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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.
Astropy provides a common framework, core package of code, and affiliated packages for astronomy in Python. Development is actively ongoing, with major packages such as PyFITS, PyWCS, vo, and asciitable already merged in. Astropy is intended to contain much of the core functionality and some common tools needed for performing astronomy and astrophysics with Python.
SuperFreq numerically estimates the fundamental frequencies and orbital actions of pre-computed orbital time series. It is an implementation of a version of the Numerical Analysis of Fundamental Frequencies close to that by Monica Valluri, which itself is an implementation of an algorithm first used by Jacques Laskar.
Gala is a Python package (and Astropy affiliated package) for Galactic astronomy and gravitational dynamics. The bulk of the package centers around implementations of gravitational potentials, numerical integration, nonlinear dynamics, and astronomical velocity transformations (i.e. proper motions). Gala uses the Astropy units and coordinates subpackages extensively to provide a clean, pythonic interface to these features but does any heavy-lifting in C and Cython for speed.
Given sparse or low-quality radial-velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and MCMC posterior sampling over the orbital parameters. The Joker is a custom-built Monte Carlo sampler that can produce a posterior sampling for orbital parameters given sparse or noisy radial-velocity measurements, even when the likelihood function is poorly behaved. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal pdfs, which are still highly informative and can be used in hierarchical (population) modeling.