Harmonic Hidden Markov Models for the Study of EEG Signals

5 pagesInternational audienceA new approach for modelling multichannel signals via hidden states models in the time-frequency space is described. Multichannel signals are expanded using a local cosine basis, and the (time-frequency labelled) coefficients are modelled as multivariate random variables, whose distribution is governed by a (hidden) Markov chain. Several models are described, together with maximum likelihood estimation algorithms. The model is applied to electroencephalogram data, and it is shown that variance-covariance matrices labelled by sensor and frequency indices can yield relevant informations on the analyzed signals. This is examplified by a case study on the characterization of alpha waves desynchronization in the context of multiple sclerosis disease

The Distribution of High Redshift Galaxy Colors: Line of Sight Variations in Neutral Hydrogen Absorption

We model, via Monte Carlo simulations, the distribution of observed U-B, B-V, V-I galaxy colors in the range 1.75<z<5 caused by variations in the line-of-sight opacity due to neutral hydrogen (HI). We also include HI internal to the source galaxies. Even without internal HI absorption, comparison of the distribution of simulated colors to the analytic approximations of Madau (1995) and Madau et al (1996) reveals systematically different mean colors and scatter. Differences arise in part because we use more realistic distributions of column densities and Doppler parameters. However, there are also mathematical problems of applying mean and standard deviation opacities, and such application yields unphysical results. These problems are corrected using our Monte Carlo approach. Including HI absorption internal to the galaxies generaly diminishes the scatter in the observed colors at a given redshift, but for redshifts of interest this diminution only occurs in the colors using the bluest band-pass. Internal column densities < 10^17 cm^2 do not effect the observed colors, while column densities > 10^18 cm^2 yield a limiting distribution of high redshift galaxy colors. As one application of our analysis, we consider the sample completeness as a function of redshift for a single spectral energy distribution (SED) given the multi-color selection boundaries for the Hubble Deep Field proposed by Madau et al (1996). We argue that the only correct procedure for estimating the z>3 galaxy luminosity function from color-selected samples is to measure the (observed) distribution of redshifts and intrinsic SED types, and then consider the variation in color for each SED and redshift. A similar argument applies to the estimation of the luminosity function of color-selected, high redshift QSOs.Comment: accepted for publication in ApJ; 25 pages text, 14 embedded figure

A Preferential Attachment Model for the Stellar Initial Mass Function

Accurate specification of a likelihood function is becoming increasingly difficult in many inference problems in astronomy. As sample sizes resulting from astronomical surveys continue to grow, deficiencies in the likelihood function lead to larger biases in key parameter estimates. These deficiencies result from the oversimplification of the physical processes that generated the data, and from the failure to account for observational limitations. Unfortunately, realistic models often do not yield an analytical form for the likelihood. The estimation of a stellar initial mass function (IMF) is an important example. The stellar IMF is the mass distribution of stars initially formed in a given cluster of stars, a population which is not directly observable due to stellar evolution and other disruptions and observational limitations of the cluster. There are several difficulties with specifying a likelihood in this setting since the physical processes and observational challenges result in measurable masses that cannot legitimately be considered independent draws from an IMF. This work improves inference of the IMF by using an approximate Bayesian computation approach that both accounts for observational and astrophysical effects and incorporates a physically-motivated model for star cluster formation. The methodology is illustrated via a simulation study, demonstrating that the proposed approach can recover the true posterior in realistic situations, and applied to observations from astrophysical simulation data

Gravelamps: gravitational wave lensing mass profile model selection

We present the package Gravelamps, which is designed to analyze gravitationally lensed gravitational wave signals in order to constrain the mass density profile of the lensing object. Gravelamps does this via parameter estimation using the framework of bilby, which enables estimation of both the lens and the source parameters. The package can be used to study both microlensing and macrolensing cases, where the lensing mass distribution is described by a point-mass and extended-mass density profile, respectively. It allows the user to easily and freely switch between a full wave optics and approximate geometric optics description. The performance of Gravelamps is demonstrated via simulated analysis of both microlensing and macrolensing events, illustrating its capability for both parameter estimation and model selection in the wave optics and hybrid environments. To further demonstrate the utility of the package, the real gravitational-wave event GW170809 was analyzed using Gravelamps; this event was found to yield no strong evidence supporting the lensing hypothesis, consistent with previously published results

Global yield curve dynamics and interactions: a dynamic Nelson-Siegel approach

The popular Nelson-Siegel (1987) yield curve is routinely fit to cross sections of intra-country bond yields, and Diebold and Li (2006) have recently proposed a dynamized version. In this paper we extend Diebold-Li to a global context, modeling a potentially large set of country yield curves in a framework that allows for both global and country-specific factors. In an empirical analysis of term structures of government bond yields for the Germany, Japan, the U.K. and the U.S., we find that global yield factors do indeed exist and are economically important, generally explaining significant fractions of country yield curve dynamics, with interesting differences across countries

Gravelamps: gravitational wave lensing mass profile model selection

We present the package Gravelamps, which is designed to analyze gravitationally lensed gravitational wave signals in order to constrain the mass density profile of the lensing object. Gravelamps does this via parameter estimation using the framework of bilby, which enables estimation of both the lens and the source parameters. The package can be used to study both microlensing and macrolensing cases, where the lensing mass distribution is described by a point-mass and extended-mass density profile, respectively. It allows the user to easily and freely switch between a full wave optics and approximate geometric optics description. The performance of Gravelamps is demonstrated via simulated analysis of both microlensing and macrolensing events, illustrating its capability for both parameter estimation and model selection in the wave optics and hybrid environments. To further demonstrate the utility of the package, the real gravitational-wave event GW170809 was analyzed using Gravelamps; this event was found to yield no strong evidence supporting the lensing hypothesis, consistent with previously published results