同样的线索，换一批人就不该给同样的概率？

"""Exact discrete label-shift examples; no fitting, sampling, or network."""
import json
import math
from pathlib import Path


def posterior(prior_one, red_given_one, red_given_zero, color):
    likelihood_one = red_given_one if color == 'red' else 1 - red_given_one
    likelihood_zero = red_given_zero if color == 'red' else 1 - red_given_zero
    numerator = prior_one * likelihood_one
    denominator = numerator + (1 - prior_one) * likelihood_zero
    if denominator <= 0:
        raise ValueError('The observation has zero probability.')
    return numerator / denominator


def correct(source_probability, source_prior, target_prior):
    if not 0 < source_prior < 1:
        raise ValueError('Source must support both classes.')
    if not 0 <= target_prior <= 1 or not 0 <= source_probability <= 1:
        raise ValueError('Probabilities must be in [0, 1].')
    one = source_probability * target_prior / source_prior
    zero = (1 - source_probability) * (1 - target_prior) / (1 - source_prior)
    if one + zero == 0:
        raise ValueError('The reweighted observation has zero probability.')
    return one / (one + zero)


def evaluate(probabilities, prior, red_one, red_zero):
    accuracy = brier = total = 0.0
    for y, weight, p_red in [(1, prior, red_one), (0, 1 - prior, red_zero)]:
        for color, likelihood in [('red', p_red), ('blue', 1 - p_red)]:
            mass = weight * likelihood
            prediction = int(probabilities[color] >= 0.5)
            total += mass
            accuracy += mass * (prediction == y)
            brier += mass * (probabilities[color] - y) ** 2
    assert math.isclose(total, 1.0, abs_tol=1e-12)
    return {'accuracy': accuracy, 'brier': brier}


def main():
    source_prior = 0.5
    source = {c: posterior(source_prior, 0.8, 0.2, c) for c in ['red', 'blue']}
    target_prior = 0.1
    corrected = {c: correct(p, source_prior, target_prior) for c, p in source.items()}
    exact = {c: posterior(target_prior, 0.8, 0.2, c) for c in source}
    for c in source:
        assert math.isclose(corrected[c], exact[c], abs_tol=1e-12)
        assert math.isclose(correct(source[c], source_prior, source_prior), source[c])
    before = evaluate(source, target_prior, 0.8, 0.2)
    after = evaluate(corrected, target_prior, 0.8, 0.2)
    assert after['brier'] < before['brier']
    print('valid label shift: prior 0.5 -> 0.1; class-conditional likelihoods unchanged')
    for c in source:
        print(f'{c}: source={source[c]:.6f}, corrected={corrected[c]:.6f}, exact={exact[c]:.6f}')
    print(f"expected accuracy: {before['accuracy']:.6f} -> {after['accuracy']:.6f}")
    print(f"expected Brier: {before['brier']:.6f} -> {after['brier']:.6f}")
    # The target now reverses class-conditional color probabilities.
    broken_prior = 0.3
    wrong = {c: correct(p, source_prior, broken_prior) for c, p in source.items()}
    oracle = {c: posterior(broken_prior, 0.2, 0.8, c) for c in source}
    wrong_metrics = evaluate(wrong, broken_prior, 0.2, 0.8)
    oracle_metrics = evaluate(oracle, broken_prior, 0.2, 0.8)
    assert wrong_metrics['accuracy'] < oracle_metrics['accuracy']
    print('invalid label shift: class-conditional likelihoods reversed')
    for c in source:
        print(f'{c}: prior-only={wrong[c]:.6f}, actual={oracle[c]:.6f}')
    print(f"expected accuracy: prior-only={wrong_metrics['accuracy']:.6f}, actual-posterior={oracle_metrics['accuracy']:.6f}")
    try:
        correct(0.5, 0.0, 0.1)
    except ValueError:
        print('zero source support: rejected')
    else:
        raise AssertionError('Missing source-support check.')
    report = {'source':source, 'valid_shift':{'prior':target_prior,'corrected':corrected,
        'exact':exact,'before':before,'after':after}, 'invalid_shift':{'prior':broken_prior,
        'prior_only':wrong,'actual':oracle,'prior_only_metrics':wrong_metrics,'actual_metrics':oracle_metrics},
        'scope':'Exact enumeration of specified distributions; target priors supplied, not estimated; no trained model.'}
    Path('report.json').write_text(json.dumps(report, indent=2, allow_nan=False)+'\n', encoding='utf-8')
    print('checks passed: exact Bayes match, identity shift, normalized mass, violated-assumption counterexample')


if __name__ == '__main__':
    main()