International Scholarly Research Notices / 2011 / Article / Tab 4

Research Article

Comparison of Two Approaches for Detection and Estimation of Radioactive Sources

Table 4

The posterior mean, posterior standard deviation, and lower and upper bounds of the 95% HPD interval of the parameters π‘₯ 𝑠 , 𝑖 (m), 𝑦 𝑠 , 𝑖 (m), and 𝑄 𝑠 , 𝑖 ( πœ‡ Sv m2  β„Ž βˆ’ 1 ) for 𝑖 = 1 , 2, and 3 calculated from samples of distributions of radiological point sources drawn from the posterior distribution of Θ using the RJMCMC algorithm. The upper and lower parts of the table show the results of the source recovery using radiological measurements with an exposure times of 𝜏 = 1 6 and 48 s, respectively.

Parameter Mean Standard deviation 95% HPD Actual

𝜏 = 1 6  s

  𝑖 = 1
π‘₯ 𝑠 8.7 0.8 ( 7 . 2 , 1 0 . 6 ) 11.0
𝑦 𝑠 10.6 0.8 ( 9 . 1 , 1 2 . 1 ) 10.0
𝑄 𝑠 1404 152 ( 1 1 0 9 , 1 7 0 4 ) 1912

  𝑖 = 2
π‘₯ 𝑠 3.0 0.6 ( 3 . 0 , 5 . 0 ) 3.0
𝑦 𝑠 49.8 0.6 ( 4 9 . 0 , 5 0 . 9 ) 50.0
𝑄 𝑠 385 81 ( 2 2 8 , 5 4 8 ) 392

  𝑖 = 3
π‘₯ 𝑠 40.9 0.5 ( 3 9 . 9 , 4 1 . 6 ) 41.0
𝑦 𝑠 5.0 0.9 ( 3 . 5 , 6 . 4 ) 5.0
𝑄 𝑠 194 46 ( 1 0 5 , 2 8 6 ) 98.1

𝜏 = 4 8  s

  𝑖 = 1
π‘₯ 𝑠 9.3 0.9 ( 7 . 6 , 1 1 . 0 ) 11.0
𝑦 𝑠 10.2 0.8 ( 8 . 7 , 1 1 . 9 ) 10.0
𝑄 𝑠 1433 156 ( 1 1 3 0 , 1 7 4 2 ) 1912

  𝑖 = 2
π‘₯ 𝑠 3.8 0.6 ( 3 . 0 , 4 . 9 ) 3.0
𝑦 𝑠 49.8 0.6 ( 4 9 . 0 , 5 0 . 9 ) 50.0
𝑄 𝑠 382 80 ( 2 2 5 , 5 4 3 ) 392

𝑖 = 3
π‘₯ 𝑠 41.1 0.5 ( 4 0 . 0 , 4 1 . 8 ) 41.0
𝑦 𝑠 4.8 0.8 ( 3 . 5 , 6 . 3 ) 5.0
𝑄 𝑠 204 52 ( 1 0 4 , 3 0 9 ) 98.1

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