Hello, I have the following stan code for SEIR modelling. I need help with setting the domain for the model priors in the parameters block since my priors assume negative values i.e lambda ~ lognormal(log(0.4), 0.5); and i have in the parameters block, real<lower=0> mu; which i have to change to include negative values. The reference code is from Bayesian workflow for disease transmission modeling in Stan

```
functions {
real[] seir(real t, real[] y, real[] theta,
real[] x_r, int[] x_i) {
real N = x_i[1];
real lambda = theta[1];
real mu = theta[2];
real sigma = theta[3];
real i0 = theta[4]; // initial number of infected people
real e0 = theta[5]; // initial number of infected people
real init[4] = {N - i0 - e0, e0, i0, 0}; // initial values
real S = y[1] + init[1];
real E = y[2] + init[2];
real I = y[3] + init[3];
real R = y[4] + init[4];
real dS_dt = - lambda * I * S / N;
real dE_dt = lambda * I * S / N - sigma * E;
real dI_dt = sigma * E - mu * I;
real dR_dt = mu * I;
return {dS_dt, dE_dt, dI_dt, dR_dt};
}
}
data {
int<lower=1> n_days;
real t0;
real ts[n_days];
int N; //population size
int cases[n_days];
}
transformed data {
real x_r[0];
int x_i[1] = { N };
}
parameters {
real<lower=0> mu;
real<lower=0> lambda;
real<lower=0> sigma;
real<lower=0> phi_inv;
real<lower=0> i0; // number of infected people inititally
real<lower=0> e0; // number of exposed people inititally
real<lower=0, upper=1> reporting_D;
}
transformed parameters{
real incidence[n_days - 1];
real y[n_days, 4];
real phi = 1. /phi_inv;
real theta[5] = {lambda, mu, sigma, i0, e0};
y = integrate_ode_rk45(seir, rep_array(0.0, 4), t0, ts, theta,
x_r, x_i);
for (i in 1:n_days-1)
incidence[i] = -(y[i+1, 2] - y[i, 2] + y[i+1, 1] -
y[i, 1]) * reporting_D ; //-(E(t+1) - E(t) + S(t+1) - S(t))
}
model {
//priors
lambda ~ lognormal(log(0.4), 0.5);
mu ~ lognormal(log(0.125), 0.2);
sigma ~ lognormal(log(0.2), 0.5);
phi_inv ~ exponential(5);
i0 ~ cauchy(0, 20);
e0 ~ cauchy(0, 20);
reporting_D ~ lognormal(log(8), 0.2);
//compute likelihood to the data
cases[1:(n_days-1)] ~ neg_binomial_2(incidence, phi);
}
generated quantities {
real R0 = lambda / mu;
real recovery_time = 1 / mu;
real incubation_time = 1 / sigma;
real pred_cases[n_days - 1];
pred_cases = neg_binomial_2_rng(incidence, phi);
}
```