basic stan fire model

fire_basic_9.stan

data {
    int<lower=0> N;

    real HP_loss_raw[N];
    real Org_loss_raw[N];
    real evade;

    real eps;
}

transformed data{
    real HP_dice_size=2;
    real Org_dice_size=4;
    real evade_hit = evade / 10;
}

parameters {
    real<lower=0> firepower;
    
    // real<lower=0> fire_heavy;
    // real<lower=0> fire_light;

    // real<lower=0> hit_heavy;
    // real<lower=0> hit_light;
    
    real<lower=0> hit_heavy_z;
    real<lower=0> hit_light_z;
}

transformed parameters{
    real fire_hit = firepower / 10;

    real fire_heavy = max([fire_hit - evade_hit, 0.]);
    real fire_light = min([fire_hit, evade_hit]);
    
    real hit_heavy = fire_heavy * 0.4 + hit_heavy_z * (sqrt(fire_heavy*0.4*0.6) + eps);
    real hit_light = fire_light * 0.1 + hit_heavy_z * (sqrt(fire_light*0.1*0.9) + eps);

    real hit = hit_light + hit_heavy;
}

model{
    // hit_heavy ~ normal(fire_heavy * 0.4, sqrt(fire_heavy*0.4*0.6) + eps);
    // hit_light ~ normal(fire_light * 0.1, sqrt(fire_light*0.1*0.9) + eps);
    hit_heavy_z ~ normal(0, 1);
    hit_light_z ~ normal(0, 1);

    HP_loss_raw  ~ normal(hit * (1 + HP_dice_size)/2,  
                          sqrt(hit * (HP_dice_size*HP_dice_size   - 1)/12 ));
    Org_loss_raw  ~ normal(hit * (1 + Org_dice_size)/2,  
                          sqrt(hit * (Org_dice_size*Org_dice_size - 1)/12 ));
}

pystan_runner.py

data5 = {
    "N": 10,
    "HP_loss_raw":  [1., 0., 0., 4., 1., 0., 0., 1., 0., 0.],
    "Org_loss_raw": [3., 0., 0., 4., 1., 0., 0., 1., 0., 0.],
    "evade": 106,
    
    "eps": 1e-6,
}

fit5 = sm5.sampling(data=data5, iter=1000, chains=4)
fit5

"""
WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated
WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed
Inference for Stan model: anon_model_de61fa4ba36aec97a90942d72fb6e60c.
4 chains, each with iter=1000; warmup=500; thin=1; 
post-warmup draws per chain=500, total post-warmup draws=2000.

              mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat
firepower    45.98    0.87  18.65  12.79  31.29  46.17  60.95  80.27    460   1.01
hit_heavy_z   0.61    0.02   0.49   0.03   0.22   0.48   0.87   1.91    453   1.01
hit_light_z   0.82    0.02   0.61   0.04   0.33   0.71    1.2   2.24    878    1.0
fire_hit       4.6    0.09   1.87   1.28   3.13   4.62    6.1   8.03    460   1.01
fire_heavy     0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan
fire_light     4.6    0.09   1.87   1.28   3.13   4.62    6.1   8.03    460   1.01
hit_heavy   6.1e-7  2.3e-8 4.9e-7 2.9e-8 2.2e-7 4.8e-7 8.7e-7 1.9e-6    453   1.01
hit_light     0.78  1.6e-3   0.07   0.65   0.73   0.77   0.82   0.93   2134    1.0
hit           0.78  1.6e-3   0.07   0.65   0.73   0.77   0.82   0.93   2134    1.0
lp__        -47.98    0.05   1.26 -51.15  -48.6 -47.69 -47.01 -46.45    656    1.0

Samples were drawn using NUTS at Fri Jul  3 22:57:55 2020.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at 
convergence, Rhat=1).
"""