Importance nested sampling with normalising flows
Abstract We present an improved version of the nested sampling algorithm nessai in which the core algorithm is modified to use importance weights. In the modified algorithm, samples are drawn from a mixture of normalising flows and the requirement for samples to be independently and identically dist...
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Published in | Machine learning: science and technology Vol. 4; no. 3; pp. 35011 - 35036 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Bristol
IOP Publishing
01.09.2023
|
Subjects | |
Online Access | Get full text |
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Summary: | Abstract
We present an improved version of the nested sampling algorithm
nessai
in which the core algorithm is modified to use importance weights. In the modified algorithm, samples are drawn from a mixture of normalising flows and the requirement for samples to be independently and identically distributed (i.i.d.) according to the prior is relaxed. Furthermore, it allows for samples to be added in any order, independently of a likelihood constraint, and for the evidence to be updated with batches of samples. We call the modified algorithm
i-nessai
. We first validate
i-nessai
using analytic likelihoods with known Bayesian evidences and show that the evidence estimates are unbiased in up to 32 dimensions. We compare
i-nessai
to standard
nessai
for the analytic likelihoods and the Rosenbrock likelihood, the results show that
i-nessai
is consistent with
nessai
whilst producing more precise evidence estimates. We then test
i-nessai
on 64 simulated gravitational-wave signals from binary black hole coalescence and show that it produces unbiased estimates of the parameters. We compare our results to those obtained using standard
nessai
and
dynesty
and find that
i-nessai
requires 2.68 and 13.3 times fewer likelihood evaluations to converge, respectively. We also test
i-nessai
of an 80 s simulated binary neutron star signal using a reduced-order-quadrature basis and find that, on average, it converges in 24 min, whilst only requiring
1.01
×
10
6
likelihood evaluations compared to
1.42
×
10
6
for
nessai
and
4.30
×
10
7
for
dynesty
. These results demonstrate that
i-nessai
is consistent with
nessai
and
dynesty
whilst also being more efficient. |
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Bibliography: | MLST-100966.R1 |
ISSN: | 2632-2153 2632-2153 |
DOI: | 10.1088/2632-2153/acd5aa |