22,526 research outputs found
Bayesian off-line detection of multiple change-points corrupted by multiplicative noise : application to SAR image edge detection
This paper addresses the problem of Bayesian off-line change-point detection in synthetic aperture radar images. The minimum mean square error and maximum a posteriori estimators of the changepoint positions are studied. Both estimators cannot be implemented because of optimization or integration problems. A practical implementation using Markov chain Monte Carlo methods is proposed. This implementation requires a priori knowledge of the so-called hyperparameters. A hyperparameter estimation procedure is proposed that alleviates the requirement of knowing the values of the hyperparameters. Simulation results on synthetic signals and synthetic aperture radar images are presented
Bayesian detection of embryonic gene expression onset in C. elegans
To study how a zygote develops into an embryo with different tissues,
large-scale 4D confocal movies of C. elegans embryos have been produced
recently by experimental biologists. However, the lack of principled
statistical methods for the highly noisy data has hindered the comprehensive
analysis of these data sets. We introduced a probabilistic change point model
on the cell lineage tree to estimate the embryonic gene expression onset time.
A Bayesian approach is used to fit the 4D confocal movies data to the model.
Subsequent classification methods are used to decide a model selection
threshold and further refine the expression onset time from the branch level to
the specific cell time level. Extensive simulations have shown the high
accuracy of our method. Its application on real data yields both previously
known results and new findings.Comment: Published at http://dx.doi.org/10.1214/15-AOAS820 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Locating and quantifying gas emission sources using remotely obtained concentration data
We describe a method for detecting, locating and quantifying sources of gas
emissions to the atmosphere using remotely obtained gas concentration data; the
method is applicable to gases of environmental concern. We demonstrate its
performance using methane data collected from aircraft. Atmospheric point
concentration measurements are modelled as the sum of a spatially and
temporally smooth atmospheric background concentration, augmented by
concentrations due to local sources. We model source emission rates with a
Gaussian mixture model and use a Markov random field to represent the
atmospheric background concentration component of the measurements. A Gaussian
plume atmospheric eddy dispersion model represents gas dispersion between
sources and measurement locations. Initial point estimates of background
concentrations and source emission rates are obtained using mixed L2-L1
optimisation over a discretised grid of potential source locations. Subsequent
reversible jump Markov chain Monte Carlo inference provides estimated values
and uncertainties for the number, emission rates and locations of sources
unconstrained by a grid. Source area, atmospheric background concentrations and
other model parameters are also estimated. We investigate the performance of
the approach first using a synthetic problem, then apply the method to real
data collected from an aircraft flying over: a 1600 km^2 area containing two
landfills, then a 225 km^2 area containing a gas flare stack
Parameter estimation by implicit sampling
Implicit sampling is a weighted sampling method that is used in data
assimilation, where one sequentially updates estimates of the state of a
stochastic model based on a stream of noisy or incomplete data. Here we
describe how to use implicit sampling in parameter estimation problems, where
the goal is to find parameters of a numerical model, e.g.~a partial
differential equation (PDE), such that the output of the numerical model is
compatible with (noisy) data. We use the Bayesian approach to parameter
estimation, in which a posterior probability density describes the probability
of the parameter conditioned on data and compute an empirical estimate of this
posterior with implicit sampling. Our approach generates independent samples,
so that some of the practical difficulties one encounters with Markov Chain
Monte Carlo methods, e.g.~burn-in time or correlations among dependent samples,
are avoided. We describe a new implementation of implicit sampling for
parameter estimation problems that makes use of multiple grids (coarse to fine)
and BFGS optimization coupled to adjoint equations for the required gradient
calculations. The implementation is "dimension independent", in the sense that
a well-defined finite dimensional subspace is sampled as the mesh used for
discretization of the PDE is refined. We illustrate the algorithm with an
example where we estimate a diffusion coefficient in an elliptic equation from
sparse and noisy pressure measurements. In the example, dimension\slash
mesh-independence is achieved via Karhunen-Lo\`{e}ve expansions
Bayesian detection of piecewise linear trends in replicated time-series with application to growth data modelling
We consider the situation where a temporal process is composed of contiguous
segments with differing slopes and replicated noise-corrupted time series
measurements are observed. The unknown mean of the data generating process is
modelled as a piecewise linear function of time with an unknown number of
change-points. We develop a Bayesian approach to infer the joint posterior
distribution of the number and position of change-points as well as the unknown
mean parameters. A-priori, the proposed model uses an overfitting number of
mean parameters but, conditionally on a set of change-points, only a subset of
them influences the likelihood. An exponentially decreasing prior distribution
on the number of change-points gives rise to a posterior distribution
concentrating on sparse representations of the underlying sequence. A
Metropolis-Hastings Markov chain Monte Carlo (MCMC) sampler is constructed for
approximating the posterior distribution. Our method is benchmarked using
simulated data and is applied to uncover differences in the dynamics of fungal
growth from imaging time course data collected from different strains. The
source code is available on CRAN.Comment: Accepted to International Journal of Biostatistic
Joint segmentation of multivariate astronomical time series : bayesian sampling with a hierarchical model
Astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series. This paper approaches such problems using Bayesian priors to represent relationships between signals with various degrees of certainty, and not just rigid constraints. The segmentation is conducted by using a hierarchical Bayesian approach to a piecewise constant Poisson rate model. A Gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters. Results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm
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