python - Python 中的相关值

Question

所以我有一个代码，它给了我一堆相关的两个参数的随机值。

import numpy as np
import matplotlib.pyplot as plt

def correlated_sample(x, y, sig_x, sig_y, corr, size):
    # Given a mean "x" value with uncertainty "sig_x", a mean "y" value
    # with uncertainty "sig_y" and there is a correlation, "corr",
    # between the two variables, then this function will return
    # a random sample of size "size" of 2D values maintaining that correlation.
    cov_mat = [[sig_x**2        , sig_x*sig_y*corr],
               [sig_y*sig_x*corr,         sig_y**2]]
    x, y = np.random.multivariate_normal(mean = [x, y], cov_mat, size).T
    return (x, y)

# PLOT EXAMPLE
x_arr, y_arr = correlated_sample(0, 5, 0.5, 0.9, 0.5, 10**4)
plt.scatter(x_arr, y_arr, color = 'k', s = 1, alpha = 0.2)
plt.xlim([-4, 4])
plt.ylim([1, 9])
plt.show()

它按预期工作并给出以下输出：

但现在我想做一些更复杂的事情：假设我现在选择一个数据点，例如 20th:x_point = x_arr[20]和y_point = y_arr[20]. 现在我想在这个分布中以小的间隔获得该点的随机邻居，但保持相关性。

如果没有相关性，我可以简单地做出：

# Size of the small region around the point.
# In this example it is 50 times smaller than the entire cloud of points.
neighbourhood_extent = 1/50

x_neighbour = np.random.normal(x_point, sig_x*neighbourhood_extent, size = 1)
y_neighbour = np.random.normal(y_point, sig_y*neighbourhood_extent, size = 1)

我会有一个相邻的点。但由于两者之间存在相关性x，y我不能这样做。我应该如何进行？

标签： pythonnumpycorrelationdistribution