Source: https://aiawww.cfa.harvard.edu/astrostat/Stat310_1617/
Timestamp: 2019-04-26 10:29:16+00:00

Document:
Abstract: Useful information to calibrate instruments used for astrophysical measurements is usually obtained by observing different sources with well-understood characteristics simultaneously with different detectors. To do this well, however, requires a careful modeling of the mean signals, the intrinsic source variations, and measurement errors. Because our data are typically large (>>30) photon counts, we propose an approximate log-normal model, with the advantage of permitting imperfection in the multiplicative mean modeling to be captured by the residual variance. The calibration then takes an analytically tractable form of power shrinkage, with a half-variance adjustment to ensure an unbiased multiplicative mean model on the original scale. We demonstrate the model fitting via data from a combination of observations of AGNs and spectral line emission from the supernova remnant E0102, obtained with a variety of X-ray telescopes like Chandra, XMM-Newton, Suzaku, Swift, etc. The data are compiled by IACHEC researchers.
Abstract: We propose a new soft clustering scheme for classifying different galaxy activity classes using 4 emission-line ratios: log(NII]/Halpha), log([SII]/Halpha), log([OI]/Halpha) and log([OIII]/Halpha). We fit a big number of multivariate Gaussian distributions to the Sloan Digital Sky Survey (SDSS) dataset in order to capture local structures and subsequently group the multivariate Gaussian distributions to represent the complex multi-dimensional structure of the joint distribution of the 4 galaxy activity classes. We also introduce linear multi-dimensional decision surfaces using support vector machines and we also discuss the sensitivity of our classification scheme when the OI is not available.
Abstract: Cataloguing, the act of identifying emission sources in an observed image and determining their properties, is a fundamental operation in astronomy. However, when there are populations of dim sources that are maginally detectable or when the sources are crowded, a single catalogue cannot capture the ambiguities of source identification. Considering cataloguing as a Bayesian inference problem, we implement a probabilistic cataloguer that samples the posterior distribution of possible catalogues. This ensemble of catalogues better recovers dim and crowded sources. Because the number of sources is an unknown, the catalogue space is transdimensional, introducing many challenges, like how to define a prior on the number of sources.
Abstract: We study the problem of model-free dependence detection. This problem can be difficult even when the marginal distributions are known. We explain this difficulty by showing the impossibility to uniformly consistently distinguish degeneracy from independence with any single test. To make model-free dependence detection a tractable problem, we introduce the concept of binary expansion statistics (BEStat) and propose the binary expansion testing (BET) framework. Through simple mathematics, we convert the dependence detection problem to a multiple testing problem. Besides being model-free, the BET also enjoys many other advantages which include (1) invariance to monotone marginal transformations, (2) clear interpretability of local relationships upon rejection, and (3) close connections to computing for efficient algorithms. We illustrate the BET by studying the distribution of the brightest stars in the night sky.
Abstract: Type Ia supernovae (SN Ia) are faraway exploding stars used as ``standardizable candles'' to determine cosmological distances, measure the accelerating expansion of the Universe, and constrain the properties of dark energy. Inferring peak luminosities of SN Ia from distance-independent observables, such as the shapes and colors of their light curves (time series), underpins the evidence for cosmic acceleration. SN Ia with broader, slower declining optical light curves are more luminous ("broader-brighter") and those with redder colors are dimmer. But the "redder-dimmer" color-luminosity relation widely used in cosmological SN Ia analyses confounds its two separate physical origins. An intrinsic correlation arises from the physics of exploding white dwarfs, while interstellar dust in the host galaxy also makes SN Ia appear redder and dimmer (extinguished). However, conventional SN Ia cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape, which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects, resulting in unusually low color-magnitude slopes. I have constructed a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of an intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude slope differs from the host galaxy dust law, this convolution results in a specific curve of mean extinguished absolute magnitude vs. apparent color. I incorporated these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze an optical light curve dataset comprising 277 nearby SN Ia at z < 0.10. The conventional linear fit obtains an effective color-magnitude slope of 3. My model finds an intrinsic slope of 2.2±0.3 and a distinct dust law of R_B = 3.7±0.3, consistent with the average properties of Milky Way dust, while correcting a systematic distance bias of ~0.10 mag in the tails of the apparent color distribution.
