Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Probability and Relative Frequency in Quantum Mechanics   We present a comparative study between classical probability and quantum
probability from the Bayesian viewpoint, where probability is construed as our
rational degree of belief on whether a given statement is true. From this
viewpoint, including conditional probability, three issues are discussed: i)
Given a measure of the rational degree of belief, does it satisfy the axioms of
the probability? ii) Given the probability satisfying these axioms, is it seen
as the measure of the rational degree of belief? iii) Can the measure of the
rational degree of belief be evaluated in terms of the relative frequency of
events occurring? Here we show that as with the classical probability, all
these issues can be resolved affirmatively in the quantum probability, provided
that the relation to the relative frequency is slightly modified in case of a
small number of observations. This implies that the relation between the
Bayesian probability and the relative frequency in quantum mechanics is the
same as that in the classical probability theory, including conditional
probability.

27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin