Towards reliable uncertainties in IR interferometry: the bootstrap for correlated statistical and systematic errors

Lachaume, R.; Jordán, Andrés; Brahm, R.; Boyajian, Tabetha S.; Braun, Kaspar von; Berger, J.‐P.

doi:10.1093/mnras/stz114

Cited by 13 publications

(13 citation statements)

References 52 publications

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“…In order to compare these covariance matrix prescriptions, I will use the typical example of an under-resolved centro-symmetric source observed at a four-telescope facility in medium spectral resolution. It is close to the context under which I serendipitiously noticed the effect while modelling stellar diameters (see Lachaume et al, 2019). The p y t h o n code to produce the results (figures in this paper) is available on github.…”

Section: Using the Naïve Estimatesupporting

confidence: 64%

“…In spite of strong evidence of correlations in the data, due to redundancy (Monnier, 2007, in the case of closure phases), calibration (Perrin, 2003), or atmospheric biases acting on all spectral channels in the same way (Lawson, 2000), only a few authors (Perrin et al, 2004;Absil et al, 2006;Berger et al, 2006;Lachaume et al, 2019;Kammerer et al, 2020) have accounted for these correlations while most assumed statistically independent errors. In particular, the only interferometric instrument I know of with a data processing software taking into account one source of correlations-calibration-is FLUOR 2 (at IOTA 3 , then CHARA 4 , Perrin et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, ignoring correlations may lead to significant errors in model parameters as Lachaume et al (2019) evidenced with stellar diameters using PIONIER 6 (Le Bouquin et al, 2011) data at the VLTI. Also Kammerer et al (2020) established that accounting for correlations is necessary to achieve a higher contrast ratio in companion detection using GRAVITY (Eisenhauer et al, 2011) at the VLTI.…”

Section: Introductionmentioning

confidence: 99%

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Bias-free model fitting of correlated data in interferometry

Lachaume

2021

Preprint

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In optical and infrared long-baseline interferometry, data often display significant correlated errors because of uncertain multiplicative factors such as the instrumental transfer function or the pixel-tovisibility matrix. In the context of model fitting, this situation often leads to a significant bias in the model parameters. In the most severe cases this can can result in a fit lying outside of the range of measurement values. This is known in nuclear physics as Peelle's Pertinent Puzzle. I show how this arises in the context of interferometry and determine that the relative bias is of the order of the square root of the correlated component of the relative uncertainty times the number of measurements. It impacts preferentially large data sets, such as those obtained in medium to high spectral resolution. I then give a conceptually simple and computationally cheap way to avoid the issue: model the data without covariances, estimate the covariance matrix by error propagation using the modelled data instead of the actual data, and perform the model fitting using the covariance matrix. I also show that a more imprecise but also unbiased result can be obtained from ignoring correlations in the model fitting.

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Section: Using the Naïve Estimatesupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bias-free model fitting of correlated data in interferometry

Lachaume

2021

Preprint

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“…We note that all targets had sequences observed over at least two nights, with the exception of 37 Lib and β Aql which had their bright and faint sequences observed on the same night. As discussed in detail by Lachaume et al (2019), there are correlated uncertainties for observations taken within a given night (e.g. atmospheric effects, instrumental drifts), reducing the accuracy of the resulting diameter fits.…”

Section: Interferometric Observationsmentioning

confidence: 99%

Precision angular diameters for 16 southern stars with VLTI/PIONIER

Rains

Ireland

White

et al. 2020

Monthly Notices of the Royal Astronomical Society

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In the current era of Gaia and large, high signal to noise stellar spectroscopic surveys, there is an unmet need for a reliable library of fundamentally calibrated stellar effective temperatures based on accurate stellar diameters. Here we present a set of precision diameters and temperatures for a sample of 6 dwarf, 5 sub-giant, and 5 giant stars observed with the PIONIER beam combiner at the VLTI. Science targets were observed in at least two sequences with five unique calibration stars each for accurate visibility calibration and to reduce the impact of bad calibrators. We use the standard PIONIER data reduction pipeline, but bootstrap over interferograms, in addition to employing a Monte-Carlo approach to account for correlated errors by sampling stellar parameters, limb darkening coefficients, and fluxes, as well as predicted calibrator angular diameters. The resulting diameters were then combined with bolometric fluxes derived from broadband Hipparcos-Tycho photometry and MARCS model bolometric corrections, plus parallaxes from Gaia to produce effective temperatures, physical radii, and luminosities for each star observed. Our stars have mean angular diameter and temperatures uncertainties of 0.8% and 0.9% respectively, with our sample including diameters for 10 stars with no pre-existing interferometric measurements. The remaining stars are consistent with previous measurements, with the exception of a single star which we observe here with PIONIER at both higher resolution and greater sensitivity than was achieved in earlier work.

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“…While Lachaume et al (2019) proposed to use the bootstrapping method (i.e. sampling with replacement, Efron & Tibshirani 1986) in order to obtain the multivariate probability density function of the squared visibility amplitudes and the closure phases, Gravity Collaboration et al (2020) extracted the covariances of the complex visibilities directly from the data.…”

Section: Introductionmentioning

confidence: 99%

Increasing the achievable contrast of infrared interferometry with an error correlation model

Kammerer

Mérand

Ireland

et al. 2020

A&A

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Context. Interferometric observables are strongly correlated, yet it is common practice to ignore these correlations in the data analysis process. Aims. We develop an empirical model for the correlations present in Very Large Telescope Interferometer GRAVITY data and show that properly accounting for them yields fainter detection limits and increases the reliability of potential detections. Methods. We extracted the correlations of the (squared) visibility amplitudes and the closure phases directly from intermediate products of the GRAVITY data reduction pipeline and fitted our empirical models to them. Then, we performed model fitting and companion injection and recovery tests with both simulated and real GRAVITY data, which are affected by correlated noise, and compared the results when ignoring the correlations and when properly accounting for them with our empirical models. Results. When accounting for the correlations, the faint source detection limits improve by a factor of up to ∼ 2 at angular separations > 20 mas. For commonly used detection criteria based on χ 2 statistics, this mostly results in claimed detections being more reliable. Conclusions. Ignoring the correlations present in interferometric data is a dangerous assumption which might lead to a large number of false detections. The commonly used detection criteria (e.g. in the model fitting pipeline CANDID) are only reliable when properly accounting for the correlations; furthermore, instrument teams should work on providing full covariance matrices instead of statistically independent error bars as part of the official data reduction pipelines.

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Towards reliable uncertainties in IR interferometry: the bootstrap for correlated statistical and systematic errors

Cited by 13 publications

References 52 publications

Bias-free model fitting of correlated data in interferometry

Bias-free model fitting of correlated data in interferometry

Precision angular diameters for 16 southern stars with VLTI/PIONIER

Increasing the achievable contrast of infrared interferometry with an error correlation model

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