Random walk in RStan

Modeling
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7

Thank you for the response @sbfnk. I tried your code on the MRE I provided here and unfortunately it still throws the same error:

# generate data
set.seed(10)
x <- 1:250
r <- rnorm(x, mean = 0, sd = x^-1)
c0 <- 2
a <- 0.01
b <- 0.07
k <- 0.01
y <- c0 * exp(-(a * x - b/k * (exp(-k * x) - 1))) + r

# write Stan code 
stan_code <- "
data {
  int n; // Number of observations
  vector[n] y;    // Response variable
  vector[n] x;    // Predictor variable
}

parameters {
  real<lower=0> sigma; // Standard deviation
  real<lower=0> a;  // Intercept
  real<lower=0> tau; // Precision of random step
  vector[n] k; // Decay rate
}

model {
  // Priors
  sigma ~ exponential( 1 );
  a ~ lognormal( log(2) , 0.05 );
  k[1] ~ lognormal( log(0.08) , 0.1 );
  tau ~ lognormal( log(0.01) , 0.1 );

  // Random walk
  for ( i in 2:n ) {
    k[i] ~ normal(k[i - 1], tau);
  }

  // Prediction function
  vector[n] mu; // Mean prediction for y
  for( i in 1:n ) {
    mu[i] = a * exp(-k[i] * x[i]); // Calculate mu using updated k
  }

  // Likelihood
  y ~ normal(mu, sigma);
}
"

# draw samples using RStan
require(rstan)
require(tidybayes)
rw.mod <- stan(model_code = stan_code,
               data = compose_data(df), iter = 1e4,
               chains = 1, cores = parallel::detectCores())

[1] "Error : Initialization failed."
error occurred during calling the sampler; sampling not done