# MIT License

# Copyright (c) 2022 Hyosub Kim

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"""
A collection of Bayesian statistical models and associated utility functions.
"""

import arviz as az
import numpy as np
import numpy.ma as ma
import pandas as pd
import pymc as pm
import pytensor
import pytensor.tensor as pt


def meta_binary_outcome(z_t_obs, n_t_obs, z_c_obs, n_c_obs, study, n_draws=1000):
    """Fits multi-level meta-analysis model of binary outcomes.

    See meta-analysis-two-proportions.ipynb in examples for usage.

    Args:
        z_t_obs: number of occurrences in treatment group
        n_t_obs: number of opportunities/participants in treatment gruops
        z_c_obs: number of occurrences in control group
        n_c_obs: number of opportunities/participants in control group
        study: list of studies included in analysis

    Returns:
        pymc.Model and arviz.InferenceData objects.
    """

    with pm.Model(coords={"study": study}) as model:
        # Hyper-priors
        mu_rho = pm.Normal("mu_rho", mu=0, sigma=10)
        sigma_rho = pm.Gamma("sigma_rho", alpha=1.64, beta=0.64)  # mode=1, sd=2

        omega_theta_c = pm.Beta("omega_theta_c", alpha=1.01, beta=1.01)
        kappa_minus_two_theta_c = pm.Gamma(
            "kappa_minus_two_theta_c", alpha=2.618, beta=0.162
        )  # mode=10, sd=10
        kappa_theta_c = pm.Deterministic("kappa_theta_c", kappa_minus_two_theta_c + 2)

        # Priors
        rho = pm.Normal("rho", mu=mu_rho, sigma=sigma_rho, dims="study")
        theta_c = pm.Beta(
            "theta_c",
            alpha=omega_theta_c * (kappa_theta_c - 2) + 1,
            beta=(1 - omega_theta_c) * (kappa_theta_c - 2) + 1,
            dims="study",
        )
        theta_t = pm.Deterministic(
            "theta_t", pm.invlogit(rho + pm.logit(theta_c))
        )  # ilogit is logistic

        # Likelihood
        z_t = pm.Binomial("z_t", n_t_obs, theta_t, observed=z_t_obs)
        z_c = pm.Binomial("z_c", n_c_obs, theta_c, observed=z_c_obs)

        # Sample from the posterior
        idata = pm.sample(draws=n_draws, target_accept=0.90)

        return model, idata


def meta_normal_outcome_beta_version(eff_size, se_eff_size, study, n_draws=1000):
    """Fits multi-level meta-analysis model of normally-distribute outcomes.

    See meta-analyses.ipynb in examples for usage.

    Args:
        eff_size: Reported standardized effect size
        se_eff_size: Reported standard error
        study: List of studies included in analysis

    Returns:
        pymc.Model and arviz.InferenceData objects.
    """

    with pm.Model(coords={"study": study}) as model:
        # Hyper-priors (assumes observations are standaradized effect sizes)
        mu_theta = pm.Normal("mu_theta", mu=0, sigma=1)  # Diffuse prior
        tau_theta = pm.Exponential("tau_theta", lam=1)  # Expected value = 1 / lam

        # Priors
        theta = pm.Normal("theta", mu=mu_theta, sigma=tau_theta, dims="study")

        # Likelihood: y is empirical effect size of each study
        y = pm.Normal("y", mu=theta, tau=1 / (se_eff_size**2), observed=eff_size)

        # Sample from the posterior
        idata = pm.sample(draws=n_draws, target_accept=0.90)

    return model, idata
