unidentifiable.R

library(rstan)
options(mc.cores = parallel::detectCores())
rstan_options(auto_write = TRUE)

##

set.seed(20180816)
N <- 100
Y <- rnorm(N, 4, 1)

stan_code1 <- "
data {
  int<lower = 0> N;
  vector[N] Y;
}
parameters {
  real beta[2];
  real<lower = 0> sigma;
}
model {
  Y ~ normal(beta[1] + beta[2], sigma);
}
"

fit1 <- stan(model_code = stan_code1, data = list(N = N, Y = Y),
             iter = 2000, warmup = 1000)
print(fit1)
rstan::traceplot(fit1)

##

stan_code2 <- "
data {
  int<lower = 0> N;
  vector[N] Y;
}
parameters {
  real beta[2];
  real<lower = 0> sigma;
}
model {
  Y ~ normal(beta[1] + beta[2], sigma);
  beta ~ normal(0, 10);
  sigma ~ cauchy(0, 5);
}
"
fit2 <- stan(model_code = stan_code2, data = list(N = N, Y = Y),
             iter = 2000, warmup = 1000)
print(fit2)
rstan::traceplot(fit2)

##

set.seed(20180817)
N <- 100
U <- 4
Y <- runif(N, 0, U)

stan_code3 <- "
data {
  int<lower = 0> N;
  real<lower = 0> U;
  vector<lower = 0, upper = U>[N] Y;
}
parameters {
  real beta;
  real<lower = 0> sigma;
}
model {
  for (n in 1:N)
    Y[n] ~ normal(beta, sigma) T[0, U];
}
"
fit3 <- stan(model_code = stan_code3, data = list(N = N, U = U, Y = Y),
             iter = 2000, warmup = 1000)
print(fit3)
rstan::traceplot(fit3)

##

stan_code4 <- "
data {
  int<lower = 0> N;
  real<lower = 0> U;
  vector<lower = 0, upper = U>[N] Y;
}
parameters {
  real beta;
  real<lower = 0> sigma;
}
model {
  for (n in 1:N)
    Y[n] ~ normal(beta, sigma) T[0, U];
  beta ~ normal(0, 10);
  sigma ~ cauchy(0, 5);
}
"
fit4 <- stan(model_code = stan_code4, data = list(N = N, U = U, Y = Y),
             iter = 2000, warmup = 1000)
print(fit4)
rstan::traceplot(fit4)