Abstract: Optical observers have monitored the Galactic Bulge for twenty five years, and have discovered roughly 18,000 unique microlensing event candidates.The number is now sufficient that overdensities, such as those associated with clusters of stars, can be identified and studied. We report on the first investigations of such overdensities, which happen to have been produced by Galactic globular clusters lying along directions to the Bulge. We expect that similar studies, using even more data to be collected by new wide-area surveys, will play important roles in identifying and studying the properties of globular clusters and dwarf galaxies in our own and other galaxies. In this talk I will also present an overview of other microlensing-related opportunities for learning which may be addressed through statistical studies.
Abstract: There are many ways to derive catalogs of astronomical objects from images, and most of them fail badly in the crowded-field limit. We are currently exploring two novel approaches. Compressed sensing allows us to rapidly find candidate stars in an image. The "probabilistic catalog" technique produces samples from the posterior probability distribution function on the space of all possible catalogs, allowing trivial marginalization of errors introduced by close neighbors. We have applied this technique to two globular clusters, and found this approach to yield impressive results. We are currently pondering a hybrid of these two techniques that retains the speed of the former and flexibility of the latter, and we welcome input from the astrostats pundits!
Abstract: As the light from quasars transverses different paths through gravitational field of a galaxy, it generated multiple images on earth with time delay, which provides a way to measure some cosmological parameters, i.e. Hubble constant. The magnitude of images fluctuating over time gives a light curve, as the brightness of source varies as well as microlensing, an low frequency extrinsic variation. Multiple images from the same lensed light source, usually double- or quadruply, produce multiple light curves with time shift. Moreover, lights from multiple filters can be measured for the same system. Estimating time delay remains challenging because of observation seasonal gap, microlensing, etc. In the paper, we introduced a hierarchical Bayesian statespace model to estimate time delay among multiple time series. Our method provides a principled way for estimating time delay, which can take into account different modelings of intrinsic variation of light source and microlensing, which adds another layer of variation independently on these light curves. It can also combine information from multiple filters. We applied our method to Q0957+561 two-filters doubly lensed data and showed benefits from combining data from multiple filters.
Abstract: A Gaussian error assumption, i.e., an assumption that the data are observed up to Gaussian noises, can bias any parameter estimation in the presence of outliers. A heavy tailed error assumption based on Student's t-distribution helps reduce the bias, but it may be less efficient in estimating parameters because the heavy-tail assumption is uniformly applied to most of the normally observed data. We propose a mixture error assumption that selectively converts Gaussian errors into Student's t errors according to latent outlier indicators, leveraging the best of the Gaussian and Student's t errors; a parameter estimation becomes not only robust but also accurate. Using simulated hospital profiling data and astronomical time series of brightness data, we demonstrate the potential for the proposed mixture error assumption to estimate parameters accurately in the presence of outliers.
Abstract: The radial velocity technique is one of the two main approaches for detecting planets outside our solar system, or exoplanets as they are known in astronomy. The method works by detecting the Doppler shift resulting from the motion of a host star caused by an orbiting planet. Unfortunately, this Doppler signal is typically contaminated by various ``stellar activity" phenomena, such as dark spots on the star surface. A principled approach to recovering the Doppler signal was proposed by Rajpaul et al. (2015), and involves the use of dependent Gaussian processes to jointly model the corrupted Doppler signal and multiple proxies for the stellar activity. Our work in progress aims to extend the Rajpaul et al. (2015) approach by (i) proposing more informative stellar activity proxies, (ii) extending the model to a class of models that can capture our new proxies, and (iii) proposing a model selection procedure to find the best model in the class.
Abstract: In physics, searches for new particles or new phenomena are mainly conducted via multiple hypothesis testing. Separate tests of hypothesis are implemented at different locations producing an ensemble of local p-values, and the smallest is reported as evidence for the new emission, once adequately adjusted to control the false detection rate. An alternative way to tackle the problem in statistical terms is via Testing One Hypothesis Multiple times (TOHM). A stochastic process or a random field indexed by the various alternatives is used to combine the outcomes of each tests into a single global p-value, that can be used as as overall standard of evidence. The resulting statistical tool is particularly well suited for searches in high energy physics and astrophysics, where the significance level necessary to claim a discovery is usually of order of $5\sigma$. Specifically, TOHM targets the identification of rare signals, and provides valid inference with respect to stringent significance requirements, without encountering the problem of over-conservativeness.
