There are lots of warnings each time run. I wonder what those warning means? Does it means anything I need to change? Thanks,

```
ARNING:theano.configdefaults:install mkl with `conda install mkl-service`: No module named mkl
WARNING:theano.tensor.blas:Using NumPy C-API based implementation for BLAS functions.
DIAGNOSTIC(S) FROM PARSER:
Warning: left-hand side variable (name=lamba) occurs on right-hand side of assignment, causing inefficient deep copy to avoid aliasing.
INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_859efd3f82721222b491da93cf8e482d NOW.
Cannot build msvcr library: "msvcr90d.dll" not found
WARNING:pystan:Multiprocessing is not supported on Windows with Python 2.X. Setting n_jobs=1
Gradient evaluation took 0.001 seconds
1000 transitions using 10 leapfrog steps per transition would take 10 seconds.
Adjust your expectations accordingly!
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: validate transformed params: cov[k0__][k1__] is 0, but must be > 0! (in 'unknown file name' at line 23)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: validate transformed params: cov[k0__][k1__] is 0, but must be > 0! (in 'unknown file name' at line 23)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: validate transformed params: cov[k0__][k1__] is 0, but must be > 0! (in 'unknown file name' at line 23)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: exponential_lpdf: Inverse scale parameter[1] is 0, but must be > 0! (in 'unknown file name' at line 64)
Iteration: 1 / 1000 [ 0%] (Warmup)
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: validate transformed params: cov[k0__][k1__] is 0, but must be > 0! (in 'unknown file name' at line 23)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: validate transformed params: cov[k0__][k1__] is not lower triangular; cov[k0__][k1__][1,2]=nan (in 'unknown file name' at line 23)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: exponential_lpdf: Inverse scale parameter[1] is 0, but must be > 0! (in 'unknown file name' at line 64)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: exponential_lpdf: Inverse scale parameter[1] is 0, but must be > 0! (in 'unknown file name' at line 64)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Iteration: 100 / 1000 [ 10%] (Warmup)
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: exponential_lpdf: Inverse scale parameter[1] is 0, but must be > 0! (in 'unknown file name' at line 64)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Iteration: 200 / 1000 [ 20%] (Warmup)
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: exponential_lpdf: Inverse scale parameter[1] is 0, but must be > 0! (in 'unknown file name' at line 64)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Iteration: 300 / 1000 [ 30%] (Warmup)
Iteration: 400 / 1000 [ 40%] (Warmup)
Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
Exception: exponential_lpdf: Inverse scale parameter[1] is 0, but must be > 0! (in 'unknown file name' at line 64)
If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
Iteration: 500 / 1000 [ 50%] (Warmup)
Iteration: 501 / 1000 [ 50%] (Sampling)
Iteration: 600 / 1000 [ 60%] (Sampling)
Iteration: 700 / 1000 [ 70%] (Sampling)
Iteration: 800 / 1000 [ 80%] (Sampling)
Iteration: 900 / 1000 [ 90%] (Sampling)
Iteration: 1000 / 1000 [100%] (Sampling)
Elapsed Time: 2.672 seconds (Warm-up)
1.957 seconds (Sampling)
4.629 seconds (Total)
WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated
WARNING:pystan:Rhat for parameter L[1,1,1] is nan!
WARNING:pystan:Rhat for parameter cov[1,1,1,2] is nan!
WARNING:pystan:Rhat for parameter Omega[1,1,1] is nan!
WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed
Inference for Stan model: anon_model_859efd3f82721222b491da93cf8e482d.
1 chains, each with iter=1000; warmup=500; thin=1;
post-warmup draws per chain=500, total post-warmup draws=500.
