A Gaussian process framework for modelling instrumental systematics: application to transmission spectroscopy

By Neale P. Gibson, Suzanne Aigrain, Stephen J. Roberts, T. Evans, Michael A. Osborne, F. U. O. Oxford, U. Exeter. 2011

224 citations recorded by the source corpus.

Transmission spectroscopy, which consists of measuring the wavelength-dependent absorption of starlight by a planet’s atmosphere during a transit, is a powerful probe of atmospheric composition. However, the expected signal is typically orders of magnitude smaller than instrumental systematics and the results are crucially dependent on the treatment of the latter. In this paper, we propose a new method to infer transit parameters in the presence of systematic noise using Gaussian processes, a technique widely used in the machine learning community for Bayesian regression and classification problems. Our method makes use of auxiliary information about the state of the instrument, but does so in a non-parametric manner, without imposing a specific dependence of the systematics on the instrumental parameters, and naturally allows for the correlated nature of the noise. We give an example application of the method to archival NICMOS transmission spectroscopy of the hot Jupiter HD 189733, which goes some way towards reconciling the controversy surrounding this data set in the literature. Finally, we provide an appendix giving a general introduction to Gaussian processes for regression, in order to encourage their application to a wider range of problems.

Subfields: Analytical Chemistry, Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/7336d9d82a2a11ac191dda2ce5da22f8edaee55b

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In Analytical Chemistry

Suzanne Aigrain

In Astronomy and Astrophysics

In Instrumentation

Citations in the corpus

A Gaussian process framework for modelling stellar activity signals in radial velocity data (2015, methodology): “The free hyper-parameters θ and φ can then be varied to maximise L m,k ; this process is known as Type-II maximum likelihood, or marginal likelihood maximisation (Gibson et al. 2012).”
EXOPLANET POPULATION INFERENCE AND THE ABUNDANCE OF EARTH ANALOGS FROM NOISY, INCOMPLETE CATALOGS (2014, methodology): “To achieve this, we model the logarithmic step heights as being drawn from a Gaussian process (Rasmussen & Williams 2006; Brewer & Stello 2009; Gibson et al. 2012; Ambikasaran et al. 2014).”
INFRARED TRANSMISSION SPECTROSCOPY OF THE EXOPLANETS HD 209458b AND XO-1b USING THE WIDE FIELD CAMERA-3 ON THE HUBBLE SPACE TELESCOPE (2013, methodology): “New methodology (Gibson et al. 2012a; Waldmann 2012; Waldmann et al. 2013) improves the reliability of NICMOS analyses.”
A CONSISTENT RETRIEVAL ANALYSIS OF 10 HOT JUPITERS OBSERVED IN TRANSMISSION (2016, methodology): “The binned NICMOS points used in this paper are as presented by Pont et al. (2013), but they were binned up from a spectrum that was originally reduced by Gibson et al. (2012).”
The Complete Transmission Spectrum of WASP-39b with a Precise Water Constraint (2017, methodology): “Observational data analysis is a non-trivial exercise and there are an array of techniques being applied to reduce data (e.g. Berta et al. 2012; Gibson et al. 2012; Deming et al. 2013; Wakeford et al. 2016).”
TAU-REX I: A NEXT GENERATION RETRIEVAL CODE FOR EXOPLANETARY ATMOSPHERES (2014, unknown): “…Swain et al. 2008; Carter & Winn 2009; Burke et al. 2010; Snellen et al. 2010; Thatte et al. 2010; Swain et al. 2010; Waldmann et al. 2012, 2013; Waldmann 2012, 2014; Gibson et al. 2012; Crouzet et al. 2012; Berta et al. 2012; Morello et al. 2014; Danielski et al. 2014; Kreidberg et al. 2014).”
Fast Direct Methods for Gaussian Processes (2014, methodology): “, assuming a model of a Gaussian process. This is a useful model because the data is “contaminated” by stochastic stellar variability and other noisy processes without a physical model. Gibson et al. [20] demonstrated the use of Gaussian processes as a model for the stochastic noise sources in a pho”
The prevalence of dust on the exoplanet HD 189733b from Hubble and Spitzer observations (2012, methodology): “Gibson et al. (2011), and Gibson et al. (2012b) reanalyse the spectroscopic data, and discuss this issue.”
DETERMINING THE MASS OF KEPLER-78b WITH NONPARAMETRIC GAUSSIAN PROCESS ESTIMATION (2015, methodology): “Gibson et al. (2012) reanalyzed the spectroscopic data with a Gaussian process to marginalize ignorance of the functional form of the systematics, giving larger but more robust errors.”
DETECTION OF H2O AND EVIDENCE FOR TiO/VO IN AN ULTRA-HOT EXOPLANET ATMOSPHERE (2016, methodology): “For the white lightcurve fitting, we treated the data as a Gaussian process (GP), using the approach described in Gibson et al. (2012).”
Precise time series photometry for the Kepler-2.0 mission (2014, background): “For example, the interested reader will find a thorough, textbook-level introduction to GPs in Rasmussen & Williams (2006), or a more succinct introduction in the context of modelling systematics in highprecision stellar photometry in Gibson et al. (2012).”
THE FLAT TRANSMISSION SPECTRUM OF THE SUPER-EARTH GJ1214b FROM WIDE FIELD CAMERA 3 ON THE HUBBLE SPACE TELESCOPE (2011, methodology): “In such cases, the Gaussian process method proposed by Gibson et al. (2011b) may be a useful alternative, and one that would appropriately account for the uncertainty involved in the systematics correction.”
An HST optical-to-near-IR transmission spectrum of the hot Jupiter WASP-19b: detection of atmospheric water and likely absence of TiO (2013, methodology): “However, with our low resolution, it is hard to tell whether the water features may be slightly muted at a similar level to XO-1b, since 1σ shifts in only two of our bins would show a smaller feature consistent with low cloud cover.”