Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating multivariate posterior distribution functions from Monte
  Carlo samples for sequential Bayesian inference   An important feature of Bayesian statistics is the opportunity to do
sequential inference: the posterior distribution obtained after seeing a
dataset can be used as prior for a second inference. However, when Monte Carlo
sampling methods are used for inference, we only have a set of samples from the
posterior distribution. To do sequential inference, we then either have to
evaluate the second posterior at only these locations and reweight the samples
accordingly, or we can estimate a functional description of the posterior
probability distribution from the samples and use that as prior for the second
inference. Here, we investigated to what extent we can obtain an accurate joint
posterior from two datasets if the inference is done sequentially rather than
jointly, under the condition that each inference step is done using Monte Carlo
sampling. To test this, we evaluated the accuracy of kernel density estimates,
Gaussian mixtures, vine copulas and Gaussian processes in approximating
posterior distributions, and then tested whether these approximations can be
used in sequential inference. In low dimensionality, Gaussian processes are
more accurate, whereas in higher dimensionality Gaussian mixtures or vine
copulas perform better. In our test cases, posterior approximations are
preferable over direct sample reweighting, although joint inference is still
preferable over sequential inference. Since the performance is case-specific,
we provide an R package mvdens with a unified interface for the density
approximation methods.

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org