Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the performance of particle filters with adaptive number of particles   We investigate the performance of a class of particle filters (PFs) that can
automatically tune their computational complexity by evaluating online certain
predictive statistics which are invariant for a broad class of state-space
models. To be specific, we propose a family of block-adaptive PFs based on the
methodology of Elvira et al (2017). In this class of algorithms, the number of
Monte Carlo samples (known as particles) is adjusted periodically, and we prove
that the theoretical error bounds of the PF actually adapt to the updates in
the number of particles. The evaluation of the predictive statistics that lies
at the core of the methodology is done by generating fictitious observations,
i.e., particles in the observation space. We study, both analytically and
numerically, the impact of the number $K$ of these particles on the performance
of the algorithm. In particular, we prove that if the predictive statistics
with $K$ fictitious observations converged exactly, then the particle
approximation of the filtering distribution would match the first $K$ elements
in a series of moments of the true filter. This result can be understood as a
converse to some convergence theorems for PFs. From this analysis, we deduce an
alternative predictive statistic that can be computed (for some models) without
sampling any fictitious observations at all. Finally, we conduct an extensive
simulation study that illustrates the theoretical results and provides further
insights into the complexity, performance and behavior of the new class of
algorithms.

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat