Normalizing flows for Bayesian Model Comparison: Detecting Extrasolar Planets
PI: Eric Ford (Astronomy & Astrophysics, ECoS, ICDS)
Astronomical surveys to detect extrasolar planets via indirect detection methods such as radial velocity and/or astrometric observations must infer the number of planets required to explain a time series of observations. In principle, Bayesian model comparison allows for quantitative comparisons between models with different numbers of planets. In practice, these can be computationally demanding and still have substantial uncertainties (Nelson et al. 2020; Hara & Ford 2023). Recent advances in normalizing flows offer a new approach to estimating the Bayesian evidence for a model and performing quantitative model comparison (e.g., Srinivasan et al. 2024). We are eager to evaluate how well this approach works in the context of analyzing astronomical observations (radial velocity and/or astrometric) of planet hosting stars. In this project, an ICDS junior researcher would implement a normalizing flow-based estimator of the Bayesian evidence of a model for radial velocity and/or astrometric observations of a distant star with N (unknown number) of exoplanets, We can provide Julia code: (1) to generate simulated data sets; (2) to compute the log likelihood and perform posterior sampling with the traditional algorithms based on the Octofitter.jl package; (3) to apply normalizing flows for alternative problems (e.g., tutorials for Lux.jl, Flux.jl, InvertibleNetworks.jl). The Junior Researcher would connect these codes and packages to create a minimal working example, evaluate the robustness of the algorithm on benchmark datasets, evaluate the computational efficiency as a function of the number of planets (and thus dimensionality of the model), and compare the results to existing algorithms.
Expertise/skills of interest:
- Bayesian Statistics, Uncertainty Quantification, Bayesian model comparison, neural networks, normalizing flows.
- Programming experience using Julia and/or JAX.
- Familiarity with the following would be helpful, but is not required: Exoplanets, MCMC, Importance sampling, Nested sampling. Time series analysis, Gaussian Processes regression.
Expectations:
- Post-comps graduate student or postdocs with at least some experience and/or training in: (1) Astronomy & Astrophysics, Physics or a related field; and (2) Applied Math, Computer Sciences, Data Sciences, IST, Statistics or a related field.
- Write code organized into small functions with appropriate documentation and unit tests that will be released as open-source software.
- Produce Jupyter notebooks, scripts, and project environment files that support conclusions and make results readily reproducible.
- Weekly meeting and project updates with faculty advisor(s). Participate in group meetings (~1 hour roughly twice a month).
Goal:
Determine whether normalizing flow-based evidence estimates would are likely to provide improved computational speed and/or robustness relative to traditional methods like nested sampling in the context of detecting exoplanets from radial velocity and/or astrometric surveys. If so, obtain preliminary results to demonstrate the potential benefits that could support a future funding proposal to NASA ROSES and/or the NSF AAG call.
Specific Objectives:
1. Produce minimal working example of code to compute a normalizing flow that approximates the posterior distribution for simulated radial velocity and/or astrometric datasets.
2. Apply code to estimate Bayesian evidence for a set of benchmark datasets and models from Nelson et al. 2020. Compare results to previous methods.
3. Compare robustness and computational efficiency of estimating evidence using normalizing flows as a function of the number of planets in the model (and thus dimensionality of the posterior).
4. Compare robustness and computational efficiency of estimating evidence using normalizing flows using various Gaussian process likelihoods. [as time permits]
Engagement:
Ford is an ICDS co-hire and an Associate Director for the Center for Astrostatistics. Ford regularly participates in activities for ICDS co-hires and has served on numerous committees and in leadership roles related to ICDS.
References
Quantifying the Bayesian Evidence for a Planet in Radial Velocity Data Nelson et al. (2020) https://ui.adsabs.harvard.edu/abs/2020AJ….159…73N/abstract
Bayesian evidence estimation from posterior samples with normalizing flows Rahul Srinivasan, Marco Crisostomi, Roberto Trotta, Enrico Barausse, Matteo Breschi (2024) https://ui.adsabs.harvard.edu/abs/2024PhRvD.110l3007S/abstract
Octofitter: Fast, Flexible, and Accurate Orbit Modeling to Detect Exoplanets (2023) William Thompson, Jensen Lawrence, Dori Blakely, Christian Marois, Jason Wang, Mosé Giordano, Timothy Brandt, Doug Johnstone, Jean-Baptiste Ruffio, S. Mark Ammons https://iopscience.iop.org/article/10.3847/1538-3881/acf5cc https://sefffal.github.io/Octofitter.jl/dev/
Statistical methods for exoplanet detection with radial velocities (2023) Ford, Eric, Hara, Nathan. https://arxiv.org/abs/2308.00701