International Scholarly Research Notices

Research Article

Inverse Dispersion for an Unknown Number of Sources: Model Selection and Uncertainty Analysis

Table 1

The posterior mean, posterior standard deviation, and lower and upper bounds of the 95% HPD interval of the parameters 𝑥 𝑠 , 𝑗 (m), 𝑦 𝑠 , 𝑗 (m), and 𝑄 𝑗 ≡ 𝑞 𝑠 , 𝑗 ( g s − 1 ) for 𝑗 = 1 , 2, 3, and 4 calculated from samples of source model 𝑚 𝑁 with 𝑁 = 4 drawn from the posterior distribution 𝑝 ( 𝜃 | 𝑚 𝑁 , 𝒟 , 𝐼 ) [cf. Figure 1(d)].
  Parameter Mean Standard deviation 95% HPD Actual
  𝑥 𝑠 (m) 3 4 . 9 4 . 3 (27.6, 44.4) 33.0
𝑗 = 1 𝑦 𝑠 (m) 1 7 0 . 8 0 . 6 (169.5, 171.8) 171.0
  𝑞 𝑠 (g s−1) 8.9 0.4 (8.0, 9.3) —
  𝑥 𝑠 (m) 3 3 . 7 1.1 (31.6, 35.9) 33.8
𝑗 = 2 𝑦 𝑠 (m) 2 4 0 . 7 0 . 3 (240.2, 241.4) 240.7
  𝑞 𝑠 (g s−1) 7.5 0.4 (6.7, 8.1) —
  𝑥 𝑠 (m) 2 5 . 4 3.9 (17.1, 31.2) 30.0
𝑗 = 3 𝑦 𝑠 (m) 3 1 3 . 2 0 . 6 (311.9, 314.6) 312.9
  𝑞 𝑠 (g s−1) 4.2 0.2 (3.7, 4.6) 3.8
  𝑥 𝑠 (m) 2 5 . 1 3.0 ( 1 8 . 9 , 3 0 . 3 ) 26.0
𝑗 = 4 𝑦 𝑠 (m) 3 8 4 . 5 0 . 5 (383.5, 385.5) 384.4
  𝑞 𝑠 (g s−1) 6.3 0.3 (5.8, 6.8) —