```

```
from __future__ import division
import pystan
import pymc3 as pm
from scipy import stats
import matplotlib.pyplot as plt
import theano.tensor as tt
import seaborn as sns
import numpy as np
import os
import pandas as pd
x = np.array([-18.59749343,9.29064092, -6.74614328, -7.58674294, 7.14575445,
6.22886667, 3.66103665, -21.24150863, 2.936587, -0.91788529])
y = np.array([-1.47716748,7.75337739,-4.81924601,-6.50501856, 0.83028804,10.83534704,
5.76506376 ,-2.51054588 , 6.62877459 ,4.1892128 ])
x=np.array(zip(x,y))
c = np.array([1.3218437633965887e-17, 0.0006677388144037628, 0.0017339911877023338, 0.00026935063841600725, 0.004014659576775406, 0.009961389820779551, 0.004177733722366306, 3.8559281009422705e-21, 0.005608820830947575, 6.89137069068125e-05])
s = np.array([0,0])
st=[[4]]*10
model='''
data {
int D; //number of dimensions
int K; //number of gaussians
int N; //number of data
int M; // patch number at time
vector[D] y[N]; // observation data
real con[N]; //concentration
vector[D] s;//oil spill location
matrix[N,M] st;
//real se[M]; // spill end time
}
parameters {
simplex[K] theta; //mixing proportions
vector<lower=-10,upper=10>[D] v[K];
//vector[D] v[K];
vector<lower=0>[D] Dif[K];
cholesky_factor_corr[D] L[K]; //cholesky factor of correlation matrix
}
transformed parameters{
cholesky_factor_cov[D,D] cov[K*M,N];
vector<lower=0>[D] sigma[K*M,N]; // standard deviations
vector[D] mu[K*M,N];
real<lower=-1,upper=1> ro[K];
matrix[D,D] Omega[K];
matrix[D,D] Sigma[K*M,N];
vector<lower=0>[N] lamba;
for (k in 1:K) {
Omega[k] = multiply_lower_tri_self_transpose(L[k]);
ro[k]=Omega[k,2,1];
for (m in 1:M){
for (n in 1:N) {sigma[k+K*(m-1),n] = 0.05 + sqrt(2*(st[n][m])*Dif[k]);
mu[k+K*(m-1),n] = s+v[k]*st[n][m];
cov[k+K*(m-1),n] = diag_pre_multiply(sigma[k+K*(m-1),n],L[k]);
Sigma[k+K*(m-1),n] = quad_form_diag(Omega[k], sigma[k+K*(m-1),n]);}
}
}
for (i in 1:N) {
lamba[i]=0;
for (k in 1:K){
for (m in 1:M)
{lamba[i] = lamba[i]+(0.25/M)*(1./2./3.1415926/sqrt(Sigma[k+K*(m-1),i, 1, 1])/sqrt (Sigma[k+K*(m-1),i, 2, 2])/sqrt (1 - ro[k]*ro[k]))*exp (-1./2./(1 - ro[k]*ro[k])*(-(y[i, 1] - mu[k+K*(m-1),i, 1])*(y[i, 1] - mu[k+K*(m-1),i, 1])/Sigma[k+K*(m-1), i,1, 1] - (y[i, 2] - mu[k+K*(m-1), i,2])*(y[i, 2] - mu[k+K*(m-1), i,2])/Sigma[k+K*(m-1),i, 2, 2]
+ 2.*ro[k]*(y[i, 1] - mu[k+K*(m-1),i, 1])*(y[i, 2] - mu[k+K*(m-1),i, 2])/sqrt (Sigma[k+K*(m-1), i,1, 1])/sqrt (Sigma[k+K*(m-1),i, 2, 2])));
// + theta[2]*(1./2./3.1415926/sqrt (Sigma[k+K*(m-1), i,1, 1])/sqrt (Sigma[2,i, 2, 2])/sqrt (1 - ro[2]*ro[2]))*exp (-1./2./(1 - ro[2]*ro[2])*(-(y[i, 1] - mu[2, i,1])*(y[i, 1] - mu[2, i,1])/Sigma[2, i,1, 1] - (y[i, 2] - mu[2,i, 2])*(y[i, 2] - mu[2, i,2])/Sigma[2,i, 2, 2]
// + 2.*ro[2]*(y[i, 1] - mu[2, i,1])*(y[i, 2] - mu[2, i,2])/sqrt (Sigma[2, i,1, 1])/sqrt (Sigma[2, i,2, 2]))));}
}
}
lamba[i]=1/lamba[i];
}
}
model {
real ps[K*M];
//theta ~ dirichlet(rep_vector(2.0, K));
for(k in 1:K){
//v[k,1] ~ normal(3.67,5.0);//normal(0,4.1);//// uniform(340/100,380/100);//
//v[k,2]~ normal(2,5.0);//normal(0,4.1);////uniform(3160/100,3190/100);//
Dif[k] ~ exponential(0.5); //normal(0.5,5);//normal(5,10);////beta(2,5);//uniform(0.1,0.89); //////normal(1,2);
L[k] ~ lkj_corr_cholesky(2);// contain rho
con ~ exponential(lamba);
}
for (i in 1:N){
con[i] ~ exponential(lamba[i]);
}
for (n in 1:N){
for (k in 1:K){
for (m in 1:M){
ps[k+K*(m-1)] = log(theta[k]/M)+multi_normal_cholesky_lpdf(y[n] | mu[k+K*(m-1),n], cov[k+K*(m-1),n]); //increment log probability of the gaussian
}
}
//increment_log_prob(log_sum_exp(ps));
//target += ps;
target += log_sum_exp(ps);
}
for(i in 1:N){
target += - lamba[i]*con[i]+log(lamba[i]);
}
}
'''
dat={'D':2,'K':4,'N':10,'y':x,'con':c,'s':s,'st':st,'M':1}
fit = pystan.stan(model_code=model,data=dat,iter=1000,warmup=500, chains=1,init_r=0.5)
print(fit)
trace = fit.extract()
print trace.keys()
```