The PHOENIX Exoplanet Retrieval Algorithm and Using H−^{-} Opacity as a Probe in Ultra-hot Jupiters

Atmospheric retrievals are now a standard tool to analyze observations of exoplanet atmospheres. This data-driven approach quantitatively compares atmospheric models to observations in order to estimate atmospheric properties and their uncertainties. In this paper, we introduce a new retrieval package, the PHOENIX Exoplanet Retrieval Analysis (PETRA). PETRA places the PHOENIX atmosphere model in a retrieval framework, allowing us to combine the strengths of a well-tested and widely-used atmosphere model with the advantages of retrieval algorithms. We validate PETRA by retrieving on simulated data for which the true atmospheric state is known. We also show that PETRA can successfully reproduce results from previously published retrievals of WASP-43b and HD 209458b. For the WASP-43b results, we show the effect that different line lists and line profile treatments have on the retrieved atmospheric properties. Lastly, we describe a novel technique for retrieving the temperature structure and $e^{-}$ density in ultra-hot Jupiters using H$^{-}$ opacity, allowing us to probe atmospheres devoid of most molecular features with JWST.Comment: 17 pages, 18 figures. Accepted for publication in A

Rank-normalization, folding, and localization: An improved R^\widehat{R} for assessing convergence of MCMC

Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic $\widehat{R}$ of Gelman and Rubin (1992) has serious flaws. Traditional $\widehat{R}$ will fail to correctly diagnose convergence failures when the chain has a heavy tail or when the variance varies across the chains. In this paper we propose an alternative rank-based diagnostic that fixes these problems. We also introduce a collection of quantile-based local efficiency measures, along with a practical approach for computing Monte Carlo error estimates for quantiles. We suggest that common trace plots should be replaced with rank plots from multiple chains. Finally, we give recommendations for how these methods should be used in practice.Comment: Minor revision for improved clarit

Testing cosmic acceleration for w(z)w(z) parameterizations using fgasf_{gas} measurements in galaxy clusters

In this paper we study the cosmic acceleration for five dynamical dark energy models whose equation of state varies with redshift. The cosmological parameters of these models are constrained by performing a MCMC analysis using mainly gas mass fraction, $f_{gas}$, measurements in two samples of galaxy clusters: one reported by Allen et al. (2004), which consists of $42$ points spanning the redshift range $0.05<z<1.1$, and the other by Hasselfield et al. (2013) from the Atacama Cosmology Telescope survey, which consists of $91$ data points in the redshift range $0.118 < \mathrm{z} < 1.36$. In addition, we perform a joint analysis with the measurements of the Hubble parameter $H(z)$, baryon acoustic oscillations and the cosmic microwave background radiation from WMAP and Planck measurements to estimate the equation of state parameters. We obtained that both $f_{gas}$ samples provide consistent constraints on the cosmological parameters. We found that the $f_{gas}$ data is consistent at the $2\sigma$ confidence level with a cosmic slowing down of the acceleration at late times for most of the parameterizations. The constraints of the joint analysis using WMAP and Planck measurements show that this trend disappears. We have confirmed that the $f_{gas}$ probe provides competitive constraints on the dark energy parameters when a $w(z)$ is assumed.Comment: 21 pages, 8 Tables, 11 Figures, accepted for publication in MNRA

A Tutorial on Fisher Information

In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different statistical paradigms. First, in the frequentist paradigm, Fisher information is used to construct hypothesis tests and confidence intervals using maximum likelihood estimators; second, in the Bayesian paradigm, Fisher information is used to define a default prior; lastly, in the minimum description length paradigm, Fisher information is used to measure model complexity

Muon Simulations for Super-Kamiokande, KamLAND and CHOOZ

Muon backgrounds at Super-Kamiokande, KamLAND and CHOOZ are calculated using MUSIC. A modified version of the Gaisser sea level muon distribution and a well-tested Monte Carlo integration method are introduced. Average muon energy, flux and rate are tabulated. Plots of average energy and angular distributions are given. Implications on muon tracker design for future experiments are discussed.Comment: Revtex4 33 pages, 16 figures and 4 table