arXiv subjects

Jessi Cisewski-Kehe

Publications and source records attributed to Jessi Cisewski-Kehe.

29 records · Page 2Linked to original sources

arXiv2020

A Hermite-Gaussian Based Radial Velocity Estimation Method

As the first successful technique used to detect exoplanets orbiting distant stars, the Radial Velocity Method aims to detect a periodic Doppler shift in a star's spectrum. We introduce a new, mathematically rigorous, approach to detect such a signal that accounts for functional relationships of neighboring wavelengths, minimizes the role of wavelength interpolation, accounts for heteroskedastic noise, and easily allows for statistical inference. Using Hermite-Gaussian functions, we show that the problem of detecting a Doppler shift in the spectrum can be reduced to linear regression in many settings. A simulation study demonstrates that the proposed method is able to accurately estimate an individual spectrum's radial velocity with precision below 0.3 m/s. Furthermore, the new method outperforms the traditional Cross-Correlation Function approach by reducing the root mean squared error up to 15 cm/s. The proposed method is also demonstrated on a new set of observations from the EXtreme PREcision Spectrometer (EXPRES) for the star 51 Pegasi, and successfully recovers estimates that agree well with previous studies of this planetary system. Data and Python3 code associated with this work can be found at https://github.com/parkerholzer/hgrv_method. The method is also implemented in the open source R package rvmethod.

astro-ph.EP↗

arXiv2020

Trend Filtering -- I. A Modern Statistical Tool for Time-Domain Astronomy and Astronomical Spectroscopy

The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. For example, in the time domain, an astronomical object may exhibit a smoothly varying intensity that is occasionally interrupted by abrupt dips or spikes. Likewise, in the spectroscopic setting, a noiseless spectrum typically contains intervals of relative smoothness mixed with localized higher frequency components such as emission peaks and absorption lines. In this work, we present trend filtering, a modern nonparametric statistical tool that yields significant improvements in this broad problem space of denoising $spatially$ $heterogeneous$ signals. When the underlying signal is spatially heterogeneous, trend filtering is superior to any statistical estimator that is a linear combination of the observed data---including kernel smoothers, LOESS, smoothing splines, Gaussian process regression, and many other popular methods. Furthermore, the trend filtering estimate can be computed with practical and scalable efficiency via a specialized convex optimization algorithm, e.g. handling sample sizes of $n\gtrsim10^7$ within a few minutes. In a companion paper, we explicitly demonstrate the broad utility of trend filtering to observational astronomy by carrying out a diverse set of spectroscopic and time-domain analyses.

astro-ph.IM↗

arXiv2020

Trend Filtering -- II. Denoising Astronomical Signals with Varying Degrees of Smoothness

Trend filtering---first introduced into the astronomical literature in Paper I of this series---is a state-of-the-art statistical tool for denoising one-dimensional signals that possess varying degrees of smoothness. In this work, we demonstrate the broad utility of trend filtering to observational astronomy by discussing how it can contribute to a variety of spectroscopic and time-domain studies. The observations we discuss are (1) the Lyman-$α$ forest of quasar spectra; (2) more general spectroscopy of quasars, galaxies, and stars; (3) stellar light curves with planetary transits; (4) eclipsing binary light curves; and (5) supernova light curves. We study the Lyman-$α$ forest in the greatest detail---using trend filtering to map the large-scale structure of the intergalactic medium along quasar-observer lines of sight. The remaining studies share broad themes of: (1) estimating observable parameters of light curves and spectra; and (2) constructing observational spectral/light-curve templates. We also briefly discuss the utility of trend filtering as a tool for one-dimensional data reduction and compression.

astro-ph.IM↗

arXiv2019

Realizing the potential of astrostatistics and astroinformatics

This Astro2020 State of the Profession Consideration White Paper highlights the growth of astrostatistics and astroinformatics in astronomy, identifies key issues hampering the maturation of these new subfields, and makes recommendations for structural improvements at different levels that, if acted upon, will make significant positive impacts across astronomy.

