parameter bounds far from optimal solution still affect optimization

[schafferEvan]

Summary:

In a simple linear regression model, I'm feeding in data for which the optimal value of parameter alpha is 0.5. If I don't put bounds on the parameter, the 'optimizing' method converges to the correct solution. If I bound alpha with <lower=-100, upper=100>, optimizing gets stuck on one of the bounds.

Description:

In pystan, I'm running the following:

N = 1000
x = np.arange(N)
y = 0.5*x/N + .5 + np.random.normal(0,.1,N)
test_data = {}
test_data['N'] = N
test_data['x'] = x
test_data['y'] = y
sm.optimizing(data=test_data)

On the following stan model:

data {
  int<lower=0> N;
  vector[N] y;
  vector[N] x;
}
parameters {
  real<lower=-100, upper=100> alpha;
  // real alpha;
  real beta;
  real<lower=0> sigma;
}
model {
  alpha ~ normal(0,10);    
  beta ~ normal(0,10);
  sigma ~ lognormal(0, 10); 
  y ~ normal( alpha + beta * x/N, sigma);
}

Reproducible Steps:

The code above returns either alpha=-100 or alpha=100. Replacing the bounded definition of alpha with the unbounded version gives the correct answer.

Current Version:

v2.23.0

[bob-carpenter]

I recreated the problem in RStan and verified that sampling gets the right answer with the interval-constrained parameter.

This is high priority to fix, though the only way to indicate that is with the next release as a milestone.

P.S. It'd be easier on the reader to just divide the predictor x by N before simulation and before feeding it in as data than to divide by N in two spots.

[schafferEvan]

Thanks! (and sorry about the stray factor of N)

[WardBrian]

This issue is because the default setting for optimization is without the jacobian adjustment for constrained variables. Enabling it in recent versions of Stan recovers alpha $\approx$ 0.5