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International Scholarly Research Notices

International Scholarly Research Notices / 2011 / Article / Tab 3

Research Article

Comparison of Two Approaches for Detection and Estimation of Radioactive Sources

Table 3

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 πœƒ ( π‘Ÿ ) ( π‘Ÿ = 3 ) using importance sampling with progressive correction. The upper and lower parts of the table show the results of the source recovery using radiological measurements with 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 10.7 0.2 ( 1 0 . 3 , 1 1 . 0 ) 11.0
𝑦 𝑠 9.9 0.2 ( 9 . 5 , 1 0 . 4 ) 10.0
𝑄 𝑠 1930 43 ( 1 8 4 8 , 2 0 1 4 ) 1912
  𝑖 = 2
π‘₯ 𝑠 2.1 0.6 ( 1 . 0 , 3 . 2 ) 3.0
𝑦 𝑠 49.8 0.3 ( 4 9 . 3 , 5 0 . 3 ) 50.0
𝑄 𝑠 330 31 ( 2 6 9 , 3 9 2 ) 392
  𝑖 = 3
π‘₯ 𝑠 40.9 0.1 ( 4 0 . 7 , 4 1 . 1 ) 41.0
𝑦 𝑠 5.0 0.3 ( 4 . 5 , 5 . 6 ) 5.0
𝑄 𝑠 92.9 15.2 ( 6 2 . 3 , 1 2 2 . 7 ) 98.1
𝜏 = 4 8  s
  𝑖 = 1
π‘₯ 𝑠 10.9 0.01 ( 1 0 . 8 9 , 1 0 . 9 0 ) 11.0
𝑦 𝑠 9.6 0.01 ( 9 . 6 2 , 9 . 6 3 ) 10.0
𝑄 𝑠 1906 1.3 ( 1 9 0 5 , 1 9 0 7 ) 1912
  𝑖 = 2
π‘₯ 𝑠 2.3 0.01 ( 2 . 3 6 , 2 . 3 8 ) 3.0
𝑦 𝑠 49.6 0.01 ( 4 9 . 6 0 , 4 9 . 6 2 ) 50.0
𝑄 𝑠 336 0.6 ( 3 3 5 . 3 , 3 3 6 . 2 ) 392
  𝑖 = 3
π‘₯ 𝑠 40.8 0.00 ( 4 0 . 8 7 , 4 0 . 8 7 ) 41.0
𝑦 𝑠 5.3 0.01 ( 5 . 2 6 , 5 . 2 8 ) 5.0
𝑄 𝑠 83.6 0.73 ( 8 3 . 0 , 8 4 . 2 ) 98.1

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