  In this paper, distributed Bayesian detection problems with unknown prior
probabilities of hypotheses are considered. The sensors obtain observations
which are conditionally dependent across sensors and their probability density
functions (pdf) are not exactly known. The observations are quantized and are
sent to the fusion center. The fusion center fuses the current quantized
observations and makes a final decision. It also designs (updated) quantizers
to be used at the sensors and the fusion rule based on all previous quantized
observations. Information regarding updated quantizers is sent back to the
sensors for use at the next time. In this paper, the conditional joint pdf is
represented in a parametric form by using the copula framework. The unknown
parameters include dependence parameters and marginal parameters. Maximum
likelihood estimation (MLE) with feedback based on quantized data is proposed
to estimate the unknown parameters. These estimates are iteratively used to
refine the quantizers and the fusion rule to improve distributed detection
performance by using feedback. Numerical examples show that the new detection
method based on MLE with feedback is much better than the usual detection
method based on the assumption of conditionally independent observations.
