ValidReuse/bayesian.py at main · wseis/ValidReuse · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
from __future__ import annotations

import math
from typing import Iterable

import numpy as np


def _sample_lognormal_posterior(vals_zu: np.ndarray, draws: int, rng: np.random.Generator) -> tuple[np.ndarray, np.ndarray]:
    log_vals = np.log(vals_zu)
    n = len(log_vals)
    mean_y = float(np.mean(log_vals))
    ssq = float(np.sum((log_vals - mean_y) ** 2))

    mu0 = mean_y
    kappa0 = 0.25
    alpha0 = 2.5
    beta0 = max(np.var(log_vals, ddof=1), 1e-6)

    kappa_n = kappa0 + n
    alpha_n = alpha0 + 0.5 * n
    beta_n = beta0 + 0.5 * ssq + (kappa0 * n * (mean_y - mu0) ** 2) / (2.0 * kappa_n)
    mu_n = (kappa0 * mu0 + n * mean_y) / kappa_n

    sigma2_draws = 1.0 / rng.gamma(shape=alpha_n, scale=1.0 / beta_n, size=draws)
    meanlog_draws = rng.normal(loc=mu_n, scale=np.sqrt(sigma2_draws / kappa_n))
    sdlog_draws = np.sqrt(sigma2_draws)
    return meanlog_draws, sdlog_draws


def _negbin_log_posterior(log_mu: float, log_size: float, vals_ab: np.ndarray) -> float:
    mu = np.exp(log_mu)
    size = np.exp(log_size)

    if not np.isfinite(mu) or not np.isfinite(size):
        return -np.inf

    lgamma = np.vectorize(math.lgamma)

    log_likelihood = np.sum(
        lgamma(vals_ab + size)
        - math.lgamma(size)
        - lgamma(vals_ab + 1.0)
        + size * (log_size - np.log(size + mu))
        + vals_ab * (log_mu - np.log(size + mu))
    )

    mean_anchor = np.log(np.mean(vals_ab) + 0.5)
    log_mu_prior = -0.5 * ((log_mu - mean_anchor) / 3.0) ** 2
    log_size_prior = -0.5 * (log_size / 2.5) ** 2
    return float(log_likelihood + log_mu_prior + log_size_prior)


def _sample_negative_binomial_posterior(
    vals_ab: np.ndarray,
    draws: int,
    warmup: int,
    chains: int,
    rng: np.random.Generator,
) -> tuple[np.ndarray, np.ndarray]:
    kept_log_mu: list[float] = []
    kept_log_size: list[float] = []
    total_steps = draws + warmup

    for chain in range(chains):
        chain_rng = np.random.default_rng(rng.integers(0, 2**32 - 1))
        current = np.array([np.log(np.mean(vals_ab) + 0.5), 0.0], dtype=float)
        current_lp = _negbin_log_posterior(current[0], current[1], vals_ab)
        proposal_scale = np.array([0.12, 0.10], dtype=float)
        accepted_window = 0

        for step in range(total_steps):
            proposal = current + chain_rng.normal(loc=0.0, scale=proposal_scale, size=2)
            proposal_lp = _negbin_log_posterior(proposal[0], proposal[1], vals_ab)

            if np.log(chain_rng.random()) < proposal_lp - current_lp:
                current = proposal
                current_lp = proposal_lp
                accepted_window += 1

            if step < warmup and (step + 1) % 50 == 0:
                acceptance_rate = accepted_window / 50.0
                if acceptance_rate < 0.20:
                    proposal_scale *= 0.8
                elif acceptance_rate > 0.40:
                    proposal_scale *= 1.2
                accepted_window = 0

            if step >= warmup:
                kept_log_mu.append(current[0])
                kept_log_size.append(current[1])

    return np.exp(np.asarray(kept_log_mu)), np.exp(np.asarray(kept_log_size))


def bayesian_q10_lrv(
    vals_zu: Iterable[int],
    vals_ab: Iterable[int],
    draws: int = 600,
    warmup: int = 300,
    chains: int = 2,
    n_sim: int = 5000,
    q: int = 10,
    alpha: float = 0.05,
    add_one: bool = True,
    seed: int | None = None,
) -> dict[str, float | np.ndarray]:
    rng = np.random.default_rng(seed)
    vals_zu_arr = np.asarray(list(vals_zu), dtype=float)
    vals_ab_arr = np.asarray(list(vals_ab), dtype=float)

    if np.any(vals_zu_arr <= 0):
        raise ValueError("Bayesian analysis requires vals_zu to be greater than 0.")

    q_prob = q / 100.0
    total_draws = draws * chains

    meanlog_draws, sdlog_draws = _sample_lognormal_posterior(vals_zu_arr, total_draws, rng)
    mu_draws, size_draws = _sample_negative_binomial_posterior(vals_ab_arr, draws, warmup, chains, rng)
    posterior_draw_count = min(len(meanlog_draws), len(mu_draws))
    q10_samples = np.empty(posterior_draw_count)

    for i in range(posterior_draw_count):
        in_sim = rng.lognormal(mean=meanlog_draws[i], sigma=sdlog_draws[i], size=n_sim)
        out_sim = rng.negative_binomial(size_draws[i], size_draws[i] / (size_draws[i] + mu_draws[i]), size=n_sim)
        out_sim = out_sim.astype(float)
        if add_one:
            out_sim = out_sim + 1.0

        lrv = np.log10(in_sim / out_sim)
        q10_samples[i] = np.percentile(lrv, q)

    return {
        "L_alpha": float(np.percentile(q10_samples, 100 * alpha)),
        "median": float(np.percentile(q10_samples, 50)),
        "upper_(1-alpha)": float(np.percentile(q10_samples, 100 * (1 - alpha))),
        "mean": float(np.mean(q10_samples)),
        "std_dev": float(np.std(q10_samples)),
        "q10_samples": q10_samples,
    }