Abstract: Current and upcoming large-scale surveys will collect multi-band images (photometry) for billions of galaxies. Before these data can be used for many science applications, however, we need to infer distances (redshifts) to them. We outline how rigorous (hierarchical) Bayesian inference -- with some "machine learning" -- can be used to quickly and robustly derive joint "photometric redshift (photo-z)" probability distribution functions (PDFs) to individual galaxies and their parent populations from training data in the "big data" limit. In tandem, we describe the ways we deal with noisy and censored data as well as domain mismatches from a statistical and computational perspective. We validate our methods using mock data and showcase preliminary results on a subset of SDSS data; a restricted implementation using HSC data also appears to perform well. Our next steps will be modeling galaxy redshifting using a continuous, latent process and determining how sensitively our redshift posteriors depend on aspects of our training data. Our code and tests can be found on GitHub.
Abstract: Measurements of radial velocity variations from the spectroscopic monitoring of stars and their companions are essential for a broad swath of astrophysics; these measurements provide access to the fundamental physical properties that dictate all phases of stellar evolution and facilitate the quantitative study of planetary systems. The conversion of those measurements into both constraints on the orbital architecture and individual component spectra can be a serious challenge, however, especially for extreme flux ratio systems and observations with relatively low sensitivity. Gaussian processes define sampling distributions of flexible, continuous functions that are well-motivated for modeling stellar spectra, enabling proficient searches for companion lines in time-series spectra. We introduce a new technique for spectral disentangling, where the posterior distributions of the orbital parameters and intrinsic, rest-frame stellar spectra are explored simultaneously without needing to invoke cross-correlation templates. To demonstrate its potential, this technique is deployed on red-optical time-series spectra of the mid-M-dwarf eclipsing binary LP661-13, recently discovered by the MEarth project at Harvard. We report orbital parameters with improved precision compared to traditional radial velocity analysis and successfully reconstruct the primary and secondary spectra. We discuss potential applications for other stellar and exoplanet radial velocity techniques and extensions to time-variable spectra. The code used in this analysis is freely available as an open-source Python package.
Siemiginowska, A. / Connors, A. / Kashyap, V. / Zezas, A. / Devor, J. / Drake, J. / Kolaczyk, E. / Izem, R. / Kang, H. / Yu, Y. / van Dyk, D.
van Dyk, D. / Ratner, M. / Jin, J. / Park, T. / CCW / Zezas, A. / Hong, J. / Siemiginowska, A. & Kashyap, V. / Meng, X.-L.
Lee, H. / Connors, A. / Protopapas, P. / McDowell, J., / Izem, R. / Blondin, S. / Lee, H. / Zezas, A., & Lee, H. / Liu, J.C. / van Dyk, D. / Rice, J.
Connors, A., & Protopapas, P. / Steiner, J. / Baines, P. / Zezas, A. / Aldcroft, T.
Meng X.-L. / Meng X.-L., K. Mandel / A. Siemiginowska / S. Vrtilek & L. Bornn / Lazhi W. / D. Jones / R. Wong / Xu J. / van Dyk D. / Feigelson E. / Gopalan G. / Min S. / Smith R. / Zezas A. / van Dyk D. / Hyungsuk T. / Czerny, B. / Jones D. / Liu K. / Zezas A.
Vegetabile, B. & Aldcroft, T., / H. Jae Sub / Siemiginowska, A. & Kashyap, V. / Pankratius, V. / Tak, H. / Brenneman, L. / Johnson, J. / Lynch, R.C. / Fan, M.J. / Meng, X.-L. / Gopalan, G. / Jiao, X. / Si, S. / Udaltsova, I. & Zezas, A. / Wang, L. / Tak, H. / Eadie, G. / Czekala, I. / Stenning, D. / Stampoulis, V. / Aitkin, M. / Algeri, S. / Barnacka, A.
DePasquale, J. / Tak, H. / Meng, X.-L. / Jones, D. / Huang, J. / Blanchard, P. / Chen, Y. & Wang, X. / Tak, H. / Mandel, K. / Jiao, X. / Wang, X. & Chen, Y. / IACHEC WG / Si, S. / Drake, J. / Stampoulis, V. / Algeri, S. / Stein, N. / Chunzhe, Z. / Andrews, J. / Vrtilek, S. / Udaltsova, I. & Stampoulis, V.
Wang, X. & Chen, Y. / Kashyap, V., Siemiginowska, A., & Zezas, A. / Stampoulis, V. / Portillo, S. / Zhang, K. / Mandel, K. / DiStefano, R. / Finkbeiner, D. & Meade, B. / Gong, R. / Shihao Y. / Zhirui, H. / Xufei, W. / Campos, L. / Tak, H. / Xufei, W. / Jones, D. / Algeri, S. / Speagle, J. / Czekala, I.

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