astro-ph.IM↗

arXiv2019

A Preferential Attachment Model for the Stellar Initial Mass Function

Accurate specification of a likelihood function is becoming increasingly difficult in many inference problems in astronomy. As sample sizes resulting from astronomical surveys continue to grow, deficiencies in the likelihood function lead to larger biases in key parameter estimates. These deficiencies result from the oversimplification of the physical processes that generated the data, and from the failure to account for observational limitations. Unfortunately, realistic models often do not yield an analytical form for the likelihood. The estimation of a stellar initial mass function (IMF) is an important example. The stellar IMF is the mass distribution of stars initially formed in a given cluster of stars, a population which is not directly observable due to stellar evolution and other disruptions and observational limitations of the cluster. There are several difficulties with specifying a likelihood in this setting since the physical processes and observational challenges result in measurable masses that cannot legitimately be considered independent draws from an IMF. This work improves inference of the IMF by using an approximate Bayesian computation approach that both accounts for observational and astrophysical effects and incorporates a physically-motivated model for star cluster formation. The methodology is illustrated via a simulation study, demonstrating that the proposed approach can recover the true posterior in realistic situations, and applied to observations from astrophysical simulation data.

astro-ph.IM↗

arXiv2019

Modeling the Echelle Spectra Continuum with Alpha Shapes and Local Regression Fitting

Continuum normalization of echelle spectra is an important data analysis step that is difficult to automate. Polynomial fitting requires a reasonably high order model to follow the steep slope of the blaze function. However, in the presence of deep spectral lines, a high order polynomial fit can result in ripples in the normalized continuum that increase errors in spectral analysis. Here, we present two algorithms for flattening the spectrum continuum. The Alpha-shape Fitting to Spectrum algorithm (AFS) is completely data-driven, using an alpha shape to obtain an initial estimate of the blaze function. The Alpha-shape and Lab Source Fitting to Spectrum algorithm (ALSFS) incorporates a continuum constraint from a lab source reference spectrum for the blaze function estimation. These algorithms are tested on a simulated spectrum, where we demonstrate improved normalization compared to polynomial regression for continuum fitting. We show an additional application, using the algorithms for mitigation of spatially correlated quantum efficiency variations and fringing in the CCD detector of the EXtreme PREcision Spectrometer (EXPRES).

astro-ph.IM↗

arXiv2019

Finding cosmic voids and filament loops using topological data analysis

(abridged) We present the Significant Cosmic Holes in Universe (SCHU) method for identifying cosmic voids and loops of filaments in cosmological datasets and assigning their statistical significance using techniques from topological data analysis. Persistent homology is used to find different dimensional holes. For dark matter halo catalogs and galaxy surveys, the 0-, 1-, and 2-dimensional holes can be identified with clusters, loops of filaments, and voids. The procedure overlays halos/galaxies on a 3D grid, and a distance-to-measure (DTM) function is calculated at each point of the grid. A filtration is generated over the lower-level sets of the DTM across increasing threshold values. The filtered simplicial complex can be used to summarize the birth/death times of the different dimension homology group generators (i.e., the holes). Persistence diagrams are produced from the dimension and birth/death times of each homology group generator. Using the persistence diagrams and bootstrap sampling, we explain how $p$-values can be assigned to each homology group generator. The homology group generators on a persistence diagram are not, in general, uniquely located back in the original dataset volume so we propose a method for finding a representation of the homology group generators. This method provides a novel, statistically rigorous approach for locating informative generators in cosmological datasets, which may be useful for providing complementary cosmological constraints on the effects of, for example, the sum of the neutrino masses. The method is tested on a Voronoi foam simulation, and then applied to a subset of the SDSS galaxy survey and a cosmological simulation. Lastly, we calculate Betti functions for two of the MassiveNuS simulations and discuss implications for using the persistent homology of the density field to help break degeneracy in the cosmological parameters.

astro-ph.CO↗

arXiv2018

Measuring precise radial velocities and cross-correlation function line-profile variations using a Skew Normal density

