9,336 research outputs found
A Nonparametric Bayesian Approach to Copula Estimation
We propose a novel Dirichlet-based P\'olya tree (D-P tree) prior on the
copula and based on the D-P tree prior, a nonparametric Bayesian inference
procedure. Through theoretical analysis and simulations, we are able to show
that the flexibility of the D-P tree prior ensures its consistency in copula
estimation, thus able to detect more subtle and complex copula structures than
earlier nonparametric Bayesian models, such as a Gaussian copula mixture.
Further, the continuity of the imposed D-P tree prior leads to a more favorable
smoothing effect in copula estimation over classic frequentist methods,
especially with small sets of observations. We also apply our method to the
copula prediction between the S\&P 500 index and the IBM stock prices during
the 2007-08 financial crisis, finding that D-P tree-based methods enjoy strong
robustness and flexibility over classic methods under such irregular market
behaviors
Independence clustering (without a matrix)
The independence clustering problem is considered in the following
formulation: given a set of random variables, it is required to find the
finest partitioning of into clusters such that the
clusters are mutually independent. Since mutual independence is
the target, pairwise similarity measurements are of no use, and thus
traditional clustering algorithms are inapplicable. The distribution of the
random variables in is, in general, unknown, but a sample is available.
Thus, the problem is cast in terms of time series. Two forms of sampling are
considered: i.i.d.\ and stationary time series, with the main emphasis being on
the latter, more general, case. A consistent, computationally tractable
algorithm for each of the settings is proposed, and a number of open directions
for further research are outlined
Nonparametric Hierarchical Clustering of Functional Data
In this paper, we deal with the problem of curves clustering. We propose a
nonparametric method which partitions the curves into clusters and discretizes
the dimensions of the curve points into intervals. The cross-product of these
partitions forms a data-grid which is obtained using a Bayesian model selection
approach while making no assumptions regarding the curves. Finally, a
post-processing technique, aiming at reducing the number of clusters in order
to improve the interpretability of the clustering, is proposed. It consists in
optimally merging the clusters step by step, which corresponds to an
agglomerative hierarchical classification whose dissimilarity measure is the
variation of the criterion. Interestingly this measure is none other than the
sum of the Kullback-Leibler divergences between clusters distributions before
and after the merges. The practical interest of the approach for functional
data exploratory analysis is presented and compared with an alternative
approach on an artificial and a real world data set
RevBayes: Bayesian Phylogenetic Inference Using Graphical Models and an Interactive Model-Specification Language.
Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]
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