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Astrometry.net is a reliable and robust system that takes as input an astronomical image and returns as output the pointing, scale, and orientation of that image (the astrometric calibration or World Coordinate System information). The system requires no first guess, and works with the information in the image pixels alone; that is, the problem is a generalization of the "lost in space" problem in which nothing—not even the image scale—is known. After robust source detection is performed in the input image, asterisms (sets of four or five stars) are geometrically hashed and compared to pre-indexed hashes to generate hypotheses about the astrometric calibration. A hypothesis is only accepted as true if it passes a Bayesian decision theory test against a null hypothesis. With indices built from the USNO-B catalog and designed for uniformity of coverage and redundancy, the success rate is >99.9% for contemporary near-ultraviolet and visual imaging survey data, with no false positives. The failure rate is consistent with the incompleteness of the USNO-B catalog; augmentation with indices built from the Two Micron All Sky Survey catalog brings the completeness to 100% with no false positives. We are using this system to generate consistent and standards-compliant meta-data for digital and digitized imaging from plate repositories, automated observatories, individual scientific investigators, and hobbyists.
SYNMAG is a tool for producing synthetic aperture magnitudes to enable fast matched photometry at the catalog level without reprocessing imaging data. Aperture magnitudes are the most widely tabulated flux measurements in survey catalogs; obtaining reliable, matched photometry for galaxies imaged by different observatories represents a key challenge in the era of wide-field surveys spanning more than several hundred square degrees. Methods such as flux fitting, profile fitting, and PSF homogenization followed by matched-aperture photometry are all computationally expensive. An alternative solution called "synthetic aperture photometry" exploits galaxy profile fits in one band to efficiently model the observed, point-spread-function-convolved light profile in other bands and predict the flux in arbitrarily sized apertures.
emcee is an extensible, pure-Python implementation of Goodman & Weare's Affine Invariant Markov chain Monte Carlo (MCMC) Ensemble sampler. It's designed for Bayesian parameter estimation. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to $sim N^2$ for a traditional algorithm in an N-dimensional parameter space. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort.
The Tractor optimizes or samples from models of astronomical objects. The approach is generative: given astronomical sources and a description of the image properties, the code produces pixel-space estimates or predictions of what will be observed in the images. This estimate can be used to produce a likelihood for the observed data given the model: assuming the model space actually includes the truth (it doesn’t, in detail), then if we had the optimal model parameters, the predicted image would differ from the actually observed image only by noise. Given a noise model of the instrument and assuming pixelwise independent noise, the log-likelihood is the negative chi-squared difference: (image - model) / noise.