self-consistent region iteration

[hyunjimoon]

What? find the self-consistency parmater regions via contraction mapping Assumption: variance of parameter samples would be similar before and after in self-consistency parmater regions How? run until the ratio < 1.1 for all parameters

Test code:

model_ncp = cmdstanr::cmdstan_model("tests/eightschools_ncp.stan")
sbc_obj_ncp = SBC::SBCModel$new(name="eightschools_ncp", stan_model=model_ncp)

model_cp = cmdstanr::cmdstan_model("tests/eightschools_cp.stan")
sbc_obj_cp = SBC::SBCModel$new(name="eightschools_cp", stan_model=model_cp)

par_names <- list("theta", "mu", "tau") #unlist(dimnames(prior_theta)[[2]]) #pars = list("theta", "mu", "tau")

N = 100
M = 10

prior_theta_ncp = sbc_obj_ncp$sample_theta_tilde_stan(par_names, N, data=data) # partial pars possible
ncp_ratio <- iter_gen_inf(sbc_obj_ncp, prior_theta_ncp, par_names, N, M, data)

prior_theta_cp = sbc_obj_cp$sample_theta_tilde_stan(par_names, N, data=data) # partial pars possible
cp_ratio <- iter_gen_inf(sbc_obj_cp, prior_theta_cp, par_names, N, M, data)

1. N,M = (10,10)

> ncp_ratio
# A tibble: 10 x 4
   par      postVar priVar ratioVar
   <chr>      <dbl>  <dbl>    <dbl>
 1 mu          9.22   39.5    0.233
 2 tau        38.0   126.     0.302
 3 theta[1]   66.5   111.     0.601
 4 theta[2]   81.4   721.     0.113
 5 theta[3]   76.2   102.     0.744
 6 theta[4]   39.9    37.9    1.05 
 7 theta[5]   42.9    50.0    0.860
 8 theta[6]   87.9    37.9    2.32 
 9 theta[7]   72.7    72.2    1.01 
10 theta[8]  112.    628.     0.178

> cp_ratio
# A tibble: 10 x 4
   par      postVar priVar ratioVar
   <chr>      <dbl>  <dbl>    <dbl>
 1 mu          11.2   22.5   0.498 
 2 tau         58.4  414.    0.141 
 3 theta[1]    56.5  971.    0.0582
 4 theta[2]    89.9 4240.    0.0212
 5 theta[3]    79.8 2056.    0.0388
 6 theta[4]    51.1  221.    0.232 
 7 theta[5]    30.4  156.    0.195 
 8 theta[6]    32.8   97.6   0.336 
 9 theta[7]    33.9  194.    0.174 
10 theta[8]    35.9   84.6   0.424 

2. N,M = (100,10)

> ncp_ratio
# A tibble: 10 x 4
   par      postVar   priVar ratioVar
   <chr>      <dbl>    <dbl>    <dbl>
 1 mu          8.57     20.6 0.415   
 2 tau       119.    39191.  0.00304 
 3 theta[1]  162.     8041.  0.0201  
 4 theta[2]  119.     6061.  0.0196  
 5 theta[3]  171.     8562.  0.0199  
 6 theta[4]  146.     2253.  0.0650  
 7 theta[5]  137.    83883.  0.00163 
 8 theta[6]  141.   170061.  0.000829
 9 theta[7]   89.4  121873.  0.000734
10 theta[8]  148.     5768.  0.0257  
> cp_ratio
# A tibble: 10 x 4
   par      postVar priVar ratioVar
   <chr>      <dbl>  <dbl>    <dbl>
 1 mu          12.4   22.7   0.544 
 2 tau         62.2 3795.    0.0164
 3 theta[1]    68.7 2550.    0.0270
 4 theta[2]    72.2 1269.    0.0569
 5 theta[3]    65.7 2647.    0.0248
 6 theta[4]   112.  4385.    0.0255
 7 theta[5]    94.3 1618.    0.0583
 8 theta[6]    91.4 4337.    0.0211
 9 theta[7]    58.2  968.    0.0601
10 theta[8]    89.2 4971.    0.0180