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. Author manuscript; available in PMC: 2014 Jun 1.
Published in final edited form as: J Biomed Inform. 2013 Apr 4;46(3):480–496. doi: 10.1016/j.jbi.2013.03.008

Algorithm 2.

Inter-site posterior update in asynchronous EXPLORER

1: Global initialization:
 Initialize all the messages mBh<sub>j</sub>(β) and mh<sub>j</sub>→B (β) between server variable node B and clients factor nodes hj, where the subscriptions Bhj and hjB indicate the message directions.

2: Local initialization for all the online sites:

3: Initialize messages mB<sub>j</sub>→h<sub>j</sub> (β) and each approximate likelihood function fij(βj) with i = mj−1 + 1, · · ·, mj.

4: Repeat:

5: for all the online sites (parallel update)

6:  Update intra-site message: mh<sub>j</sub>→ B<sub>j</sub>(βj)= ∫ δ(β, βj) mBh<sub>j</sub> (β) dβ

7:  Set approximate posterior: qj(βj)=mhjBj(βj)i=1mj-mj-1fij(βj)

8:  Update approximate posterior qj(βj) according to Algorithm 1.

9:  Update intra-site messages at variable node Bj :
mBjhj(βj)=qj(βj)/mhjBj(βj)

10:  Upload message at factor node hj :
mhjB(β)=δ(β,βj)mBjhj(βj)dβj.

11: end for

12: Send out message at server node B:
mBhj(β)=mg0B(β)k=1kjnmhkB(β).

13: Until parameters converge

14: Get the final approximate posterior distribution by multiply- ing all the incoming messages at the server node B.
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