Testing Confidence Intervals on the Duration of an Event Based on the Copernican Principle
Abstract
J. R. Gott proposed a method for placing confidence intervals (CIs) on the remaining duration of an ongoing event, where an event can be a phenomenon, process, failure-free operation of an item, or existence of an object. Gott's method can provide a lower bound and upper bound on event duration without any knowledge of its underlying distribution: it requires knowing only the past duration of the event. Its only necessary assumption is that the "Copernican Principle" holds, meaning that the observation of the ongoing event occurs at "no special time." The bounds on the remaining duration of an event obtained by Gott's method are very wide, being 1/39 and 39 times the observed past duration for a 95 percent CI; other techniques that use knowledge of the underlying distribution can yield much tighter bounds, but such information may not be known or even knowable. Gott's method was tested using Monte Carlo simulation with populations of events that satisfied the Copernican Principle and it was shown to yield 95 percent CIs regardless of the underlying distribution of event durations. It was also tested using "baby boom" populations that violated that principle and it was found to be tolerant of those violations. Gott's 95 percent CIs can also be continuously recalculated throughout the entire duration of an event (another violation of the Copernican Principle) and the true end time will still be found to have been within those bounds for 95 percent of that duration. The lower bound provided by Gott's method may closely approximate that obtained from the conditional survival method that uses the true underlying distribution; this is significant because the lower bound on remaining duration can be a useful measure of the statistical level of trust that a critical function will not fail within a quantifiable period of time.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 25, 2024
- Accession Number
- AD1224428
Entities
People
- Warren H. Jr Debany