Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Confidence intervals for nonhomogeneous branching processes and
  polymerase chain reactions   We extend in two directions our previous results about the sampling and the
empirical measures of immortal branching Markov processes. Direct applications
to molecular biology are rigorous estimates of the mutation rates of polymerase
chain reactions from uniform samples of the population after the reaction.
First, we consider nonhomogeneous processes, which are more adapted to real
reactions. Second, recalling that the first moment estimator is analytically
known only in the infinite population limit, we provide rigorous confidence
intervals for this estimator that are valid for any finite population. Our
bounds are explicit, nonasymptotic and valid for a wide class of nonhomogeneous
branching Markov processes that we describe in detail. In the setting of
polymerase chain reactions, our results imply that enlarging the size of the
sample becomes useless for surprisingly small sizes. Establishing confidence
intervals requires precise estimates of the second moment of random samples.
The proof of these estimates is more involved than the proofs that allowed us,
in a previous paper, to deal with the first moment. On the other hand, our
method uses various, seemingly new, monotonicity properties of the harmonic
moments of sums of exchangeable random variables.

35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom