My research focuses on understanding young stars and their protoplanetary disks during the planet formation epoch. For a number of reasons, I was particularly excited about attending the Statistical and Applied Mathematics Institute (SAMSI) Hierarchical Bayesian Modeling of Exoplanet Populations, October 17-28. The main reason was that my previous experiences at SAMSI have always been so positive. For example, I first learned about many of the topics and techniques that I use on a regular basis in my research through a similar SAMSI workshop in 2013. Three years later, I was again eager to learn new analysis methods from the statistical expertise gathered at SAMSI. Although two weeks may seem like a long time for a workshop, I knew that the close-knit environment would foster collaboration, catalyze many new projects, and make the conference pass by way too quickly. The following is a brief account of the conference with highlights of aspects that I found particularly interesting, by no way is this a complete or unbiased survey of all that transpired!
First, allow me to explain the context for our workshop. In August, 80 researchers from the fields of exoplanets, gravitational waves, and statistics converged upon Research Triangle Park to kick off the year-long SAMSI program on Statistical, Mathematical and Computational Methods for Astronomy. At the Opening Workshop for this program, we explored ideas and statistical techniques common to these fields and brainstormed interesting projects to work on over the next year. We splintered into five “working groups,” each focused on a particular topic or technique. I joined Working Group IV – Astrophysical Populations, which was focused on hierarchical Bayesian inference of exoplanet populations. Each working group has maintained momentum through weekly teleconferences, and most groups will have a workshop at SAMSI at some point during the academic year. The year-long program will be capped by a “transition” workshop in May 2017.
Angie Wolfgang, a National Science Foundation Fellow at Penn State University and Eric Ford, a professor, also at Penn State, were the main organizers of the Astrophysical Populations workshop. We had about 20 participants split equally between astrophysics and statistics. Our first morning was spent discussing our research interests and what we hoped to accomplish over the next two weeks. Two major groups evolved from this discussion. The first was centered on exploring the mass-radius relationship of exoplanets from photometric transit and radial velocity datasets. The second was focused on spectroscopic techniques to characterize stars and measure their radial velocity. Although our workshop was nominally about exoplanets, it turns out that a proper understanding of stars is fundamental to detecting and understanding the exoplanets that orbit them.
Understanding the Planet Mass-Radius Relationship…
In the past decade, astronomers have transitioned from knowing of the existence of only a handful of exoplanets to discovering a vast collection of several thousand. Most planets have been discovered by the Kepler Mission, which finds planets by measuring the dip in light as a planet transits its host star. It is most informative about a planet’s radius. For a select subset of these planets, precise radial velocity monitoring yields the masses of the planets as well. Because we are necessarily operating at the detection limit of our telescopes when studying small planets, it is very important to utilize proper statistical analysis lest our interpretation be biased. The fundamental unknown that links a planet’s mass and radius is the planets composition, and so with a proper statistical framework we might hope to infer how planet composition varies amongst the thousands of known exoplanets, telling us something deep about the planet formation process in general.
Angie Wolfgang, Bo Ning, a Ph.D. candidate in the Department of Statistics at N.C. State University, and Sujit Ghosh, SAMSI Deputy Director, explored using Bernstein Polynomials to model the planet mass-radius relationship non-parametrically, and showed promising results that included measurement uncertainties. Leslie Rogers, an Assistant Professor in the Department of Astronomy and Astrophysics at the University of Chicago, talked about the planet composition distribution. In addition, she also discussed how to link physically motivated models of planet composition to data and determine if this composition changes as a function of planet formation mechanism. Kaisey Mandel, a Postdoctroal Fellow at the Harvard-Smithsonian Center for Astrophysics, worked on understanding selection effects as they apply to exoplanet surveys. This was his focus since he is also interested in selection effects of Type Ia supernovae surveys.
A sizable group of people worked on translating hierarchical sampling code into the new language STAN. In particular, Megan Shabram, a Postdoctoral Fellow with NASA’s Kepler Mission and Joe Catanzarite, a SOC Scientific Programmer with NASA’s Kepler team, produced an open-source Jupyter notebook that implemented planet occurrence rate calculations in PySTAN.
Central to many of our problems discussed at this workshop was the topic of “emulation” or “uncertainty quantification,” which is actually the primary topic of Working Group I – Uncertainty Quantification and Astrophysical Emulation. Bekki Dawson, an Assistant Professor in the Penn State Department of Astronomy and Astrophysics, and Assistant Professor, Anirban Mondal of the Mathematics, Applies Mathematics and Statistics Department at Case Western Reserve University, worked on developing astrophysical emulators for planet formation models, so that more accurate (and computationally expensive) models could be used in hierarchical Bayesian inference to understand the formation of super-Earths and mini-Neptunes. Related to this problem, Jessi Cisewski, Assistant Professor in Yale’s Department of Statistics, made several informative presentations on Approximate Bayesian Computing (ABC) to solve inference problems where it is difficult to write down a likelihood function.
Hierarchical Spectroscopic Inference with Time Series Stellar Spectroscopy…
A large group of astronomers and statisticians worked on techniques to improve radial velocity precision, with the hopes of finding planets with the mass of earth and below. Eric Ford, Jessi Cisewski, David Stenning and David Jones, Postdoctoral Fellows at SAMSI, Robert Wolpert, a Professor of Statistical Science and the Environment at Duke Univesity; Tom Loredo, a Senior Research Associate in Astronomy at Cornell; Ben Montet, a Postdoctoral Researcher from the University of Chicago and I worked on radial velocity fitting using mock spectral datasets with known statistical characteristics. These datasets are comprised of real stellar spectra of the sun to which have been added planets (the signal of interest) and star spots (a confounding signal). We examined interesting principal component analysis with the hope of isolating the orbiting planet from stellar activity. During this period, we were also treated to two presentations by the SAMSI postdocs David Stenning and David Jones about using Gaussian processes to correlate stellar activity indicators with radial velocity jitter and using diffusion mapping to understand stellar variability.
By the end of the workshop, we were all knee-deep in immersive projects that we had started just 10 days prior – we were reluctant to leave! The collaborative working environment, with daily updates of what we had accomplished certainly fueled an exciting work schedule, since everyone was motivated to complete new ideas to share with the group. By the end of the workshop, several of us remarked that in fact two weeks was not a long enough period for us to get anything done – we were all so dedicated to the research, we wanted to stay! To cap it all off, we were treated to a tasty “special presentation” by Tom Loredo, who shared with us how chocolate is made.
These researchers will collaborate over the next several months on this continued analysis of exoplanet discovery.