Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unified Bayesian theory of sparse linear regression with nuisance
  parameters   We study frequentist asymptotic properties of Bayesian procedures for
high-dimensional Gaussian sparse regression when unknown nuisance parameters
are involved. Nuisance parameters can be finite-, high-, or
infinite-dimensional. A mixture of point masses at zero and continuous
distributions is used for the prior distribution on sparse regression
coefficients, and appropriate prior distributions are used for nuisance
parameters. The optimal posterior contraction of sparse regression
coefficients, hampered by the presence of nuisance parameters, is also examined
and discussed. It is shown that the procedure yields strong model selection
consistency. A Bernstein-von Mises-type theorem for sparse regression
coefficients is also obtained for uncertainty quantification through credible
sets with guaranteed frequentist coverage. Asymptotic properties of numerous
examples are investigated using the theories developed in this study.

8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th