ABSTRACT
Lacking an exact measurement of the true position process, the simplest approach is to use the posterior predictive mean for the process and pretend that it is the truth. The imputation concept of “doing statistics on statistics” may not accommodate the proper uncertainty pertaining to knowledge of the process. However, a technique referred to as “multiple imputation” can help account for the uncertainty associated with the modeled process we intend to use as data in a secondary model. The heuristic for multiple imputation is to use an imputation distribution that closely resembles the true posterior predictive distribution of interest and then fit a secondary model while conditioning on the imputation distribution, allowing the uncertainty to propagate into the secondary inference. The secondary modeling approaches presented thus far are powerful in that they allow for additional inference that would be difficult to obtain using the correlated random walk models conditioned directly on the original telemetry data.
