distributions_cholesky.md
In greta: Simple and Scalable Statistical Modelling in R

Cholesky factor of Wishart should be a lower triangular matrix

Code
  calculate(chol_x, nsim = 1, seed = 2024 - 10 - 31 - 1338)$chol_x[1, , ]
Output
           [,1]      [,2]       [,3]
  [1,] 1.205827 -0.283302 -0.2737789
  [2,] 0.000000  1.318010 -2.3508394
  [3,] 0.000000  0.000000  0.2704156

Code
  calc_chol$x[1, , ]
Output
            [,1]       [,2]       [,3]
  [1,] 2.5280832  0.8034031  3.4674274
  [2,] 0.8034031  4.7851721 -0.8106264
  [3,] 3.4674274 -0.8106264  8.1530456

Code
  calc_chol$chol_x[1, , ]
Output
           [,1]      [,2]       [,3]
  [1,] 1.589995 0.5052867  2.1807792
  [2,] 0.000000 2.1283462 -0.8986062
  [3,] 0.000000 0.0000000  1.6092714

Cholesky factor of LJK_correlation should be a lower triangular matrix

Code
  calculate(chol_x, nsim = 1, seed = 2024 - 7 - 30 - 1431)$chol_x[1, , ]
Output
       [,1]       [,2]      [,3]
  [1,]    1 -0.1775724 0.2806787
  [2,]    0  0.9841077 0.7509681
  [3,]    0  0.0000000 0.5977177

Code
  calc_chol$x[1, , ]
Output
             [,1]       [,2]      [,3]
  [1,]  1.0000000 -0.1775724 0.2806787
  [2,] -0.1775724  1.0000000 0.6891927
  [3,]  0.2806787  0.6891927 1.0000000

Code
  calc_chol$chol_x[1, , ]
Output
       [,1]       [,2]      [,3]
  [1,]    1 -0.1775724 0.2806787
  [2,]    0  0.9841077 0.7509681
  [3,]    0  0.0000000 0.5977177

Post-MCMC, Wishart distribution stays symmetric, chol remains lower tri

Code
  calcs
Output
  $x
  , , 1

           [,1]         [,2]      [,3]
  [1,] 3.104011 -0.009006277 -1.697785

  , , 2

               [,1]     [,2]      [,3]
  [1,] -0.009006277 3.009727 -1.500175

  , , 3

            [,1]      [,2]    [,3]
  [1,] -1.697785 -1.500175 2.25295


  $`chol(x)`
  , , 1

          [,1] [,2] [,3]
  [1,] 1.76182    0    0

  , , 2

               [,1]     [,2] [,3]
  [1,] -0.005111915 1.734849    0

  , , 3

             [,1]       [,2]      [,3]
  [1,] -0.9636536 -0.8675692 0.7560725

Post-MCMC, LKJ distribution stays symmetric, chol remains lower tri

Code
  calcs
Output
  $x
  , , 1

       [,1]       [,2]      [,3]
  [1,]    1 -0.1775724 0.2806787

  , , 2

             [,1] [,2]      [,3]
  [1,] -0.1775724    1 0.6891927

  , , 3

            [,1]      [,2] [,3]
  [1,] 0.2806787 0.6891927    1


  $`chol(x)`
  , , 1

       [,1] [,2] [,3]
  [1,]    1    0    0

  , , 2

             [,1]      [,2] [,3]
  [1,] -0.1775724 0.9841077    0

  , , 3

            [,1]      [,2]      [,3]
  [1,] 0.2806787 0.7509681 0.5977177