我在 R 到 python 的翻译中做错了什么？

Question

I have a code in R which implements the Metropolis Hastings algorithm:

trials <- 100000
sim <- numeric(trials)
sim[1] <- 2
for (i in 2: trials) {
   old <- sim[i-1]
   prop <- runif(1,0,5)
   acc <- (exp(-(prop-1)^2/2) + exp(-(prop-4)^2/2)) /
     ( (exp(-(old-1)^2/2) + exp(-(old-4)^2/2)) )
   if (runif(1) < acc) 
     sim[i] <- prop
   else
     sim[i] <- old }
mean(sim)
var(sim)

and the results are right.

But when I translate it in Python the results are different.

trials = 100000
sim = np.repeat(0,trials+1)
sim[0] = 2
for i in range (2, trials):
    old = sim[i-1]
    prop = np.random.uniform(0,5,1)
    acc = (np.exp(-(prop-1)**2/2) + np.exp(-(prop-4)**2/2)) /( (np.exp(-(old-1)**2/2) + np.exp(-(old-4)**2/2)) )
    if np.random.uniform(1) < acc:
        sim[i] = prop
    else:
        sim[i] = old 

Why? What I am doing wrong here?

Answer 1

Firstly, you want to start your python for loop at i=1 in the range(1, trials) since Python starts at 0 .

Secondly, at if np.random.uniform(1) you are just producing 1.0 , so that needs to change, eg np.random.uniform(min, max, size=1) or np.random.uniform(size=1) if you just want a uniform number between 0 and 1. Have a look at the documentation for np.random.uniform if this isn't clear.

Update
Thirdly, you are unknowingly casting to integers, so this needs to be handled also. When being used to R this is easy to forget (I just did myself). I have refactored your code below, and this solution should provide you with a similar result to what you see in R.

Here I turned sim into a float vector, and I made sure to subtract and divide using floats inside the exp -functions. Hope this works for you.

trials = 100000
sim = np.repeat(0,trials).astype(np.float64)
sim[0] = 2.0
for i in range (1, trials):
    old = sim[i-1]
    prop = np.random.uniform(0,5,1)
    acc = (np.exp(-(prop-1.0)**2/2.0) + np.exp(-(prop-4.0)**2/2.0)) \
    / ( (np.exp(-(old-1.0)**2/2.0) + np.exp(-(old-4.0)**2/2.0)) )
    if np.random.uniform(size=1) < acc:
        sim[i] = prop
    else:
        sim[i] = old