38,760 research outputs found
Bayesian separation of spectral sources under non-negativity and full additivity constraints
This paper addresses the problem of separating spectral sources which are
linearly mixed with unknown proportions. The main difficulty of the problem is
to ensure the full additivity (sum-to-one) of the mixing coefficients and
non-negativity of sources and mixing coefficients. A Bayesian estimation
approach based on Gamma priors was recently proposed to handle the
non-negativity constraints in a linear mixture model. However, incorporating
the full additivity constraint requires further developments. This paper
studies a new hierarchical Bayesian model appropriate to the non-negativity and
sum-to-one constraints associated to the regressors and regression coefficients
of linear mixtures. The estimation of the unknown parameters of this model is
performed using samples generated using an appropriate Gibbs sampler. The
performance of the proposed algorithm is evaluated through simulation results
conducted on synthetic mixture models. The proposed approach is also applied to
the processing of multicomponent chemical mixtures resulting from Raman
spectroscopy.Comment: v4: minor grammatical changes; Signal Processing, 200
Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging
Mapping white matter tracts is an essential step towards understanding brain
function. Diffusion Magnetic Resonance Imaging (dMRI) is the only noninvasive
technique which can detect in vivo anisotropies in the 3-dimensional diffusion
of water molecules, which correspond to nervous fibers in the living brain. In
this process, spectral data from the displacement distribution of water
molecules is collected by a magnetic resonance scanner. From the statistical
point of view, inverting the Fourier transform from such sparse and noisy
spectral measurements leads to a non-linear regression problem. Diffusion
tensor imaging (DTI) is the simplest modeling approach postulating a Gaussian
displacement distribution at each volume element (voxel). Typically the
inference is based on a linearized log-normal regression model that can fit the
spectral data at low frequencies. However such approximation fails to fit the
high frequency measurements which contain information about the details of the
displacement distribution but have a low signal to noise ratio. In this paper,
we directly work with the Rice noise model and cover the full range of
-values. Using data augmentation to represent the likelihood, we reduce the
non-linear regression problem to the framework of generalized linear models.
Then we construct a Bayesian hierarchical model in order to perform
simultaneously estimation and regularization of the tensor field. Finally the
Bayesian paradigm is implemented by using Markov chain Monte Carlo.Comment: 37 pages, 3 figure
Likelihood informed dimension reduction for inverse problems in remote sensing of atmospheric constituent profiles
We use likelihood informed dimension reduction (LIS) (T. Cui et al. 2014) for
inverting vertical profile information of atmospheric methane from ground based
Fourier transform infrared (FTIR) measurements at Sodankyl\"a, Northern
Finland. The measurements belong to the word wide TCCON network for greenhouse
gas measurements and, in addition to providing accurate greenhouse gas
measurements, they are important for validating satellite observations. LIS
allows construction of an efficient Markov chain Monte Carlo sampling algorithm
that explores only a reduced dimensional space but still produces a good
approximation of the original full dimensional Bayesian posterior distribution.
This in effect makes the statistical estimation problem independent of the
discretization of the inverse problem. In addition, we compare LIS to a
dimension reduction method based on prior covariance matrix truncation used
earlier (S. Tukiainen et al. 2016)
Assessing the relationship between spectral solar irradiance and stratospheric ozone using Bayesian inference
We investigate the relationship between spectral solar irradiance (SSI) and
ozone in the tropical upper stratosphere. We find that solar cycle (SC) changes
in ozone can be well approximated by considering the ozone response to SSI
changes in a small number individual wavelength bands between 176 and 310 nm,
operating independently of each other. Additionally, we find that the ozone
varies approximately linearly with changes in the SSI. Using these facts, we
present a Bayesian formalism for inferring SC SSI changes and uncertainties
from measured SC ozone profiles. Bayesian inference is a powerful,
mathematically self-consistent method of considering both the uncertainties of
the data and additional external information to provide the best estimate of
parameters being estimated. Using this method, we show that, given measurement
uncertainties in both ozone and SSI datasets, it is not currently possible to
distinguish between observed or modelled SSI datasets using available estimates
of ozone change profiles, although this might be possible by the inclusion of
other external constraints. Our methodology has the potential, using wider
datasets, to provide better understanding of both variations in SSI and the
atmospheric response.Comment: 21 pages, 4 figures, Journal of Space Weather and Space Climate
(accepted), pdf version is in draft mode of Space Weather and Space Climat
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