arXiv subjects

Daniel Foreman-Mackey

Publications and source records attributed to Daniel Foreman-Mackey.

At least 91 records · Page 5Linked to original sources

arXiv2017

Data analysis recipes: Using Markov Chain Monte Carlo

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data. In this primarily pedagogical contribution, we give a brief overview of the most basic MCMC method and some practical advice for the use of MCMC in real inference problems. We give advice on method choice, tuning for performance, methods for initialization, tests of convergence, troubleshooting, and use of the chain output to produce or report parameter estimates with associated uncertainties. We argue that autocorrelation time is the most important test for convergence, as it directly connects to the uncertainty on the sampling estimate of any quantity of interest. We emphasize that sampling is a method for doing integrals; this guides our thinking about how MCMC output is best used.

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arXiv2017

Seeing double with K2: Testing re-inflation with two remarkably similar planets around red giant branch stars

Despite more than 20 years since the discovery of the first gas giant planet with an anomalously large radius, the mechanism for planet inflation remains unknown. Here, we report the discovery of EPIC228754001.01, an inflated gas giant planet found with the NASA K2 Mission, and a revised mass for another inflated planet, K2-97b. These planets reside on ~9 day orbits around host stars which recently evolved into red giants. We constrain the irradiation history of these planets using models constrained by asteroseismology and Keck/HIRES spectroscopy and radial velocity measurements. We measure planet radii of 1.31 +\- 0.11 Rjup and and 1.30 +\- 0.07 Rjup, respectively. These radii are typical for planets receiving the current irradiation, but not the former, zero age main sequence irradiation of these planets. This suggests that the current sizes of these planets are directly correlated to their current irradiation. Our precise constraints of the masses and radii of the stars and planets in these systems allow us to constrain the planetary heating efficiency of both systems as 0.03% +0.03%/-0.02%. These results are consistent with a planet re-inflation scenario, but suggest the efficiency of planet re-inflation may be lower than previously theorized. Finally, we discuss the agreement within 10% of stellar masses and radii, and planet masses, radii, and orbital periods of both systems and speculate that this may be due to selection bias in searching for planets around evolved stars.

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arXiv2017

A pixel-level model for event discovery in time-domain imaging

Difference imaging or image subtraction is a method that measures differential photometry by matching the pointing and point-spread function (PSF) between image frames. It is used for the detection of time-variable phenomena. Here we present a new category of method---CPM Difference Imaging, in which differences are not measured between matched images but instead between image frames and a data-driven predictive model that has been designed only to predict the pointing, PSF, and detector effects but not astronomical variability. In CPM Difference Imaging each pixel is modelled by the Causal Pixel Model (CPM) originally built for modeling Kepler data, in which pixel values are predicted by a linear combination of other pixels at the same epoch but far enough away such that these pixels are causally disconnected, astrophysically. It does not require that the user have any explicit model or description of the pointing or point-spread function of any of the images. Its principal drawback is that---in its current form---it requires an imaging campaign with many epochs and fairly stable telescope pointing. The method is applied to simulated data and also the K2 Campaign 9 microlensing data. We show that CPM Difference Imaging can detect variable objects and produce precise differentiate photometry in a crowded field. CPM Difference Imaging is capable of producing image differences at nearly photon-noise precision.

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arXiv2017

Fast and scalable Gaussian process modeling with applications to astronomical time series

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose but, since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small datasets. In this paper, we present a novel method for Gaussian Process modeling in one-dimension where the computational requirements scale linearly with the size of the dataset. We demonstrate the method by applying it to simulated and real astronomical time series datasets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically-driven damped harmonic oscillators -- providing a physical motivation for and interpretation of this choice -- but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable Gaussian Process methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.

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arXiv2017

Inferring probabilistic stellar rotation periods using Gaussian processes

Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic --- spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly periodic sinusoid therefore cannot accurately model a rotationally modulated stellar light curve. Physical models of stellar surfaces have many drawbacks preventing effective inference, such as highly degenerate or high-dimensional parameter spaces. In this work, we test an appropriate effective model: a Gaussian Process with a quasi-periodic covariance kernel function. This highly flexible model allows sampling of the posterior probability density function of the periodic parameter, marginalising over the other kernel hyperparameters using a Markov Chain Monte Carlo approach. To test the effectiveness of this method, we infer rotation periods from 333 simulated stellar light curves, demonstrating that the Gaussian process method produces periods that are more accurate than both a sine-fitting periodogram and an autocorrelation function method. We also demonstrate that it works well on real data, by inferring rotation periods for 275 Kepler stars with previously measured periods. We provide a table of rotation periods for these 1132 Kepler objects of interest and their posterior probability density function samples. Because this method delivers posterior probability density functions, it will enable hierarchical studies involving stellar rotation, particularly those involving population modelling, such as inferring stellar ages, obliquities in exoplanet systems, or characterising star-planet interactions. The code used to implement this method is available online.

