Extreme-deconvolution is a general algorithm to infer a d-dimensional distribution function from a set of heterogeneous, noisy observations or samples. It is fast, flexible, and treats the data's individual uncertainties properly, to get the best description possible for the underlying distribution. It performs well over the full range of density estimation, from small data sets with only tens of samples per dimension, to large data sets with hundreds of thousands of data points.

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.

XDQSO, written in IDL, calculates photometric quasar probabilities to mimick SDSS-III’s BOSS quasar target selection or photometric redshifts for quasars, whether in three redshift ranges (z < 2.2; 2.2 leq z leq 3.5; z > 3.5) or arbitrary redshift ranges.

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.

Magnetron, written in Python, decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. Markov Chain Monte Carlo (MCMC) sampling and reversible jumps between models with different numbers of parameters are used to characterize the posterior distributions of the model parameters and the number of components per burst.

Starfish is a set of tools used for spectroscopic inference. It robustly determines stellar parameters using high resolution spectral models and uses Markov Chain Monte Carlo (MCMC) to explore the full posterior probability distribution of the stellar parameters. Additional potential applications include other types of spectra, such as unresolved stellar clusters or supernovae spectra.

CCDtoRGB produces red‐green‐blue (RGB) composites from three‐band astronomical images, ensuring an object with a specified astronomical color has a unique color in the RGB image rather than burnt‐out white stars. Use of an arcsinh stretch shows faint objects while simultaneously preserving the structure of brighter objects in the field, such as the spiral arms of large galaxies.

The Cannon is a data-driven method for determining stellar labels (physical parameters and chemical abundances) from stellar spectra in the context of vast spectroscopic surveys. It fits for the spectral model given training spectra and labels, with the polynomial order for the spectral model decided by the user, infers labels for the test spectra, and provides diagnostic output for monitoring and evaluating the process. It offers SNR-independent continuum normalization, performs well at lower signal-to-noise, and is very accurate.

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.

AGNfitter is a fully Bayesian MCMC method to fit the spectral energy distributions (SEDs) of active galactic nuclei (AGN) and galaxies from the sub-mm to the UV; it enables robust disentanglement of the physical processes responsible for the emission of sources. Written in Python, AGNfitter makes use of a large library of theoretical, empirical, and semi-empirical models to characterize both the nuclear and host galaxy emission simultaneously. The model consists of four physical emission components: an accretion disk, a torus of AGN heated dust, stellar populations, and cold dust in star forming regions. AGNfitter determines the posterior distributions of numerous parameters that govern the physics of AGN with a fully Bayesian treatment of errors and parameter degeneracies, allowing one to infer integrated luminosities, dust attenuation parameters, stellar masses, and star formation rates.

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.

BEAST (Bayesian Extinction and Stellar Tool) fits the ultraviolet to near-infrared photometric SEDs of stars to extract stellar and dust extinction parameters. The stellar parameters are age (t), mass (M), metallicity (M), and distance (d). The dust extinction parameters are dust column (Av), average grain size (Rv), and mixing between type A and B extinction curves (fA).

wobble analyzes time-series spectra. It was designed with stabilized extreme precision radial velocity (EPRV) spectrographs in mind, but is highly flexible and extensible to a variety of applications. It takes a data-driven approach to deriving radial velocities and requires no a priori knowledge of the stellar spectrum or telluric features.

K2-CPM captures variability while preserving transit signals in Kepler data. Working at the pixel level, the model captures very fine-grained information about the variation of the spacecraft. The CPM models the systematic effects in the time series of a pixel using the pixels of many other stars and the assumption that any shared signal in these causally disconnected light curves is caused by instrumental effects. The target star's future and past are used and the data points are separated into training and test sets to ensure that information about any transit is perfectly isolated from the model. The method has four tuning parameters, the number of predictor stars or pixels, the autoregressive window size, and two L2-regularization amplitudes for model components, and consistently produces low-noise light curves.

unpopular is an implementation of the Causal Pixel Model (CPM) de-trending method to obtain TESS Full-Frame Image (FFI) light curves. The code, written in Python, models the systematics in the light curves of individual pixels as a linear combination of light curves from many other distant pixels and removes shared flux variations. unpopular is able to preserve sector-length astrophysical signals, allowing for the extraction of multi-sector light curves from the FFI data.

maelstrom models binary orbits through the phase modulation technique. This set of custom PyMC3 models and solvers fit each individual datapoint in the time series by forward modeling the time delay onto the light curve. This approach fully captures variations in a light curve caused by an orbital companion.

Delight infers photometric redshifts in deep galaxy and quasar surveys. It uses a data-driven model of latent spectral energy distributions (SEDs) and a physical model of photometric fluxes as a function of redshift, thus leveraging the advantages of both machine- learning and template-fitting methods by building template SEDs directly from the training data. Delight obtains accurate redshift point estimates and probability distributions and can also be used to predict missing photometric fluxes or to simulate populations of galaxies with realistic fluxes and redshifts.

PhotoParallax calculates photometric parallaxes for distant stars in the Gaia TGAS catalog without any use of physical stellar models or stellar density models of the Milky Way. It uses the geometric parallaxes to calibrate a photometric model that is purely statistical, which is a model of the data rather than a model of stars per se.