Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Effect of the Prior and the Experimental Design on the Inference of
  the Precision Matrix in Gaussian Chain Graph Models   Here, we investigate whether (and how) experimental design could aid in the
estimation of the precision matrix in a Gaussian chain graph model, especially
the interplay between the design, the effect of the experiment and prior
knowledge about the effect. We approximate the marginal posterior precision of
the precision matrix via Laplace approximation under different priors: a flat
prior, the conjugate prior Normal-Wishart, the unconfounded prior Normal-Matrix
Generalized Inverse Gaussian (MGIG) and a general independent prior. We show
that the approximated posterior precision is not a function of the design
matrix for the cases of the Normal-Wishart and flat prior, but it is for the
cases of the Normal-MGIG and the general independent prior. However, for the
Normal-MGIG and the general independent prior, we find a sharp upper bound on
the approximated posterior precision that does not involve the design matrix
which translates into a bound on the information that could be extracted from a
given experiment. We confirm the theoretical findings via a simulation study
comparing the KL divergence between the prior and the posterior (i.e.
information gain by the experiment) and the Stein's loss difference between
random versus no experiment (design matrix equal to zero). Our findings provide
practical advice for domain scientists conducting experiments to infer the
interactions between a multidimensional response.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas