Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normalizations of the Proposal Density in Markov Chain Monte Carlo
  Algorithms   We explore the effects of normalizing the proposal density in Markov Chain
Monte Carlo algorithms in the context of reconstructing the conductivity term
$K$ in the $2$-dimensional heat equation, given temperatures at the boundary
points, $d$. We approach this nonlinear inverse problem by implementing a
Metropolis-Hastings Markov Chain Monte Carlo algorithm. Markov Chains produce a
probability distribution of possible solutions conditional on the observed
data. We generate a candidate solution $K'$ and solve the forward problem,
obtaining $d'$. At step $n$, with some probability $\alpha$, we set
$K_{n+1}=K'$. We identify certain issues with this construction, stemming from
large and fluctuating values of our data terms. Using this framework, we
develop normalization terms $z_0,z$ and parameters $\lambda$ that preserve the
inherently sparse information at our disposal. We examine the results of this
variant of the MCMC algorithm on the reconstructions of several $2$-dimensional
conductivity functions.

22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int