Analysis_25JUN2019_modular.ipynb

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    "import pystan\n",
    "\n",
    "code = \"\"\"\n",
    "functions{\n",
    "  // below taken from https://discourse.mc-stan.org/t/quantile-function-in-stan/3642/13\n",
    "  // as Stan doesn't have a quantile function nor supports real-to-int conversion.\n",
    "  int ub(real x) {\n",
    "    int ub = 1;\n",
    "    while (ub < x) ub *= 2;\n",
    "    return ub;\n",
    "  }\n",
    "\n",
    "  int closest(real x, int a, int b) {\n",
    "    return fabs(x - a) < fabs(x - b) ? a : b;\n",
    "  }\n",
    "\n",
    "  // L <= x <= U\n",
    "  int to_int_bsearch(real x, int L, int U);\n",
    "\n",
    "  int to_int_bsearch(real x, int L, int U) {\n",
    "    int mid = (L + U) / 2;\n",
    "    if (L == U) return L;\n",
    "    if (L + 1 == U) return closest(x, L, U);\n",
    "    return x <= mid? to_int_bsearch(x, L, mid) : to_int_bsearch(x, mid, U);\n",
    "  }\n",
    "\n",
    "  int to_int(real x);\n",
    "\n",
    "  int to_int(real x) {\n",
    "    if (fabs(x) >= 2^31) reject(\"to_int arugment must be < 2^31, found x = \", x);\n",
    "    if (x < 0) return -to_int(-x);\n",
    "    return to_int_bsearch(x, 0, ub(x));\n",
    "  }\n",
    "}\n",
    "\n",
    "data {\n",
    "  int<lower=0> N;\n",
    "  int<lower=0> N_quantiles;\n",
    "  real<lower=0, upper=1> r;\n",
    "  int<lower=0, upper=1> decision[N];\n",
    "  real X[N];\n",
    "  real<lower=0, upper=1> quantiles[N_quantiles];\n",
    "}\n",
    "\n",
    "parameters {\n",
    "  real Z[N];\n",
    "}\n",
    "\n",
    "model {\n",
    "  Z ~ normal(0, 1);\n",
    "  \n",
    "  for(i in 1:N){\n",
    "    decision ~ bernoulli(inv_logit(X[i] + Z[i]) >= quantiles[to_int(r*N_quantiles)] ? 1 : 0);\n",
    "  }\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "dat = dict()\n",
    "\n",
    "sm = pystan.StanModel(model_code=code)\n",
    "fit = sm.sampling(data=dat, iter=4000, chains=4)"
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  }
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