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arXiv2017

A seven-planet resonant chain in TRAPPIST-1

The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star. At least seven planets similar to Earth in radius and in mass were previously found to transit this host star. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1h has a radius of 0.727 Earth radii and an equilibrium temperature of 173 K. We have also measured the rotational period of the star at 3.3 d and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf.

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arXiv2017

The Joker: A custom Monte Carlo sampler for binary-star and exoplanet radial velocity data

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. Here we create a custom Monte Carlo sampler for sparse or noisy radial-velocity measurements of two-body systems that can produce posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four non-linear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior pdf in the non-linear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. 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 informative and can be used in hierarchical (population) modeling. We give some examples that show how the posterior pdf depends sensitively on the number and time coverage of the observations and their uncertainties.

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arXiv2017

An update to the EVEREST K2 pipeline: Short cadence, saturated stars, and Kepler-like photometry down to Kp = 15

We present an update to the EVEREST K2 pipeline that addresses various limitations in the previous version and improves the photometric precision of the de-trended light curves. We develop a fast regularization scheme for third order pixel level decorrelation (PLD) and adapt the algorithm to include the PLD vectors of neighboring stars to enhance the predictive power of the model and minimize overfitting, particularly for faint stars. We also modify PLD to work for saturated stars and improve its performance on extremely variable stars. On average, EVEREST 2.0 light curves have 10-20% higher photometric precision than those in the previous version, yielding the highest precision light curves at all Kp magnitudes of any publicly available K2 catalog. For most K2 campaigns, we recover the original Kepler precision to at least Kp = 14, and to at least Kp = 15 for campaigns 1, 5, and 6. We also de-trend all short cadence targets observed by K2, obtaining even higher photometric precision for these stars. All light curves for campaigns 0-8 are available online in the EVEREST catalog, which will be continuously updated with future campaigns. EVEREST 2.0 is open source and is coded in a general framework that can be applied to other photometric surveys, including Kepler and the upcoming TESS mission.

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arXiv2016

DNest4: Diffusive Nested Sampling in C++ and Python

In probabilistic (Bayesian) inferences, we typically want to compute properties of the posterior distribution, describing knowledge of unknown quantities in the context of a particular dataset and the assumed prior information. The marginal likelihood, also known as the "evidence", is a key quantity in Bayesian model selection. The Diffusive Nested Sampling algorithm, a variant of Nested Sampling, is a powerful tool for generating posterior samples and estimating marginal likelihoods. It is effective at solving complex problems including many where the posterior distribution is multimodal or has strong dependencies between variables. DNest4 is an open source (MIT licensed), multi-threaded implementation of this algorithm in C++11, along with associated utilities including: i) RJObject, a class template for finite mixture models, (ii) A Python package allowing basic use without C++ coding, and iii) Experimental support for models implemented in Julia. In this paper we demonstrate DNest4 usage through examples including simple Bayesian data analysis, finite mixture models, and Approximate Bayesian Computation.

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arXiv2016

The population of long-period transiting exoplanets

The Kepler Mission has discovered thousands of exoplanets and revolutionized our understanding of their population. This large, homogeneous catalog of discoveries has enabled rigorous studies of the occurrence rate of exoplanets and planetary systems as a function of their physical properties. However, transit surveys like Kepler are most sensitive to planets with orbital periods much shorter than the orbital periods of Jupiter and Saturn, the most massive planets in our Solar System. To address this deficiency, we perform a fully automated search for long-period exoplanets with only one or two transits in the archival Kepler light curves. When applied to the $\sim 40,000$ brightest Sun-like target stars, this search produces 16 long-period exoplanet candidates. Of these candidates, 6 are novel discoveries and 5 are in systems with inner short-period transiting planets. Since our method involves no human intervention, we empirically characterize the detection efficiency of our search. Based on these results, we measure the average occurrence rate of exoplanets smaller than Jupiter with orbital periods in the range 2-25 years to be $2.0\pm0.7$ planets per Sun-like star.

