Estimation of Spatially Varying Parameters with Application to Hyperbolic SPDES

Algorithm 3

EnKBF likelihood with MH.

Require:, , , , , , and .

Ensure:.

1: fortodo

2: Draw .

3: Compute .

4: forto, do

5:  fortodo

6:   Run a single-step EnKBF prediction ensemble

7:   Run a single-step EnKBF analysis ensemble

8:  end for

9:  Compute prediction ensemble mean: .

10:  Compute analysis ensemble mean: .

11:  Compute covariance: .

12: end for

13: Metropolis-Hastings

14: Compute

15: Compute

16: ifthen

17:  

18: else

19:  

20: end if

21: end for