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

set.seed(1)
morie_ghosal_dirichlet_posterior(x = rnorm(50))
#> $estimate
#> [1] 0.5007844
#> 
#> $alpha_post
#> [1] 51
#> 
#> $n
#> [1] 50
#> 
#> $cdf_grid
#>  [1] -2.69569796 -2.60025842 -2.50481888 -2.40937935 -2.31393981 -2.21850027
#>  [7] -2.12306074 -2.02762120 -1.93218166 -1.83674213 -1.74130259 -1.64586305
#> [13] -1.55042352 -1.45498398 -1.35954444 -1.26410491 -1.16866537 -1.07322583
#> [19] -0.97778630 -0.88234676 -0.78690723 -0.69146769 -0.59602815 -0.50058862
#> [25] -0.40514908 -0.30970954 -0.21427001 -0.11883047 -0.02339093  0.07204860
#> [31]  0.16748814  0.26292768  0.35836721  0.45380675  0.54924629  0.64468582
#> [37]  0.74012536  0.83556490  0.93100443  1.02644397  1.12188351  1.21732304
#> [43]  1.31276258  1.40820212  1.50364165  1.59908119  1.69452072  1.78996026
#> [49]  1.88539980  1.98083933  2.07627887
#> 
#> $cdf_post
#>  [1] 6.886405e-05 9.132704e-05 1.201119e-04 1.566635e-04 2.026571e-04
#>  [6] 2.600073e-04 1.993871e-02 2.002548e-02 3.973860e-02 3.986518e-02
#> [11] 4.001599e-02 4.019404e-02 4.040235e-02 6.025170e-02 8.013700e-02
#> [16] 8.045287e-02 8.080920e-02 8.120755e-02 8.164882e-02 8.213323e-02
#> [21] 1.218758e-01 1.420517e-01 2.014819e-01 2.021241e-01 2.420134e-01
#> [26] 2.623214e-01 3.022582e-01 3.422099e-01 4.606014e-01 4.809553e-01
#> [31] 5.013041e-01 5.216411e-01 5.419601e-01 6.210787e-01 6.413447e-01
#> [36] 7.204007e-01 7.602037e-01 8.391824e-01 8.789034e-01 8.989737e-01
#> [41] 9.190009e-01 9.389855e-01 9.393210e-01 9.592248e-01 9.594836e-01
#> [46] 9.989235e-01 9.991160e-01 9.992798e-01 9.994179e-01 9.995332e-01
#> [51] 9.996287e-01
#> 
#> $cdf_var
#>  [1] 1.324217e-06 1.756129e-06 2.309566e-06 3.012288e-06 3.896462e-06
#>  [6] 4.998840e-06 3.757916e-04 3.773935e-04 7.338354e-04 7.360758e-04
#> [11] 7.387444e-04 7.418938e-04 7.455770e-04 1.088874e-03 1.417597e-03
#> [16] 1.422696e-03 1.428444e-03 1.434863e-03 1.441967e-03 1.449757e-03
#> [21] 2.058118e-03 2.343712e-03 3.093980e-03 3.101345e-03 3.527748e-03
#> [26] 3.721325e-03 4.055734e-03 4.328890e-03 4.777841e-03 4.800717e-03
#> [31] 4.807660e-03 4.798686e-03 4.773834e-03 4.525768e-03 4.423494e-03
#> [36] 3.873530e-03 3.505655e-03 2.595295e-03 2.046773e-03 1.746538e-03
#> [41] 1.431505e-03 1.101764e-03 1.096098e-03 7.521652e-04 7.475929e-04
#> [46] 2.067956e-05 1.698467e-05 1.384001e-05 1.118803e-05 8.971922e-06
#> [51] 7.136898e-06
#> 
#> $method
#> [1] "Dirichlet process posterior (conjugate)"
#>