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arXiv2016

Chemical tagging can work: Identification of stellar phase-space structures purely by chemical-abundance similarity

Chemical tagging promises to use detailed abundance measurements to identify spatially separated stars that were in fact born together (in the same molecular cloud), long ago. This idea has not yielded much practical success, presumably because of the noise and incompleteness in chemical-abundance measurements. We have succeeded in substantially improving spectroscopic measurements with The Cannon, which has now delivered 15 individual abundances for ~100,000 stars observed as part of the APOGEE spectroscopic survey, with precisions around 0.04 dex. We test the chemical-tagging hypothesis by looking at clusters in abundance space and confirming that they are clustered in phase space. We identify (by the k-means algorithm) overdensities of stars in the 15-dimensional chemical-abundance space delivered by The Cannon, and plot the associated stars in phase space. We use only abundance-space information (no positional information) to identify stellar groups. We find that clusters in abundance space are indeed clusters in phase space. We recover some known phase-space clusters and find other interesting structures. This is the first-ever project to identify phase-space structures at survey-scale by blind search purely in abundance space; it verifies the precision of the abundance measurements delivered by The Cannon; the prospects for future data sets appear very good.

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arXiv2016

EVEREST: Pixel Level Decorrelation of K2 Light curves

We present EVEREST, an open-source pipeline for removing instrumental noise from K2 light curves. EVEREST employs a variant of pixel level decorrelation (PLD) to remove systematics introduced by the spacecraft's pointing error and a Gaussian process (GP) to capture astrophysical variability. We apply EVEREST to all K2 targets in campaigns 0-7, yielding light curves with precision comparable to that of the original Kepler mission for stars brighter than $K_p \approx 13$, and within a factor of two of the Kepler precision for fainter targets. We perform cross-validation and transit injection and recovery tests to validate the pipeline, and compare our light curves to the other de-trended light curves available for download at the MAST High Level Science Products archive. We find that EVEREST achieves the highest average precision of any of these pipelines for unsaturated K2 stars. The improved precision of these light curves will aid in exoplanet detection and characterization, investigations of stellar variability, asteroseismology, and other photometric studies. The EVEREST pipeline can also easily be applied to future surveys, such as the TESS mission, to correct for instrumental systematics and enable the detection of low signal-to-noise transiting exoplanets. The EVEREST light curves and the source code used to generate them are freely available online.

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arXiv2016

State of the Field: Extreme Precision Radial Velocities

The Second Workshop on Extreme Precision Radial Velocities defined circa 2015 the state of the art Doppler precision and identified the critical path challenges for reaching 10 cm/s measurement precision. The presentations and discussion of key issues for instrumentation and data analysis and the workshop recommendations for achieving this precision are summarized here. Beginning with the HARPS spectrograph, technological advances for precision radial velocity measurements have focused on building extremely stable instruments. To reach still higher precision, future spectrometers will need to produce even higher fidelity spectra. This should be possible with improved environmental control, greater stability in the illumination of the spectrometer optics, better detectors, more precise wavelength calibration, and broader bandwidth spectra. Key data analysis challenges for the precision radial velocity community include distinguishing center of mass Keplerian motion from photospheric velocities, and the proper treatment of telluric contamination. Success here is coupled to the instrument design, but also requires the implementation of robust statistical and modeling techniques. Center of mass velocities produce Doppler shifts that affect every line identically, while photospheric velocities produce line profile asymmetries with wavelength and temporal dependencies that are different from Keplerian signals. Exoplanets are an important subfield of astronomy and there has been an impressive rate of discovery over the past two decades. Higher precision radial velocity measurements are required to serve as a discovery technique for potentially habitable worlds and to characterize detections from transit missions. The future of exoplanet science has very different trajectories depending on the precision that can ultimately be achieved with Doppler measurements.

