Statistical Asynchronous Regression : Determining the Relationship Between two Quantities that are not Measured Simultaneously

We introduce the Statistical Asynchronous Regression (SAR) method: a technique for determining a relationship between two time varying quantities without simultaneous measurements of both quantities. We require that there is a time invariant, monotonic function Y = u(X) relating the two quantities, Y and X. In order to determine u(X), we only need to know the statistical distributions of X and Y. We show that u(X) is the change of variables that converts the distribution of X into the distribution of Y, while conserving probability. We describe an algorithm for implementing this method and apply it to several example distributions. We also demonstrate how the method can separate spatial and temporal variations from a time series of energetic electron flux measurements made by a spacecraft in geosynchronous orbit. We expect this method will be useful to the general problem of spacecraft instrument calibration. We also suggest some applications of the SAR method outside of space physics. 3