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Verification

Since we broken the single-chain into multi-chain by broken some dependent relationships, will it influence the sampling? And how big the influence will be? To varify whether or not the duel chain works becomes important part in this section. The comparision is given between the results generated by sequential Gibbs Sampler(single-chain) and the results generated by parallel Gibbs Sampler(duel-chain). We compared the average value of every single variable, and the number of points that fall in the range of a fixed bound.

	Serial Result	Parallel Result	Mistake
Average A	1685.33	1651.12	2.03%
Average B	2885.60	2881.36	0.15%
Average x	600.131	615.124	2.50%
Average y	2285.47	2266.24	0.84%
x - #point in (400, 2000)/#total points	195/333	185/333	5.13%
y - #point in (400, 2000)/#total points	162/333	155/333	4.32%

Parallel Result	Serial Result

All the data calculated, collected and showed above are based on the Console version of Parallel Gibbs sampler,
and the following parameters:
Initial x = 750, y = 200, High Bound = 2000, Low Bound = 400,
Burning = 1000, Iteration = 1000, Thinning = 3, Volumn of Data Set = 898.

Performance Evaluation

Performance evaluation is given by the comparision of the speed on the Sequential Method and Parallel Method: