25,261 research outputs found
Segmentation of the Poisson and negative binomial rate models: a penalized estimator
We consider the segmentation problem of Poisson and negative binomial (i.e.
overdispersed Poisson) rate distributions. In segmentation, an important issue
remains the choice of the number of segments. To this end, we propose a
penalized log-likelihood estimator where the penalty function is constructed in
a non-asymptotic context following the works of L. Birg\'e and P. Massart. The
resulting estimator is proved to satisfy an oracle inequality. The performances
of our criterion is assessed using simulated and real datasets in the RNA-seq
data analysis context
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
Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
In performing a Bayesian analysis of astronomical data, two difficult
problems often emerge. First, in estimating the parameters of some model for
the data, the resulting posterior distribution may be multimodal or exhibit
pronounced (curving) degeneracies, which can cause problems for traditional
MCMC sampling methods. Second, in selecting between a set of competing models,
calculation of the Bayesian evidence for each model is computationally
expensive. The nested sampling method introduced by Skilling (2004), has
greatly reduced the computational expense of calculating evidences and also
produces posterior inferences as a by-product. This method has been applied
successfully in cosmological applications by Mukherjee et al. (2006), but their
implementation was efficient only for unimodal distributions without pronounced
degeneracies. Shaw et al. (2007), recently introduced a clustered nested
sampling method which is significantly more efficient in sampling from
multimodal posteriors and also determines the expectation and variance of the
final evidence from a single run of the algorithm, hence providing a further
increase in efficiency. In this paper, we build on the work of Shaw et al. and
present three new methods for sampling and evidence evaluation from
distributions that may contain multiple modes and significant degeneracies; we
also present an even more efficient technique for estimating the uncertainty on
the evaluated evidence. These methods lead to a further substantial improvement
in sampling efficiency and robustness, and are applied to toy problems to
demonstrate the accuracy and economy of the evidence calculation and parameter
estimation. Finally, we discuss the use of these methods in performing Bayesian
object detection in astronomical datasets.Comment: 14 pages, 11 figures, submitted to MNRAS, some major additions to the
previous version in response to the referee's comment
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