Fast arbitrary distribution random sampling (inverse transform sampling)

Question

The random module (http://docs.python.org/2/library/random.html) has several fixed functions to randomly sample from. For example random.gauss

Answer 1

I was in a similar situation but I wanted to sample from a multivariate distribution, so, I implemented a rudimentary version of Metropolis-Hastings (which is an MCMC method).

def metropolis_hastings(target_density, size=500000):
    burnin_size = 10000
    size += burnin_size
    x0 = np.array([[0, 0]])
    xt = x0
    samples = []
    for i in range(size):
        xt_candidate = np.array([np.random.multivariate_normal(xt[0], np.eye(2))])
        accept_prob = (target_density(xt_candidate))/(target_density(xt))
        if np.random.uniform(0, 1) < accept_prob:
            xt = xt_candidate
        samples.append(xt)
    samples = np.array(samples[burnin_size:])
    samples = np.reshape(samples, [samples.shape[0], 2])
    return samples

This function requires a function target_density which takes in a data-point and computes its probability.

For details check-out this detailed answer of mine.