  In this paper, we propose an efficient multi-stage algorithm for non-adaptive
Group Testing (GT) with general correlated prior statistics. The proposed
solution can be applied to any correlated statistical prior represented in
trellis, e.g., finite state machines and Markov processes. We introduce a
variation of List Viterbi Algorithm (LVA) to enable accurate recovery using
much fewer tests than objectives, which efficiently gains from the correlated
prior statistics structure. Our numerical results demonstrate that the proposed
Multi-Stage GT (MSGT) algorithm can obtain the optimal Maximum A Posteriori
(MAP) performance with feasible complexity in practical regimes, such as with
COVID-19 and sparse signal recovery applications, and reduce in the scenarios
tested the number of pooled tests by at least $25\%$ compared to existing
classical low complexity GT algorithms. Moreover, we analytically characterize
the complexity of the proposed MSGT algorithm that guarantees its efficiency.
