I received a text where the author was employing Stan language in order to show how to create a random walk with normally distributed parameters.

His model had parameters $\mu\_{t}$, ($1,2,...,T$), such that, $\mu\_{t}$ had a priori $N(\mu\_{t-1}, 0.0025)$. He also defined $N(0.5, 0.00001)$ for $\mu\_1$, and $N(0.6, 0.00001)$ for $\mu\_{T}$. His code was like this:

```
data {
  int<lower=1> n_days; 
}
parameters {
  real<lower=0, upper=1> mu[n_days];               
}
model {
  mu[1]  ~ normal(0.5,0.00001);
  for (i in 2:(n_days))
      mu[i] ~ normal(mu[i - 1], 0.005);

mu[n_days] ~ normal(0.6,0.00001);
}

```

This model generated this image. 
[![Image1](https://i.stack.imgur.com/oQiEk.png)](https://i.stack.imgur.com/oQiEk.png)

I noticed, however, that this model indicates two different distributions for $\mu[n\_days]$, $N(\mu[i-1], 0.005)$ and $N(0.6, 0.00001)$. What is happening here? Is this possible?

In order to change this possibility, I removed the second distribution using the following code: 

```
data {
  int<lower=1> n_days; 
}
parameters {
  real<lower=0, upper=1> mu[n_days];               
}
model {
  mu[1]  ~ normal(0.5,0.00001);
  for (i in 2:(n_days - 1))
      mu[i] ~ normal(mu[i - 1], 0.005);

mu[n_days] ~ normal(0.6,0.00001);
}

```

However, this different graph was generated.

[![Image2](https://i.stack.imgur.com/w8KXL.png)](https://i.stack.imgur.com/w8KXL.png)

Why does this difference happen? Are we talking about two different prioris for the same parameter?