## Issue

I am trying to impement the random walk metropolis hastings algorithm which my code is :

``````import numpy as np
def rwmetrop(data,mu0=0,kappa0=1,alpha0=1,lambda0=1,nburn=1000,ndraw=10000,vmu=1,vomega=1):

n = len(data)
alpha1 = (n/2) + alpha0 - 1

stdvmu = np.sqrt(vmu)
stdvomega = np.sqrt(vomega)

mu = np.random.normal(mu0,
np.sqrt(1/kappa0),
size =1)

omega = np.random.gamma(shape = alpha0,
scale = 1/alpha0,
size  = 1)

draws  =  np.empty([ndraw,2])

acceptmu = 0
acceptomega = 0

it = -nburn

while it < ndraw:

mucan = np.random.normal(mu,stdvmu,1)
logp = (kappa0/2)*((mu-mu0)**2-((mucan-mu0)**2)) + np.sum( np.log( 1+omega*(  (data-mu)**2 )  - np.log(1+omega*(data-mucan)**2)))

u  = np.random.uniform(0,1,1)

if np.log(u) < logp:
acceptmu = acceptmu + 1
mu  = mucan

omegacan = np.random.normal(omega,stdvomega,1)

if omegacan > 0:
logp = alpha1*(np.log(omegacan)-np.log(omega)) + lambda0*(omega-omegacan)+ sum(np.log(1+omega*( ((data-mu)**2)))- np.log(1+omegacan*( (data-mu)**2)) )
u = np.random.uniform(0,1,1)

if np.log(u) < logp:
acceptomega = acceptomega + 1
omega = omegacan

if it>0:
draws[it,0] = mu
draws[it,1] = omega

it = it+1

return(draws)

from scipy.stats import cauchy
data = cauchy.rvs(loc=1, scale=1, size=100)
``````

But when i run the created function i receive a warning that says

``````draws4=rwmetrop(data=data,mu0=0,kappa0=1,alpha0=1,lambda0=1,nburn=1000,ndraw=10000,vmu=1,vomega=1)
mu=draws4[:,0];mu
``````
`````` RuntimeWarning: invalid value encountered in log
logp = (kappa0/2)*((mu-mu0)**2-((mucan-mu0)**2)) + np.sum( np.log( 1+omega*(  (data-mu)**2 )  - np.log(1+omega*(data-mucan)**2)))
``````

i checked the parenthesis but it seem to me ok.Probably some 0 (zero) creates the warning ?

what is wrong with my code?

I would appreciate any help from anybody.

## Solution

When you call the function with this variables. The result of `1+omega*(data-mucan)**2` has a lot of negative number and when calculate `np.log(1+omega*(data-mucan)**2)` code calculate np.log(negative number) and this is `invalid value encountered in log`. negative number for log is out of the range