Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: About the posterior distribution in hidden Markov models with unknown
  number of states   We consider finite state space stationary hidden Markov models (HMMs) in the
situation where the number of hidden states is unknown. We provide a
frequentist asymptotic evaluation of Bayesian analysis methods. Our main result
gives posterior concentration rates for the marginal densities, that is for the
density of a fixed number of consecutive observations. Using conditions on the
prior, we are then able to define a consistent Bayesian estimator of the number
of hidden states. It is known that the likelihood ratio test statistic for
overfitted HMMs has a nonstandard behaviour and is unbounded. Our conditions on
the prior may be seen as a way to penalize parameters to avoid this phenomenon.
Inference of parameters is a much more difficult task than inference of
marginal densities, we still provide a precise description of the situation
when the observations are i.i.d. and we allow for $2$ possible hidden states.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph