Sham - 3 months ago 26

Python Question

I am trying to implement a fucntion which returns 100 samples from three different multivariate gaussian distributions.

numpy provides a way to sample from a sinle multivariate gaussian. But I could not find a way to sample from three different multivariate with different sampling probability.

My requirement is to sample with probability $[0.7, 0.2, 0.1]$ from three multivariate gaussians with mean and covariances as given below

`G_1 mean = [1,1] cov =[ [ 5, 1] [1,5]]`

G_2 mean = [0,0] cov =[ [ 5, 1] [1,5]]

G_3 mean = [-1,-1] cov =[ [ 5, 1] [1,5]]

Any idea ?

Answer

Say you create an array of your generators:

```
generators = [
np.random.multivariate_normal([1, 1], [[5, 1], [1, 5]]),
np.random.multivariate_normal([0, 0], [[5, 1], [1, 5]]),
np.random.multivariate_normal([-1, -1], [[5, 1], [1, 5]])]
```

Now you can create a weighted random of generator indices, since `np.random.choice`

supports weighted sampling:

```
draw = np.random.choice([0, 1, 2], 100, p=[0.7, 0.2, 0.1])
```

(`draw`

is a length-100 array of entries, each from *{0, 1, 2}* with probability *0.7, 0.2, 0.1*, respectively.)

Now just generate the samples:

```
[generators[i] for i in draw]
```