后验概率 Python 示例

Question

我正在构建一个简单的近似贝叶斯计算应用程序，但遇到了问题。 我不知道如何正确实现 后验概率。

我的先验：非信息量（均匀分布）

生成模型：使用numpy二项分布实现随机是/否猜测

以下是代码：

import numpy as np
import pandas as pd

def pprob():
    pass

def generative_model(n_events, p):
    return np.random.binomial(n_events, p)

def ABC(n_occured, n_events, n_draws=100000):
    prior = pd.Series(np.random.uniform(0, 1, size=n_draws))
    sim_data = [generative_model(n_events, p) for p in prior]
    posterior = prior[list(map(lambda x: x == n_occured, sim_data))]
    posterior_probability = pprob()

ABC(10, 16)

提前致谢！

- user10300706

Answer 1

感谢: 这个网站 我的解决方案的完整代码是：

import math
from scipy import stats
from scipy.special import factorial
from matplotlib import pyplot as plt

def likelihood(theta, n, x):
    return (factorial(n) / (factorial(x) * factorial(n - x))) * (theta  x) * ((1 - theta)  (n - x))

def pprob(prior, posterior, n_occured, n_events):
    return pd.Series(map(lambda theta: likelihood(theta, n_events, n_occured), prior))

def generative_model(n_events, p):
    return np.random.binomial(n_events, p)

def ABC(n_occured, n_events, n_draws=1000):
    prior = pd.Series(sorted(np.random.uniform(0, 1, size=n_draws)))
    sim_data = [generative_model(n_events ,p) for p in prior]
    posterior = prior[list(map(lambda x: x == n_occured, sim_data))]
    posterior_probability = pprob(prior, posterior, n_occured, n_events)

    # let's see what we got
    f, ax = plt.subplots(1)
    ax.plot(prior, posterior_probability)
    ax.set_xlabel("Theta")
    ax.set_ylabel("Likelihood")
    ax.grid()
    ax.set_title("Likelihood of Theta for New Campaign")
    plt.show()

ABC(10, 16)

产生了这个可爱的可能性：

]

- user10300706

---

这篇文章中引用的源已经更改。可以在这里找到它。 - ZdWhite

Answer 2

我添加了一些更正，这样它第一次就能运行：

import math
from scipy import stats
from scipy.special import factorial
from matplotlib import pyplot as plt
import pandas as pd
import numpy as np

def likelihood(theta, n, x):
    return (factorial(n) / (factorial(x) * factorial(n - x))) * (theta ** x) * ((1 - theta) ** (n - x))

def pprob(prior, posterior, n_occured, n_events):
    return pd.Series(map(lambda theta: likelihood(theta, n_events, n_occured), prior))

def generative_model(n_events, p):
    return np.random.binomial(n_events, p)

def ABC(n_occured, n_events, n_draws=1000):
    prior = pd.Series(sorted(np.random.uniform(0, 1, size=n_draws)))
    sim_data = [generative_model(n_events ,p) for p in prior]
    posterior = prior[list(map(lambda x: x == n_occured, sim_data))]
    posterior_probability = pprob(prior, posterior, n_occured, n_events)

    # let's see what we got
    f, ax = plt.subplots(1)
    ax.plot(prior, posterior_probability)
    ax.set_xlabel("Theta")
    ax.set_ylabel("Likelihood")
    ax.grid()
    ax.set_title("Likelihood of Theta for New Campaign")
    plt.show()

ABC(10, 16)

- jam