Kepler Planet Reliability Metrics: Astrophysical Positional Probabilities for Data Release 25

This document is very similar to KSCI-19092-003, Planet Reliability Metrics: Astrophysical Positional Probabilities, which describes the previous release of the astrophysical positional probabilities for Data Release 24. The important changes for Data Release 25 are:1. The computation of the astrophysical positional probabilities uses the Data Release 25 processed pixel data for all Kepler Objects of Interest.2. Computed probabilities now have associated uncertainties, whose computation is described in x4.1.3.3. The scene modeling described in x4.1.2 uses background stars detected via ground-based high-resolution imaging, described in x5.1, that are not in the Kepler Input Catalog or UKIRT catalog. These newly detected stars are presented in Appendix B. Otherwise the text describing the algorithms and examples is largely unchanged from KSCI-19092-003.