Stellar activity is one of the primary limitations to the detection of low-mass exoplanets using the radial-velocity (RV) technique. We propose to estimate the variations in shape of the CCF by fitting a Skew Normal (SN) density which, unlike the commonly employed Normal density, includes a skewness parameter to capture the asymmetry of the CCF induced by stellar activity and the convective blueshift. The performances of the proposed method are compared to the commonly employed Normal density using both simulations and real observations, with different levels of activity and signal-to-noise ratio. When considering real observations, the correlation between the RV and the asymmetry of the CCF and between the RV and the width of the CCF are stronger when using the parameters estimated with the SN density rather than the ones obtained with the commonly employed Normal density. Using the proposed SN approach, the uncertainties estimated on the RV defined as the median of the SN are on average 10% smaller than the uncertainties calculated on the mean of the Normal. The uncertainties estimated on the asymmetry parameter of the SN are on average 15% smaller than the uncertainties measured on the Bisector Inverse Slope Span (BIS SPAN), which is the commonly used parameter to evaluate the asymmetry of the CCF. We also propose a new model to account for stellar activity when fitting a planetary signal to RV data. Based on simple simulations, we were able to demonstrate that this new model improves the planetary detection limits by 12% compared to the model commonly used to account for stellar activity. The SN density is a better model than the Normal density for characterizing the CCF since the correlations used to probe stellar activity are stronger and the uncertainties of the RV estimate and the asymmetry of the CCF are both smaller.

astro-ph.EP↗

arXiv2018

Incorporating Uncertainties in Atomic Data Into the Analysis of Solar and Stellar Observations: A Case Study in Fe XIII

Information about the physical properties of astrophysical objects cannot be measured directly but is inferred by interpreting spectroscopic observations in the context of atomic physics calculations. Ratios of emission lines, for example, can be used to infer the electron density of the emitting plasma. Similarly, the relative intensities of emission lines formed over a wide range of temperatures yield information on the temperature structure. A critical component of this analysis is understanding how uncertainties in the underlying atomic physics propagates to the uncertainties in the inferred plasma parameters. At present, however, atomic physics databases do not include uncertainties on the atomic parameters and there is no established methodology for using them even if they did. In this paper we develop simple models for the uncertainties in the collision strengths and decay rates for Fe XIII and apply them to the interpretation of density sensitive lines observed with the EUV Imagining spectrometer (EIS) on Hinode. We incorporate these uncertainties in a Bayesian framework. We consider both a pragmatic Bayesian method where the atomic physics information is unaffected by the observed data, and a fully Bayesian method where the data can be used to probe the physics. The former generally increases the uncertainty in the inferred density by about a factor of 5 compared with models that incorporate only statistical uncertainties. The latter reduces the uncertainties on the inferred densities, but identifies areas of possible systematic problems with either the atomic physics or the observed intensities.

astro-ph.SR↗

arXiv2018

Statistical challenges in the search for dark matter

The search for the particle nature of dark matter has given rise to a number of experimental, theoretical and statistical challenges. Here, we report on a number of these statistical challenges and new techniques to address them, as discussed in the DMStat workshop held Feb 26 - Mar 3 2018 at the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Alberta.

hep-ph↗

arXiv2018

Functional Summaries of Persistence Diagrams

One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However, persistence diagrams do not naturally lend themselves to statistical goals, such as inferring certain population characteristics, because their complicated structure makes common algebraic operations--such as addition, division, and multiplication-- challenging (e.g., the mean might not be unique). To bypass these issues, several functional summaries of persistence diagrams have been proposed in the literature (e.g. landscape and silhouette functions). The problem of analyzing a set of persistence diagrams then becomes the problem of analyzing a set of functions, which is a topic that has been studied for decades in statistics. First, we review the various functional summaries in the literature and propose a unified framework for the functional summaries. Then, we generalize the definition of persistence landscape functions, establish several theoretical properties of the persistence functional summaries, and demonstrate and discuss their performance in the context of classification using simulated prostate cancer histology data, and two-sample hypothesis tests comparing human and monkey fibrin images, after developing a simulation study using a new data generator we call the Pickup Sticks Simulator (STIX).

stat.ME↗