Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian inference under small sample size -- A noninformative prior
  approach   A Bayesian inference method for problems with small samples and sparse data
is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is
proposed to formulate the Bayesian posterior for inference problems under small
sample size. It is shown that this type of prior can represents a broad range
of priors such as classical noninformative priors and asymptotically locally
invariant priors. It is further shown in this study that such priors can be
derived as the limiting states of Normal-Inverse-Gamma conjugate priors,
allowing for analytical evaluations of Bayesian posteriors and predictors. The
performance of different noninformative priors under small sample size is
compared using the global likelihood. The method of Laplace approximation is
employed to evaluate the global likelihood. A numerical linear regression
problem and a realistic fatigue reliability problem are used to demonstrate the
method and identify the optimal noninformative prior. Results indicate the
predictor using Jeffreys' prior outperforms others. The advantage of the
noninformative Bayesian estimator over the regular least square estimator under
small sample size is shown.

2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys