A Method for 21cm Power Spectrum Estimation in the Presence of Foregrounds

21cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However, realizing this promise will require the extraction of a cosmological power spectrum from beneath overwhelmingly large sources of foreground contamination. In this paper, we develop a unified matrix-based framework for foreground subtraction and power spectrum estimation, which allows us to quantify the errors and biases that arise in the power spectrum as a result of foreground subtraction. We find that existing line-of-sight foreground subtraction proposals can lead to substantial mode-mixing as well as residual noise and foreground biases, whereas our proposed inverse variance foreground subtraction eliminates noise and foreground biases, gives smaller error bars, and produces less correlated measurements of the power spectrum. We also numerically confirm the intuitive belief in the literature that 21cm foreground subtraction is best done using frequency rather than angular information.Comment: 24 pages, 11 figures; replaced with accepted PRD version (minor editorial changes to text; methods, results, and conclusions unchanged

Constraining cosmology and ionization history with combined 21 cm power spectrum and global signal measurements

Improvements in current instruments and the advent of next-generation instruments will soon push observational 21 cm cosmology into a new era, with high significance measurements of both the power spectrum and the mean ("global") signal of the 21 cm brightness temperature. In this paper we use the recently commenced Hydrogen Epoch of Reionization Array as a worked example to provide forecasts on astrophysical and cosmological parameter constraints. In doing so we improve upon previous forecasts in a number of ways. First, we provide updated forecasts using the latest best-fit cosmological parameters from the Planck satellite, exploring the impact of different Planck datasets on 21 cm experiments. We also show that despite the exquisite constraints that other probes have placed on cosmological parameters, the remaining uncertainties are still large enough to have a non-negligible impact on upcoming 21 cm data analyses. While this complicates high-precision constraints on reionization models, it provides an avenue for 21 cm reionization measurements to constrain cosmology. We additionally forecast HERA's ability to measure the ionization history using a combination of power spectrum measurements and semi-analytic simulations. Finally, we consider ways in which 21 cm global signal and power spectrum measurements can be combined, and propose a method by which power spectrum results can be used to train a compact parameterization of the global signal. This parameterization reduces the number of parameters needed to describe the global signal, increasing the likelihood of a high significance measurement.Comment: 16 pages, 8 figures. Revised to match accepted MNRAS version: expanded discussion of covariances between astrophysics and cosmology in Section 2.2, including two new figures; short discussion relating to KL modes added to Section 4; final results unchange

A conjugate prior for discrete hierarchical log-linear models

In Bayesian analysis of multi-way contingency tables, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of conjugate priors for the wide class of discrete hierarchical log-linear models, which includes the class of graphical models. These priors are defined as the Diaconis--Ylvisaker conjugate priors on the log-linear parameters subject to "baseline constraints" under multinomial sampling. We also derive the induced prior on the cell probabilities and show that the induced prior is a generalization of the hyper Dirichlet prior. We show that this prior has several desirable properties and illustrate its usefulness by identifying the most probable decomposable, graphical and hierarchical log-linear models for a six-way contingency table.Comment: Published in at http://dx.doi.org/10.1214/08-AOS669 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Jacquet Conjecture on the Local Converse Problem for p-adic GL_n

Based on previous results of Jiang, Nien and the third author, we prove that any two minimax unitarizable supercuspidals of GL_N that have the same depth and central character admit a special pair of Whittaker functions. This result gives a new reduction towards a final proof of Jacquet's conjecture on the local converse problem for GL_N. As a corollary of our result, we prove Jacquet's conjecture for GL_N, when N is prime

Affirmative Action & Negative Action: How Jian Li\u27s Case Can Benefit Asian Americans

In October 2006, Asian American student Jian D filed a civil rights complaint against Princeton University claiming that Princeton\u27s affirmative action policies were discriminatory. Li argues that affirmative action gives preferences to non-Asian minorities at the expense of Asian students. Li\u27s case aligns the interests of Asian Americans with Whites who challenge affirmative action and suggests that such policies are inherently discriminatory because they exclude students based on race and sacrifice merit. This Article argues that Li\u27s exclusion is not due to affirmative action but is likely due to negative action, the unfavorable treatment of Asian Americans relative to Whites. Affirmative action is not discriminatory because it considers a multitude of factors, including race, to achieve a diverse student population. Nor does affirmative action sacrifice merit; rather, it redefines merit in a way that can benefit students of all racial groups. On the other hand, negative action is discriminatory and prevalent. Whether it takes the form of legacies, admission limits or racial group comparisons, negative action discriminates against Asian Americans based on their race and contributes to existing inequalities in admissions. Framing Li\u27s case as a claim against negative action instead of affirmative action is a more accurate analysis that attacks ongoing discrimination in admissions, but preserves affirmative action\u27s benefit for all racial groups

Precision Calibration of Radio Interferometers Using Redundant Baselines

Growing interest in 21 cm tomography has led to the design and construction of broadband radio interferometers with low noise, moderate angular resolution, high spectral resolution, and wide fields of view. With characteristics somewhat different from traditional radio instruments, these interferometers may require new calibration techniques in order to reach their design sensitivities. Self-calibration or redundant calibration techniques that allow an instrument to be calibrated off complicated sky emission structures are ideal. In particular, the large number of redundant baselines possessed by these new instruments makes redundant calibration an especially attractive option. In this paper, we explore the errors and biases in existing redundant calibration schemes through simulations, and show how statistical biases can be eliminated. We also develop a general calibration formalism that includes both redundant baseline methods and basic point source calibration methods as special cases, and show how slight deviations from perfect redundancy and coplanarity can be taken into account.Comment: 18 pages, 13 figures; Replaced to match accepted MNRAS versio