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Robert J. Webber

Publications and source records attributed to Robert J. Webber.

38 records · Page 3Linked to original sources

Unifying Sequential Monte Carlo with Resampling Matrices

Sequential Monte Carlo (SMC) is a class of algorithms that approximate high-dimensional expectations of a Markov chain. SMC algorithms typically include a resampling step. There are many possible ways to resample, but the relative advantages of different resampling schemes remains poorly understood. Here, a theoretical framework for comparing resampling schemes is presented. The framework uses resampling matrices to provide a simple description for the SMC resampling step. The framework identifies the matrix resampling scheme that gives the lowest possible error. The framework leads to new asymptotic error formulas that can be used to compare different resampling schemes.

math.NA↗

A Statistical Comparative Planetology Approach to Maximize the Scientific Return of Future Exoplanet Characterization Efforts

Provided that sufficient resources are deployed, we can look forward to an extraordinary future in which we will characterize potentially habitable planets. Until now, we have had to base interpretations of observations on habitability hypotheses that have remained untested. To test these theories observationally, we propose a statistical comparative planetology approach to questions of planetary habitability. The key objective of this approach will be to make quick and cheap measurements of critical planetary characteristics on a large sample of exoplanets, exploiting statistical marginalization to answer broad habitability questions. This relaxes the requirement of obtaining multiple types of data for a given planet, as it allows us to test a given hypothesis from only one type of measurement using the power of an ensemble. This approach contrasts with a "systems science" approach, where a few planets would be extensively studied with many types of measurements. A systems science approach is associated with a number of difficulties which may limit overall scientific return, including: the limited spectral coverage and noise of instruments, the diversity of exoplanets, and the extensive list of potential false negatives and false positives. A statistical approach could also be complementary to a systems science framework by providing context to interpret extensive measurements on planets of particular interest. We strongly recommend future missions with a focus on exoplanet characterization, and with the capability to study large numbers of planets in a homogenous way, rather than exclusively small, intense studies directed at a small sample of planets.

astro-ph.EP↗