Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Quantile Trend Filtering on Graphs using Shrinkage Priors   Quantiles are useful characteristics of random variables that can provide
substantial information of distributions compared with commonly used summary
statistics such as means. In this paper, we propose a Bayesian quantile trend
filtering method to estimate non-stationary trend of quantiles on graphs. We
introduce general shrinkage priors for graph differences to induce locally
adaptive Bayesian inference on trends. Introducing so-called shadow priors with
multivariate truncated distribution for local scale parameters and mixture
representation of the asymmetric Laplace distribution, we provide a simple
Gibbs sampling algorithm to generate posterior samples. We also develop
variational Bayes approximation to quickly compute point estimates (e.g.
posterior means). The numerical performance of the proposed method is
demonstrated through simulation study with time series data, application of
quantile regression and robust spatial quantile smoothing.

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The categories of this paper are: math
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci