International Scholarly Research Notices

Research Article

Comparison of Two Approaches for Detection and Estimation of Radioactive Sources

Algorithm 1

Importance sampling with progressive correction algorithm.
(1) 𝑠 = 0 , 𝐺 0 = 0 , πœ‡ 𝑏 = πœ‡ βˆ— 𝑏 , π‘Ÿ = π‘Ÿ βˆ— ;
(2) for 𝑛 = 1 , … , 𝑁 do
(3)   Draw 𝜽 0 , 𝑛 ( π‘Ÿ ) ∼ 𝑝 ( 𝜽 ( π‘Ÿ ) ∣ π‘Ÿ , 𝐼 ) ;
(4)   Compute 𝑙 ( 𝐳 ∣ πœ‡ 𝑏 , π‘Ÿ , 𝜽 0 , 𝑛 ( π‘Ÿ ) ) ;
(5) end for
(6) while 𝐺 𝑠 < 𝛼 and 𝑠 < 𝑆 do
(7)   𝑠 ← 𝑠 + 1 ;
(8)   Select 𝛾 𝑠 ;
(9)   𝐺 𝑠 = 𝐺 𝑠 βˆ’ 1 + 𝛾 𝑠 ;
(10)  for 𝑛 = 1 , … , 𝑁 do
(11)    Weights: 𝑀 𝑠 , 𝑛 = 𝑙 ( 𝐳 ∣ πœ‡ 𝑏 , π‘Ÿ , 𝜽 𝑠 βˆ’ 1 , 𝑛 ( π‘Ÿ ) ) 𝛾 𝑠 / βˆ‘ 𝑁 𝑗 = 1 𝑙 ( 𝐳 ∣ πœ‡ 𝑏 , π‘Ÿ , 𝜽 𝑠 βˆ’ 1 , 𝑛 ( π‘Ÿ ) ) 𝛾 𝑠 ;
(12)  end for
(13)  Resample { 𝜽 𝑠 βˆ’ 1 , 𝑛 ( π‘Ÿ ) } 𝑁 𝑛 = 1 with weights { 𝑀 𝑠 , 𝑛 } 𝑁 𝑛 = 1 to give { 𝜽 𝑛 βˆ— } 𝑁 𝑛 = 1 with uniform weights
(14)  for 𝑛 = 1 , … , 𝑁 do
(15)     𝜽 𝑠 , 𝑛 ( π‘Ÿ ) = 𝜽 𝑛 βˆ— + 𝝐 𝑠 , 𝑛 , where 𝝐 ∼ 𝑔 𝑠 ;
(16)  end for
(17) end while