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Register a new userStellar Content from high resolution galactic spectra via Maximum A Posteriori
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P. Ocvirk
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This paper describes STECMAP (STEllar Content via Maximum A Posteriori), a flexible, non-parametric inversion method for the interpretation of the integrated light spectra of galaxies, based on synthetic spectra of single stellar populations (SSPs). We focus on the recovery of a galaxys star formation history and stellar age-metallicity relation. We use the high resolution SSPs produced by PEGASE-HR to quantify the informational content of the wavelength range 4000 - 6800 Angstroms. A detailed investigation of the properties of the corresponding simplified linear problem is performed using singular value decomposition. It turns out to be a powerful tool for explaining and predicting the behaviour of the inversion. We provide means of quantifying the fundamental limitations of the problem considering the intrinsic properties of the SSPs in the spectral range of interest, as well as the noise in these models and in the data. We performed a systematic simulation campaign and found that, when the time elapsed between two bursts of star formation is larger than 0.8 dex, the properties of each episode can be constrained with a precision of 0.04 dex in age and 0.02 dex in metallicity from high quality data (R=10 000, signal-to-noise ratio SNR=100 per pixel), not taking model errors into account. The described methods and error estimates will be useful in the design and in the analysis of extragalactic spectroscopic surveys.
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We introduce STECKMAP (STEllar Content and Kinematics via Maximum A Posteriori), a method to recover the kinematical properties of a galaxy simultaneously with its stellar content from integrated light spectra. It is an extension of STECMAP (astro-ph/0505209) to the general case where the velocity distribution of the underlying stars is also unknown. %and can be used as is for the analysis of large sets of data. The reconstructions of the stellar age distribution, the age-metallicity relation, and the Line-Of-Sight Velocity Distribution (LOSVD) are all non-parametric, i.e. no specific shape is assumed. The only a propri we use are positivity and the requirement that the solution is smooth enough. The smoothness parameter can be set by GCV according to the level of noise in the data in order to avoid overinterpretation. We use single stellar populations (SSP) from PEGASE-HR (R=10000, lambda lambda = 4000-6800 Angstrom, Le Borgne et al. 2004) to test the method through realistic simulations. Non-Gaussianities in LOSVDs are reliably recovered with SNR as low as 20 per 0.2 Angstrom pixel. It turns out that the recovery of the stellar content is not degraded by the simultaneous recovery of the kinematic distribution, so that the resolution in age and error estimates given in Ocvirk et al. 2005 remain appropriate when used with STECKMAP. We also explore the case of age-dependent kinematics (i.e. when each stellar component has its own LOSVD). We separate the bulge and disk components of an idealized simplified spiral galaxy in integrated light from high quality pseudo data (SNR=100 per pixel, R=10000), and constrain the kinematics (mean projected velocity, projected velocity dispersion) and age of both components.
This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic result from extreme value statistics asserts that perturb-max operations generate unbiased samples from the Gibbs distribution using high-dimensional perturbations. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. However, when the perturbations are of low dimension, sampling the perturb-max prediction is as efficient as MAP optimization. This paper shows that the expected value of perturb-max inference with low dimensional perturbations can be used sequentially to generate unbiased samples from the Gibbs distribution. Furthermore the expected value of the maximal perturbations is a natural bound on the entropy of such perturb-max models. A measure concentration result for perturb-max values shows that the deviation of their sampled average from its expectation decays exponentially in the number of samples, allowing effective approximation of the expectation.
We introduce a new algorithm for reinforcement learning called Maximum aposteriori Policy Optimisation (MPO) based on coordinate ascent on a relative entropy objective. We show that several existing methods can directly be related to our derivation. We develop two off-policy algorithms and demonstrate that they are competitive with the state-of-the-art in deep reinforcement learning. In particular, for continuous control, our method outperforms existing methods with respect to sample efficiency, premature convergence and robustness to hyperparameter settings while achieving similar or better final performance.
Gravitational lensing of the CMB is a valuable cosmological signal that correlates to tracers of large-scale structure and acts as a important source of confusion for primordial $B$-mode polarization. State-of-the-art lensing reconstruction analyses use quadratic estimators, which are easily applicable to data. However, these estimators are known to be suboptimal, in particular for polarization, and large improvements are expected to be possible for high signal-to-noise polarization experiments. We develop a method and numerical code, $rm{LensIt}$, that is able to find efficiently the most probable lensing map, introducing no significant approximations to the lensed CMB likelihood, and applicable to beamed and masked data with inhomogeneous noise. It works by iteratively reconstructing the primordial unlensed CMB using a deflection estimate and its inverse, and removing residual lensing from these maps with quadratic estimator techniques. Roughly linear computational cost is maintained due to fast convergence of iterative searches, combined with the local nature of lensing. The method achieves the maximal improvement in signal to noise expected from analytical considerations on the unmasked parts of the sky. Delensing with this optimal map leads to forecast tensor-to-scalar ratio parameter errors improved by a factor $simeq 2 $ compared to the quadratic estimator in a CMB stage IV configuration.
We present an extended ultraviolet-blue (850-4700 AA) library of theoretical stellar spectral energy distributions (SEDs) computed at high resolution, R= 50,000. The UVBLUE grid, as we named the library, is based on LTE calculations carried out with ATLAS9 and SYNTHE codes developed by R. L. Kurucz and consists of nearly 1800 entries that cover a large volume of the parameter space. It spans a range in effective temperature from 3000 to 50,000 K, the surface gravity ranges from log g= 0.0 to 5.0 with a step of 0.5 dex, while seven chemical compositions are considered: [Fe/H]= -2.0, -1.5, -1.0, -0.5, +0.0, +0.3 and +0.5 dex. For its coverage across the H-R diagram, this library is the most comprehensive one ever computed at high resolution in the short-wavelength spectral range, and useful application can be foreseen both for the study of single stars and in population synthesis models of galaxies and other stellar systems.
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