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T. J. Loredo, D. F. Chernoff (Department of Astronomy, Cornell University)
We will describe work in progress on the development of Bayesian methodology for the analysis of data from the Space Interferometry Mission (SIM). There are two main thrusts to this work: development of new methods for the detection and analysis of Keplerian reflex motion in astrometric data; and adaptive experimental design for on-the-fly refinement of the SIM grid.
For detection and measurement of reflex motions (e.g., from planetary companions), we use the algorithm developed by Bretthorst for the Bayesian analysis of superposed nonlinear models to develop an alternative to the commonly used Lomb-Scargle (LS) periodogram that we call the Kepler periodogram. The LS periodogram emerges as a special case of the Kepler periodogram when the data are 1-dimensional (e.g., radial velocity (RV) measurements) and the bodies in question are in a circular orbit. But the Kepler periodogram generalizes the LS periodogram to account for orbital eccentricity, higher dimensional data (e.g., astrometric data, or a combination of astrometric and RV data), and sources of systematic error such as uncertainty in inertial motion.
We use the Bayesian theory of experimental design to develop adaptive strategies for SIM observing. This includes identifying the best sampling scheme for detecting and monitoring Keplerian reflex motions in science targets, and (perhaps more crucially) the adaptive refinement of the SIM astrometric grid from observations of candidate grid stars throughout the SIM mission. Included in this latter task are classification of candidate grid objects as inertial or noninertial and scheduling of observations to best update our knowledge of grid star motions.