[Python - scipy]：从自定义多元概率密度生成随机样本 Function (PDF)

Question

I want to generate random sample (vector X) :

X = [x1, x2, x3, ..., x_d]

where X follows a custom multivariate Probability Density Function .

I am using Python - scipy and I overvide the PDF function to follow a combination of multivariate normal distributions.

For example:

import plotly.graph_objects as go
import numpy as np
from scipy.stats._multivariate import multivariate_normal_gen, multivariate_normal, _squeeze_output


class multivar_rv(multivariate_normal_gen):

    def pdf(self, x, mean=None, cov=1, allow_singular=True):
        mean = [
            [0, 1],
            [2, 5]
        ]
        cov = [
            [
                [1, 0],
                [0, 1]
            ],
            [
                [1.5, 0],
                [0, 1.5]
            ]
        ]
        weight = [.5, .5]
        return sum(weight[i] * multivariate_normal(mean[i], cov[i]).pdf(x) for i in range(len(mean)))

The following image shows the plot of the above code.

Now I want to generate samples given the above distribution , however if I use rvs() (from scipy.stats._multivariate.multivariate_normal_gen) the function is not overrided and the results will be generated from the default normal distribution:

P.rvs()

What do I have to do in order to change this and override this function so that the generated samples follow my PDF?

Thank you!

Answer 1

That is because the the rvs method that your class inherits (ie that of multivariate_normal_gen) uses an instance of multivariate_normal_gen directly that is declared outside of the class definition ( see lines 657 and 682 in the source ) to generate samples. You have to write your own rvs method explicitly.