Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Probabilistic Numerical Integration with Tree-Based Models   Bayesian quadrature (BQ) is a method for solving numerical integration
problems in a Bayesian manner, which allows users to quantify their uncertainty
about the solution. The standard approach to BQ is based on a Gaussian process
(GP) approximation of the integrand. As a result, BQ is inherently limited to
cases where GP approximations can be done in an efficient manner, thus often
prohibiting very high-dimensional or non-smooth target functions. This paper
proposes to tackle this issue with a new Bayesian numerical integration
algorithm based on Bayesian Additive Regression Trees (BART) priors, which we
call BART-Int. BART priors are easy to tune and well-suited for discontinuous
functions. We demonstrate that they also lend themselves naturally to a
sequential design setting and that explicit convergence rates can be obtained
in a variety of settings. The advantages and disadvantages of this new
methodology are highlighted on a set of benchmark tests including the Genz
functions, and on a Bayesian survey design problem.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph