Dirichlet-process posterior (conjugate update) — morie_ghosal_dirichlet

Posterior of G given X_1, ..., X_n for G ~ DP(alpha, G0) with G0 = N(base_mean, base_sd^2). Returns the posterior-mean CDF evaluated on a grid plus the headline estimate at mean(x).

Usage

morie_ghosal_dirichlet_posterior(
  x,
  alpha = 1,
  base_mean = 0,
  base_sd = 1,
  grid = NULL
)

Arguments

x: numeric vector.
alpha: concentration.
base_mean, base_sd: base measure (N).
grid: optional grid (default: 51 pts spanning x).

Value

named list with estimate, cdf_grid, cdf_post, cdf_var, alpha_post, n, method.

Examples

morie_ghosal_dirichlet_posterior(x = rnorm(50))
#> $estimate
#> [1] 0.5018408
#> 
#> $alpha_post
#> [1] 51
#> 
#> $n
#> [1] 50
#> 
#> $cdf_grid
#>  [1] -3.21358433 -3.07941267 -2.94524102 -2.81106937 -2.67689772 -2.54272606
#>  [7] -2.40855441 -2.27438276 -2.14021110 -2.00603945 -1.87186780 -1.73769615
#> [13] -1.60352449 -1.46935284 -1.33518119 -1.20100953 -1.06683788 -0.93266623
#> [19] -0.79849458 -0.66432292 -0.53015127 -0.39597962 -0.26180797 -0.12763631
#> [25]  0.00653534  0.14070699  0.27487865  0.40905030  0.54322195  0.67739360
#> [31]  0.81156526  0.94573691  1.07990856  1.21408021  1.34825187  1.48242352
#> [37]  1.61659517  1.75076683  1.88493848  2.01911013  2.15328178  2.28745344
#> [43]  2.42162509  2.55579674  2.68996840  2.82414005  2.95831170  3.09248335
#> [49]  3.22665501  3.36082666  3.49499831
#> 
#> $cdf_post
#>  [1] 1.285189e-05 2.033423e-05 3.163757e-05 4.840896e-05 7.285031e-05
#>  [6] 1.971568e-02 1.976486e-02 1.983277e-02 1.992488e-02 2.004757e-02
#> [11] 3.981593e-02 4.002220e-02 4.028254e-02 4.060527e-02 6.060605e-02
#> [16] 8.068380e-02 1.008436e-01 1.210882e-01 1.610253e-01 2.206518e-01
#> [21] 2.803530e-01 3.401188e-01 3.999360e-01 4.597886e-01 4.804433e-01
#> [26] 4.814892e-01 5.217313e-01 5.423284e-01 6.020885e-01 6.421749e-01
#> [31] 6.625780e-01 7.221149e-01 7.815668e-01 8.409341e-01 8.806120e-01
#> [36] 8.809978e-01 9.009219e-01 9.011766e-01 9.013781e-01 9.015346e-01
#> [41] 9.016540e-01 9.017434e-01 9.410250e-01 9.606804e-01 9.803221e-01
#> [46] 9.803457e-01 9.999697e-01 9.999805e-01 9.999877e-01 9.999924e-01
#> [51] 9.999954e-01
#> 
#> $cdf_var
#>  [1] 2.471486e-07 3.910350e-07 6.083955e-07 9.308965e-07 1.400865e-06
#>  [6] 3.716725e-04 3.725810e-04 3.738353e-04 3.755361e-04 3.778012e-04
#> [11] 7.352043e-04 7.388543e-04 7.434588e-04 7.491630e-04 1.094865e-03
#> [16] 1.426422e-03 1.743734e-03 2.046650e-03 2.598003e-03 3.307011e-03
#> [21] 3.879908e-03 4.316116e-03 4.615138e-03 4.776597e-03 4.800337e-03
#> [26] 4.801103e-03 4.798611e-03 4.773237e-03 4.607268e-03 4.418967e-03
#> [31] 4.299392e-03 3.858942e-03 3.283079e-03 2.572383e-03 2.021818e-03
#> [36] 2.016167e-03 1.716570e-03 1.712641e-03 1.709532e-03 1.707115e-03
#> [41] 1.705271e-03 1.703889e-03 1.067249e-03 7.264140e-04 3.709746e-04
#> [46] 3.705390e-04 5.831821e-07 3.742185e-07 2.361328e-07 1.465102e-07
#> [51] 8.937831e-08
#> 
#> $method
#> [1] "Dirichlet process posterior (conjugate)"
#>