I am currently trying to **approximate** the Poisson distribution with Normal for my prior in the Bayesian model. The code has no error, but then I keep encountering this error, which I think is due to the very sparse data feed into the model.

```
data {
int<lower=1> ncol;
int<lower=1> nrow;
vector[ncol] yH;
vector[nrow] x;
#int x[nrow];
matrix[nrow, ncol] A;
vector[nrow] sigma_x;
vector[ncol] sigma_y;
#matrix[nrow,ncol] sigma_x;
#matrix[nrow,ncol] sigma_y;
vector[nrow] epsilon;
}
parameters {
vector<lower = 0>[ncol] yT;
}
model {
yT ~ normal(yH, sqrt(yH)); //to approximate the fact that yT ~ poisson(yH)
x ~ normal(A*yT + epsilon, sigma_x);
//x ~ multi_normal(A*yT + epsilon, sigma_x);
}
```

I used the following R code to feed in the data and run:

foreach(i = 1:20) %dopar% {

nrow = nrow(rte_m[[i]]);

ncol = ncol(rte_m[[i]]);

A <- as.matrix(rte_m[[i]]);

sigma_x <- as.vector(sample.int(10, nrow(kf_vect[[i]]), replace=TRUE))

sigma_y <- as.vector(eps_vect[[i]])

yH <- as.vector(dh_vect[[i]]$X);

yT <- yH + as.vector(eps_vect[[i]]);

epsilon <- sample.int(15, nrow(kf_vect[[i]]), replace=TRUE)

x <- round(as.vector(as.matrix(rte_m[[i]])%*%yT) + epsilon)

iterations = 200;

#input it into our Stan model file âstamodeling.stanâ

stanmodel1 <- stan_model(file = âpoissnorm.stanâ,

model_name = âstanmodel1â);#NUTS (No U-Turn) sampler to generate posterior distribution

stanfit <- sampling(stanmodel1, cores = parallel::detectCores(), data = list(ncol = ncol,nrow = nrow,

yH = yH,

x=x, epsilon = epsilon,

A = A, sigma_y = sigma_y)

,iter=iterations, chains = 3, control = list(max_treedepth=13));

print(i)

When I run, it starts very fast, but then it gave me this error message that I cannot fix:

Rejecting initial value:

Error evaluating the log probability at the initial value.

Exception: normal_lpdf: Random variable[1] is nan, but must not be nan! (in âmodel23728163056_stanmodel1â at line 24)

I remember I could add something to change the initial starting point of MCMC, but I am not sure if that even helps in this case. Can someone please help me on this issue? I encountered it twice, but failed to overcome it:((