened" can be reached without identifying what happened, and that this conclusion should trigger a change of decision. We relate the model to cure models in survival analysis, statistical process control, change-point detection and the psychology of waiting, and outline applications in B2B sales, asset monitoring, logistics, project management and personal safety.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Statistical Process Monitoring
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