# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0

"""
Example: Generalized Linear Mixed Models
========================================

The UCBadmit data is sourced from the study [1] of gender biased in graduate admissions at
UC Berkeley in Fall 1973:

.. table:: UCBadmit dataset
   :align: center

   ====== ====== ============== =======
    dept   male   applications   admit
   ====== ====== ============== =======
     0      1         825         512
     0      0         108          89
     1      1         560         353
     1      0          25          17
     2      1         325         120
     2      0         593         202
     3      1         417         138
     3      0         375         131
     4      1         191          53
     4      0         393          94
     5      1         373          22
     5      0         341          24
   ====== ====== ============== =======

This example replicates the multilevel model `m_glmm5` at [3], which is used to evaluate whether
the data contain evidence of gender biased in admissions across departments. This is a form of
Generalized Linear Mixed Models for binomial regression problem, which models

    - varying intercepts across departments,
    - varying slopes (or the effects of being male) across departments,
    - correlation between intercepts and slopes,

and uses non-centered parameterization (or whitening).

A more comprehensive explanation for binomial regression and non-centered parameterization can be
found in Chapter 10 (Counting and Classification) and Chapter 13 (Adventures in Covariance) of [2].

**References:**

    1. Bickel, P. J., Hammel, E. A., and O'Connell, J. W. (1975), "Sex Bias in Graduate Admissions:
       Data from Berkeley", Science, 187(4175), 398-404.
    2. McElreath, R. (2018), "Statistical Rethinking: A Bayesian Course with Examples in R and Stan",
       Chapman and Hall/CRC.
    3. https://github.com/rmcelreath/rethinking/tree/Experimental#multilevel-model-formulas

.. image:: ../_static/img/examples/ucbadmit.png
    :align: center
"""

import argparse
import os

import matplotlib.pyplot as plt
import numpy as np

from jax import random
import jax.numpy as jnp
from jax.scipy.special import expit

import numpyro
import numpyro.distributions as dist
from numpyro.examples.datasets import UCBADMIT, load_dataset
from numpyro.infer import MCMC, NUTS, Predictive


def glmm(dept, male, applications, admit=None):
    v_mu = numpyro.sample("v_mu", dist.Normal(0, jnp.array([4.0, 1.0])))

    sigma = numpyro.sample("sigma", dist.HalfNormal(jnp.ones(2)))
    L_Rho = numpyro.sample("L_Rho", dist.LKJCholesky(2, concentration=2))
    scale_tril = sigma[..., jnp.newaxis] * L_Rho
    # non-centered parameterization
    num_dept = len(np.unique(dept))
    z = numpyro.sample("z", dist.Normal(jnp.zeros((num_dept, 2)), 1))
    v = jnp.dot(scale_tril, z.T).T

    logits = v_mu[0] + v[dept, 0] + (v_mu[1] + v[dept, 1]) * male
    if admit is None:
        # we use a Delta site to record probs for predictive distribution
        probs = expit(logits)
        numpyro.sample("probs", dist.Delta(probs), obs=probs)
    numpyro.sample("admit", dist.Binomial(applications, logits=logits), obs=admit)


def run_inference(dept, male, applications, admit, rng_key, args):
    kernel = NUTS(glmm)
    mcmc = MCMC(
        kernel,
        num_warmup=args.num_warmup,
        num_samples=args.num_samples,
        num_chains=args.num_chains,
        progress_bar=False if "NUMPYRO_SPHINXBUILD" in os.environ else True,
    )
    mcmc.run(rng_key, dept, male, applications, admit)
    return mcmc.get_samples()


def print_results(header, preds, dept, male, probs):
    columns = ["Dept", "Male", "ActualProb", "Pred(p25)", "Pred(p50)", "Pred(p75)"]
    header_format = "{:>10} {:>10} {:>10} {:>10} {:>10} {:>10}"
    row_format = "{:>10.0f} {:>10.0f} {:>10.2f} {:>10.2f} {:>10.2f} {:>10.2f}"
    quantiles = jnp.quantile(preds, jnp.array([0.25, 0.5, 0.75]), axis=0)
    print("\n", header, "\n")
    print(header_format.format(*columns))
    for i in range(len(dept)):
        print(row_format.format(dept[i], male[i], probs[i], *quantiles[:, i]), "\n")


def main(args):
    _, fetch_train = load_dataset(UCBADMIT, split="train", shuffle=False)
    dept, male, applications, admit = fetch_train()
    rng_key, rng_key_predict = random.split(random.key(1))
    zs = run_inference(dept, male, applications, admit, rng_key, args)
    pred_probs = Predictive(glmm, zs)(rng_key_predict, dept, male, applications)[
        "probs"
    ]
    header = "=" * 30 + "glmm - TRAIN" + "=" * 30
    print_results(header, pred_probs, dept, male, admit / applications)

    # make plots
    fig, ax = plt.subplots(figsize=(8, 6), constrained_layout=True)

    ax.plot(range(1, 13), admit / applications, "o", ms=7, label="actual rate")
    ax.errorbar(
        range(1, 13),
        jnp.mean(pred_probs, 0),
        jnp.std(pred_probs, 0),
        fmt="o",
        c="k",
        mfc="none",
        ms=7,
        elinewidth=1,
        label=r"mean $\pm$ std",
    )
    ax.plot(range(1, 13), jnp.percentile(pred_probs, 5, 0), "k+")
    ax.plot(range(1, 13), jnp.percentile(pred_probs, 95, 0), "k+")
    ax.set(
        xlabel="cases",
        ylabel="admit rate",
        title="Posterior Predictive Check with 90% CI",
    )
    ax.legend()

    plt.savefig("ucbadmit_plot.pdf")


if __name__ == "__main__":
    assert numpyro.__version__.startswith("0.21.0")
    parser = argparse.ArgumentParser(
        description="UCBadmit gender discrimination using HMC"
    )
    parser.add_argument("-n", "--num-samples", nargs="?", default=2000, type=int)
    parser.add_argument("--num-warmup", nargs="?", default=500, type=int)
    parser.add_argument("--num-chains", nargs="?", default=1, type=int)
    parser.add_argument("--device", default="cpu", type=str, help='use "cpu" or "gpu".')
    args = parser.parse_args()

    numpyro.set_platform(args.device)
    numpyro.set_host_device_count(args.num_chains)

    main(args)