Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Using flexible noise models to avoid noise model misspecification in
  inference of differential equation time series models   When modelling time series, it is common to decompose observed variation into
a "signal" process, the process of interest, and "noise", representing nuisance
factors that obfuscate the signal. To separate signal from noise, assumptions
must be made about both parts of the system. If the signal process is
incorrectly specified, our predictions using this model may generalise poorly;
similarly, if the noise process is incorrectly specified, we can attribute too
much or too little observed variation to the signal. With little justification,
independent Gaussian noise is typically chosen, which defines a statistical
model that is simple to implement but often misstates system uncertainty and
may underestimate error autocorrelation. There are a range of alternative noise
processes available but, in practice, none of these may be entirely
appropriate, as actual noise may be better characterised as a time-varying
mixture of these various types. Here, we consider systems where the signal is
modelled with ordinary differential equations and present classes of flexible
noise processes that adapt to a system's characteristics. Our noise models
include a multivariate normal kernel where Gaussian processes allow for
non-stationary persistence and variance, and nonparametric Bayesian models that
partition time series into distinct blocks of separate noise structures. Across
the scenarios we consider, these noise processes faithfully reproduce true
system uncertainty: that is, parameter estimate uncertainty when doing
inference using the correct noise model. The models themselves and the methods
for fitting them are scalable to large datasets and could help to ensure more
appropriate quantification of uncertainty in a host of time series models.

2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs