A Probabilistic Time Reversal Theorem (Poster)

Combining independent observations is commonly performed by using a least squares technique, as it is thought that this is necessary to achieve an optimal solution. The purpose of this article is to show that this is not always the case. The particular example combines observations that are exponentially distributed. One application of this technique is to determine the time of a singular event which initiated a set of decay processes having known half-lives. The time of the singular event decays backwards in time with an exponential distribution. We find that the accuracy of this method is significantly better than the accuracy of a least squares technique. The improved accuracy can be important for applications that require combining many noisy observations, such as situation awareness.