使用不了scale_inv_chisq函数，请帮我重新写一段代码

如果你无法直接使用`scale_inv_chisq`函数，那我们可以手动计算共轭先验的后验密度。以下是基于`norm`和`chi2`分布的简单实现：

from scipy.special import gammaln
import numpy as np

def scale_inv_chisq_pdf(x, nu, kappa):
    """
    Scale-Inverse Chi-squared (SIC) posterior density function.
    """
    return (x**(-nu - 1)) * np.exp(-kappa / x) / (2**(nu / 2) * gamma(nu / 2))

def compute_posterior_sigma(data, mean, kappa_0, sigma_0):
    """
    Compute the posterior standard deviation using manual SIC calculation.
    """
    nu = kappa_0 - 2
    precision = np.sum((data - mean)**2) + kappa_0 * sigma_0**2
    sigma_posterior = np.sqrt(precision) / (nu + len(data))
    return sigma_posterior

# 假设data是一个包含星系速度的数据数组
mean_speed = 6500
kappa_0 = 10
sigma_0 = 1500
data = ...  # 从你的数据文件读取数据

sigma_posterior = compute_posterior_sigma(data, mean_speed, kappa_0, sigma_0)

# 绘制后验分布
x_range = np.linspace(min(data), max(data), 100)
posterior_pdf = scale_inv_chisq_pdf(x_range, nu, kappa_0)
empirical_pdf = np.histogram(data, bins='auto', density=True)[0]

fig, ax = plt.subplots()
ax.bar(x_range[:-1], empirical_pdf, width=np.diff(x_range)[0], alpha=0.5, label='Empirical distribution')
ax.plot(x_range, posterior_pdf, 'r-', lw=2, alpha=0.7, label='Posterior distribution (manual)')
ax.set_xlabel('Galaxy Speed (km/s)')
ax.set_ylabel('Probability Density')
ax.legend()
plt.title(f"Speed Dispersion Posterior for Coma Galaxy Cluster")
plt.show()