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

Emulating Simulations of Cosmic Dawn for 21cm Power Spectrum Constraints on Cosmology, Reionization, and X-ray Heating

Current and upcoming radio interferometric experiments are aiming to make a statistical characterization of the high-redshift 21cm fluctuation signal spanning the hydrogen reionization and X-ray heating epochs of the universe. However, connecting 21cm statistics to underlying physical parameters is complicated by the theoretical challenge of modeling the relevant physics at computational speeds quick enough to enable exploration of the high dimensional and weakly constrained parameter space. In this work, we use machine learning algorithms to build a fast emulator that mimics expensive simulations of the 21cm signal across a wide parameter space to high precision. We embed our emulator within a Markov-Chain Monte Carlo framework, enabling it to explore the posterior distribution over a large number of model parameters, including those that govern the Epoch of Reionization, the Epoch of X-ray Heating, and cosmology. As a worked example, we use our emulator to present an updated parameter constraint forecast for the Hydrogen Epoch of Reionization Array experiment, showing that its characterization of a fiducial 21cm power spectrum will considerably narrow the allowed parameter space of reionization and heating parameters, and could help strengthen Planck's constraints on $\sigma_8$. We provide both our generalized emulator code and its implementation specifically for 21cm parameter constraints as publicly available software.Comment: 22 pages, 9 figures; accepted to Ap

Less Than 2 °C Warming by 2100 Unlikely.

The recently published Intergovernmental Panel on Climate Change (IPCC) projections to 2100 give likely ranges of global temperature increase in four scenarios for population, economic growth and carbon use1. However these projections are not based on a fully statistical approach. Here we use a country-specific version of Kaya's identity to develop a statistically-based probabilistic forecast of CO2 emissions and temperature change to 2100. Using data for 1960-2010, including the UN's probabilistic population projections for all countries2-4, we develop a joint Bayesian hierarchical model for GDP per capita and carbon intensity. We find that the 90% interval for cumulative CO2 emissions includes the IPCC's two middle scenarios but not the extreme ones. The likely range of global temperature increase is 2.0-4.9°C, with median 3.2°C and a 5% (1%) chance that it will be less than 2°C (1.5°C). Population growth is not a major contributing factor. Our model is not a "business as usual" scenario, but rather is based on data which already show the effect of emission mitigation policies. Achieving the goal of less than 1.5°C warming will require carbon intensity to decline much faster than in the recent past