Hi - I am writing up some examples, and am encountering some strange behavior. I have the following model straight from the manual:

```
data{
int N;
int K;
matrix[N, K] X;
vector[N] y;
}
parameters{
real alpha;
vector[K] beta;
real<lower = 0> sigma;
}
model{
y ~ normal(X * beta + alpha, sigma);
}
```

This give the following estimates:

```
mean se_mean sd 5% 95% n_eff Rhat
alpha 40.92 0.10 2.84 36.38 45.59 841 1
beta[1] -1.30 0.02 0.68 -2.40 -0.17 913 1
beta[2] 0.01 0.00 0.01 -0.01 0.03 791 1
beta[3] -0.02 0.00 0.01 -0.04 0.00 1115 1
beta[4] -3.88 0.03 1.05 -5.60 -2.08 924 1
sigma 2.62 0.01 0.38 2.08 3.31 847 1
lp__ -45.22 0.08 1.95 -48.83 -42.81 539 1
```

Changing the likelihood line to:

```
target += normal_lpdf(y | X * beta + alpha, sigma);
```

Results in these estimates:

```
mean se_mean sd 5% 95% n_eff Rhat
alpha 33.78 0.11 2.97 28.55 38.40 668 1.01
betas[1] -0.29 0.02 0.71 -1.42 0.90 980 1.00
betas[2] -0.01 0.00 0.01 -0.04 0.01 764 1.00
betas[3] -0.02 0.00 0.01 -0.04 0.00 1178 1.00
betas[4] -1.87 0.04 1.05 -3.48 -0.05 834 1.00
sigma 2.91 0.02 0.48 2.24 3.81 709 1.00
lp__ -91.35 0.09 2.03 -95.39 -88.80 562 1.00
```

The data are the mtcars dataset in R, with the model mpg ~ cyl + disp + hp + wt.

This happens in both rstan and cmdstan. Any help appreciated.