I am trying to do a reliability simulation project, and I kept getting this ‘Chain 1: Log probability evaluates to log(0), i.e. negative infinity. Chain 1: Stan can’t start sampling from this initial value.’ error. I guess I need some reparameterization but have no clue where to begin.

Here is how I simulated the data.

```
set.seed(666)
alpha = matrix(c(0.001, 0.05, 0.0001, 0.08), ncol = 2, byrow = TRUE)
w = c(45, 55)
t = matrix(seq(10, 40, 10), ncol = 2, byrow = TRUE)
K = c(10, 50, 100)
lambda = function(r = 1:2, j = 1:2) {
alpha_r0 = alpha[r, 1]
alpha_r1 = alpha[r, 2]
return(alpha_r0*exp(alpha_r1*w[j]))
}
p = function(i = 1:2, j = 1:2){
lam1j = lambda(1, j)
lam2j = lambda(2, j)
p0 = exp(-(lam1j + lam2j)*t[i, j])
p1 = (lam1j/(lam1j + lam2j))*(1 - p0)
p2 = (lam2j/(lam1j + lam2j))*(1 - p0)
return(c(p0, p1, p2))
}
Tmatrxi = t(rmultinom(10, K[1], prob = p(1, 1)))
```

This simulated data is then estimated using a multinomial distribution. I guess the only thing that makes this a little bit trickier is the \theta (p in Stan code) in the multinomial distribution are dependent on other parameters (`a00`

and `a11`

in this case).

```
data {
int<lower=0> n;
int DAT[n, 3];
vector[2] W;
vector[4] Tim;
}
parameters{
real<lower=0> a00;
real<lower=0> a01;
}
transformed parameters{
real<lower=0, upper=1> p0;
real<lower=0, upper=1> p1;
real<lower=0, upper=1> p2;
vector[3] p;
p0 = exp(-(a00*exp(a01*W[1]) + a00*exp(a01*W[2]))*Tim[1]);
p1 = (a00*exp(a01*W[1])/(a00*exp(a01*W[1]) + a00*exp(a01*W[2])))*(1 - p0);
p2 = 1-p0-p1;
p[1] = p0; p[2] = p1; p[3] = p2;
}
model{
for (i in 1:n)
target += multinomial_lpmf(DAT[i,] | p);
//DAT[i,] ~ multinomial(p);
a00 ~ gamma(1, 10);
a01 ~ gamma(1, 10);
}
```

Then I run this model with rstan using the following code.

```
library(rstan)
rstan_options(auto_write = TRUE)
stan_dat = list(
n = nrow(Tmatrxi),
DAT = Tmatrxi,
W = w,
Tim = seq(10, 40, 10)
)
fit <- stan(
model_code = reliab, data = stan_dat, init_r = 0.0001,
warmup = 500, iter = 1000, chains = 1, cores = 1)
```

However, Stan keeps giving me the error `Chain 1: Log probability evaluates to log(0), i.e. negative infinity. Chain 1: Stan can't start sampling from this initial value.`

Specifying initial values does not work here as I have tried different `init_r`

. Even if I narrow that down to 0.0001, Stan can not sample from this distribution. I guess the other approach could be reparameterizing the model. My prior experience of reparameterization is limited non-centered parameterization, which may not be applied here.

Is there another way to get around this error? Thanks!