Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in
  Ultrahigh-Dimensional Settings   Bayesian model selection procedures based on nonlocal alternative prior
densities are extended to ultrahigh dimensional settings and compared to other
variable selection procedures using precision-recall curves. Variable selection
procedures included in these comparisons include methods based on $g$-priors,
reciprocal lasso, adaptive lasso, scad, and minimax concave penalty criteria.
The use of precision-recall curves eliminates the sensitivity of our
conclusions to the choice of tuning parameters. We find that Bayesian variable
selection procedures based on nonlocal priors are competitive to all other
procedures in a range of simulation scenarios, and we subsequently explain this
favorable performance through a theoretical examination of their consistency
properties. When certain regularity conditions apply, we demonstrate that the
nonlocal procedures are consistent for linear models even when the number of
covariates $p$ increases sub-exponentially with the sample size $n$. A model
selection procedure based on Zellner's $g$-prior is also found to be
competitive with penalized likelihood methods in identifying the true model,
but the posterior distribution on the model space induced by this method is
much more dispersed than the posterior distribution induced on the model space
by the nonlocal prior methods. We investigate the asymptotic form of the
marginal likelihood based on the nonlocal priors and show that it attains a
unique term that cannot be derived from the other Bayesian model selection
procedures. We also propose a scalable and efficient algorithm called
Simplified Shotgun Stochastic Search with Screening (S5) to explore the
enormous model space, and we show that S5 dramatically reduces the computing
time without losing the capacity to search the interesting region in the model
space. The S5 algorithm is available in an \verb R ~package {\it BayesS5} on
\texttt{CRAN}.

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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an