Please share your Stan program and accompanying data if possible.

I am implementing stan code for posterior

I want to get posterior

X \sim \mathcal{N}(\sqrt{\theta_1}+\sqrt{\theta_2},2 ), \theta_1 \geq 0, \theta_2 \geq 0, (\theta_1^0,\theta_2^0 =)=(1/4,1/4)

And followings are my code with stan

```
library(tidyverse)
library(rstan)
library(ggmcmc)
N <- 5500
sample_num <-N
x <- list()
y <- list()
theta1 <- 0.25
theta2 <- 0.25
# generate samples
for (i in (1:sample_num)){
x[i] <- rnorm(1,sqrt(theta1)+sqrt(theta2),sqrt(2))
}
model1 <- '
data{
int<lower = 0> N;
real x[N];
}
parameters{
real<lower=0> theta1;
real<lower=0> theta2;
}
transformed parameters{
real theta_base[N];
for (n in 1:N)
theta_base[n]=sqrt(theta1)+sqrt(theta2);
}
model{
for(n in 1:N){
x[n] ~ normal(theta_base[n],sqrt(2));
}
}
'
# fit <- stan(model_code = model1, data = x )
fit <- stan(model_code = model1,
data = list(N = N, x = x, 'theta1' = theta1, 'theta2'=theta2),
iter = 5000, warmup = 500)
```

But I got error messages

"Error in new_CppObject_xp(fields$.module, fields$.pointer, …) :

Exception: mismatch in number dimensions declared and found in context; processing stage=data initialization; variable name=x; dims declared=(5500); dims found=(5500,1) (in ‘model4892c4eff02_3a7f0cbb8d98b7cdc4a85cd3401a90be’ at line 4)

failed to create the sampler; sampling not done"

I am wondering how to fix my model.

Thank you.