Model selection in cosmology

Model selection aims to determine which theoretical models are most plausible given some data, without necessarily considering preferred values of model parameters. A common model selection question is to ask when new data require introduction of an additional parameter, describing a newly discovered physical effect. We review model selection statistics, then focus on the Bayesian evidence, which implements Bayesian analysis at the level of models rather than parameters. We describe our CosmoNest code, the first computationally efficient implementation of Bayesian model selection in a cosmological context. We apply it to recent WMAP satellite data, examining the need for a perturbation spectral index differing from the scaleinvariant (Harrison–Zel'dovich) case

Foundations of Inference

We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symmetries. With other applications such as measure theory in mind, our derivations assume minimal symmetries, relying on neither negation nor continuity nor differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of quantifying rules that form the familiar probability calculus. We also derive a unique quantification of divergence, entropy and information

Feedback Heating by Cosmic Rays in Clusters of Galaxies

Recent observations show that the cooling flows in the central regions of galaxy clusters are highly suppressed. Observed AGN-induced cavities/bubbles are a leading candidate for suppressing cooling, usually via some form of mechanical heating. At the same time, observed X-ray cavities and synchrotron emission point toward a significant non-thermal particle population. Previous studies have focused on the dynamical effects of cosmic-ray pressure support, but none have built successful models in which cosmic-ray heating is significant. Here we investigate a new model of AGN heating, in which the intracluster medium is efficiently heated by cosmic-rays, which are injected into the ICM through diffusion or the shredding of the bubbles by Rayleigh-Taylor or Kelvin-Helmholtz instabilities. We include thermal conduction as well. Using numerical simulations, we show that the cooling catastrophe is efficiently suppressed. The cluster quickly relaxes to a quasi-equilibrium state with a highly reduced accretion rate and temperature and density profiles which match observations. Unlike the conduction-only case, no fine-tuning of the Spitzer conduction suppression factor f is needed. The cosmic ray pressure, P_c/P_g <~ 0.1 and dP_c/dr <~ 0.1 \rho g, is well within observational bounds. Cosmic ray heating is a very attractive alternative to mechanical heating, and may become particularly compelling if GLAST detects the gamma-ray signature of cosmic-rays in clusters.Comment: Revised version accepted for publication in MNRAS. Significantly expanded discussion and new simulations exploring parameter space/model robustness; conclusions unchange

Nested sampling for materials: the case of hard spheres

The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by studying the three dimensional hard sphere model. Having obtained the partition function, we show how easy it is to calculate the compressibility and the free energy as functions of the packing fraction and local order, verifying that the transition to crystallinity has a very small barrier, and that the entropic contribution of jammed states to the free energy is negligible for packing fractions above the phase transition. We quantify the previously proposed schematic phase diagram and estimate the extent of the region of jammed states. We find that within our samples, the maximally random jammed configuration is surprisingly disordered

Application of Bayesian model averaging to measurements of the primordial power spectrum

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model Evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940 < n_s < 1.000, where n_s is specified at a pivot scale 0.015 Mpc^{-1}. For the tensors model averaging can tighten the credible upper limit, depending on prior assumptions.Comment: 7 pages with 7 figures include

Quantum critical dynamics of a S = 1/2 antiferromagnetic Heisenberg chain studied by 13C-NMR spectroscopy

We present a 13C-NMR study of the magnetic field driven transition to complete polarization of the S=1/2 antiferromagnetic Heisenberg chain system copper pyrazine dinitrate Cu(C_4H_4N_2)(NO_3)_2 (CuPzN). The static local magnetization as well as the low-frequency spin dynamics, probed via the nuclear spin-lattice relaxation rate 1/T_1, were explored from the low to the high field limit and at temperatures from the quantum regime (k_B T << J) up to the classical regime (k_B T >> J). The experimental data show very good agreement with quantum Monte Carlo calculations over the complete range of parameters investigated. Close to the critical field, as derived from static experiments, a pronounced maximum in 1/T_1 is found which we interpret as the finite-temperature manifestation of a diverging density of zero-energy magnetic excitations at the field-driven quantum critical point.Comment: 5 pages, 4 figure

A method for spatial deconvolution of spectra

A method for spatial deconvolution of spectra is presented. It follows the same fundamental principles as the ``MCS image deconvolution algorithm'' (Magain, Courbin, Sohy, 1998) and uses information contained in the spectrum of a reference Point Spread Function (PSF) to spatially deconvolve spectra of very blended sources. An improved resolution rather than an infinite one is aimed at, overcoming the well known problem of ``deconvolution artefacts''. As in the MCS algorithm, the data are decomposed into a sum of analytical point sources and a numerically deconvolved background, so that the spectrum of extended sources in the immediate vicinity of bright point sources may be accurately extracted and sharpened. The algorithm has been tested on simulated data including seeing variation as a function of wavelength and atmospheric refraction. It is shown that the spectra of severely blended point sources can be resolved while fully preserving the spectrophotometric properties of the data. Extended objects ``hidden'' by bright point sources (up to 4-5 magnitudes brighter) can be accurately recovered as well, provided the data have a sufficiently high total signal-to-noise ratio (200-300 per spectral resolution element). Such spectra are relatively easy to obtain, even down to faint magnitudes, within a few hours of integration time with 10m class telescopes.Comment: 18 pages, 6 postscript figures, in press in Ap

Extending emission line Doppler tomography ; mapping modulated line flux

Emission line Doppler tomography is a powerful tool that resolves the accretion flow in binaries on micro-arcsecond scales using time-resolved spectroscopy. I present an extension to Doppler tomography that relaxes one of its fundamental axioms and permits the mapping of time-dependent emission sources. Significant variability on the orbital period is a common characteristic of the emission sources that are observed in the accretion flows of cataclysmic variables and X-ray binaries. Modulation Doppler tomography maps sources varying harmonically as a function of the orbital period through the simultaneous reconstruction of three Doppler tomograms. One image describes the average flux distribution like in standard tomography, while the two additional images describe the variable component in terms of its sine and cosine amplitudes. I describe the implementation of such an extension in the form of the maximum entropy based fitting code MODMAP. Test reconstructions of synthetic data illustrate that the technique is robust and well constrained. Artifact free reconstructions of complex emission distributions can be achieved under a wide range of signal to noise levels. An application of the technique is illustrated by mapping the orbital modulations of the asymmetric accretion disc emission in the dwarf nova IP Pegasi.Comment: 8 pages, 4 figures; accepted for publication in MNRA