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arXiv2015

Stellar and Planetary Properties of K2 Campaign 1 Candidates and Validation of 17 Planets, Including a Planet Receiving Earth-like Insolation

The extended Kepler mission, K2, is now providing photometry of new fields every three months in a search for transiting planets. In a recent study, Foreman-Mackey and collaborators presented a list of 36 planet candidates orbiting 31 stars in K2 Campaign 1. In this contribution, we present stellar and planetary properties for all systems. We combine ground-based seeing-limited survey data and adaptive optics imaging with an automated transit analysis scheme to validate 21 candidates as planets, 17 for the first time, and identify 6 candidates as likely false positives. Of particular interest is K2-18 (EPIC 201912552), a bright (K=8.9) M2.8 dwarf hosting a 2.23 \pm 0.25 R_Earth planet with T_eq = 272 \pm 15 K and an orbital period of 33 days. We also present two new open-source software packages which enable this analysis. The first, isochrones, is a flexible tool for fitting theoretical stellar models to observational data to determine stellar properties using a nested sampling scheme to capture the multimodal nature of the posterior distributions of the physical parameters of stars that may plausibly be evolved. The second is vespa, a new general-purpose procedure to calculate false positive probabilities and statistically validate transiting exoplanets.

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arXiv2015

A systematic search for transiting planets in the K2 data

Photometry of stars from the K2 extension of NASA's Kepler mission is afflicted by systematic effects caused by small (few-pixel) drifts in the telescope pointing and other spacecraft issues. We present a method for searching K2 light curves for evidence of exoplanets by simultaneously fitting for these systematics and the transit signals of interest. This method is more computationally expensive than standard search algorithms but we demonstrate that it can be efficiently implemented and used to discover transit signals. We apply this method to the full Campaign 1 dataset and report a list of 36 planet candidates transiting 31 stars, along with an analysis of the pipeline performance and detection efficiency based on artificial signal injections and recoveries. For all planet candidates, we present posterior distributions on the properties of each system based strictly on the transit observables.

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arXiv2015

Systematics-insensitive periodic signal search with K2

From pulsating stars to transiting exoplanets, the search for periodic signals in K2 data, Kepler's 2-wheeled extension, is relevant to a long list of scientific goals. Systematics affecting K2 light curves due to the decreased spacecraft pointing precision inhibit the easy extraction of periodic signals from the data. We here develop a method for producing periodograms of K2 light curves that are insensitive to pointing-induced systematics; the Systematics-Insensitive Periodogram (SIP). Traditional sine-fitting periodograms use a generative model to find the frequency of a sinusoid that best describes the data. We extend this principle by including systematic trends, based on a set of 'Eigen light curves', following Foreman-Mackey et al. (2015), in our generative model as well as a sum of sine and cosine functions over a grid of frequencies. Using this method we are able to produce periodograms with vastly reduced systematic features. The quality of the resulting periodograms are such that we can recover acoustic oscillations in giant stars and measure stellar rotation periods without the need for any detrending. The algorithm is also applicable to the detection of other periodic phenomena such as variable stars, eclipsing binaries and short-period exoplanet candidates. The SIP code is available at https://github.com/RuthAngus/SIPK2.

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arXiv2015

Removing systematic errors for exoplanet search via latent causes

We describe a method for removing the effect of confounders in order to reconstruct a latent quantity of interest. The method, referred to as half-sibling regression, is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification and illustrate the potential of the method in a challenging astronomy application.

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arXiv2015

The Five Planets in the Kepler-296 Binary System All Orbit the Primary: A Statistical and Analytical Analysis

Kepler-296 is a binary star system with two M-dwarf components separated by 0.2 arcsec. Five transiting planets have been confirmed to be associated with the Kepler-296 system; given the evidence to date, however, the planets could in principle orbit either star. This ambiguity has made it difficult to constrain both the orbital and physical properties of the planets. Using both statistical and analytical arguments, this paper shows that all five planets are highly likely to orbit the primary star in this system. We performed a Markov-Chain Monte Carlo simulation using a five transiting planet model, leaving the stellar density and dilution with uniform priors. Using importance sampling, we compared the model probabilities under the priors of the planets orbiting either the brighter or the fainter component of the binary. A model where the planets orbit the brighter component, Kepler-296A, is strongly preferred by the data. Combined with our assertion that all five planets orbit the same star, the two outer planets in the system, Kepler-296 Ae and Kepler-296 Af, have radii of 1.53 +/- 0.26 and 1.80 +/- 0.31 R_earth, respectively, and receive incident stellar fluxes of 1.40 +/- 0.23 and 0.62 +/- 0.10 times the incident flux the Earth receives from the Sun. This level of irradiation places both planets within or close to the circumstellar habitable zone of their parent star.

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