Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Nonparametric Monotone Regression   In many applications there is interest in estimating the relation between a
predictor and an outcome when the relation is known to be monotone or otherwise
constrained due to the physical processes involved. We consider one such
application--inferring time-resolved aerosol concentration from a low-cost
differential pressure sensor. The objective is to estimate a monotone function
and make inference on the scaled first derivative of the function. We proposed
Bayesian nonparametric monotone regression which uses a Bernstein polynomial
basis to construct the regression function and puts a Dirichlet process prior
on the regression coefficients. The base measure of the Dirichlet process is a
finite mixture of a mass point at zero and a truncated normal. This
construction imposes monotonicity while clustering the basis functions.
Clustering the basis functions reduces the parameter space and allows the
estimated regression function to be linear. With the proposed approach we can
make closed-formed inference on the derivative of the estimated function
including full quantification of uncertainty. In a simulation study the
proposed method performs similar to other monotone regression approaches when
the true function is wavy but performs better when the true function is linear.
We apply the method to estimate time-resolved aerosol concentration with a
newly-developed portable aerosol monitor. The R package bnmr is made available
to implement the method.

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The categories of this paper are: acc-phys
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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: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: adap-org