Hi, I’m having some trouble understanding why the following simple model has a different standard deviation (hence, different posterior, right?) when using the default guide and when using a guide that is exactly the model itself, for instance:

```
import numpy as np
import matplotlib.pyplot as plt
try:
import seaborn as sns
sns.set()
except ImportError:
pass
import torch
from torch.autograd import Variable
import pyro
import pyro.infer
import pyro.optim
import pyro.distributions as dist
torch.manual_seed(101)
def scale(guess):
weight = pyro.sample("weight", dist.normal, guess,
Variable(torch.ones(1)))
return weight
def scale_prior_guide(guess):
return pyro.sample("weight", dist.normal, guess, Variable(torch.ones(1)))
def scale_prior_guide_weird(guess):
return pyro.sample("weight", dist.normal, guess+3, Variable(torch.ones(1))+2)
posterior = pyro.infer.Importance(scale, num_samples=1000)
guess = Variable(torch.Tensor([8.5]))
marginal = pyro.infer.Marginal(posterior)
res_importance = np.array([marginal(guess).data[0] for _ in range(10000)])
posterior = pyro.infer.Importance(scale, num_samples=1000, guide=scale_prior_guide)
guess = Variable(torch.Tensor([8.5]))
marginal = pyro.infer.Marginal(posterior)
res_importance_guide = np.array([marginal(guess).data[0] for _ in range(10000)])
posterior = pyro.infer.Importance(scale, num_samples=1000, guide=scale_prior_guide_weird)
guess = Variable(torch.Tensor([8.5]))
marginal = pyro.infer.Marginal(posterior)
res_importance_guide_weird = np.array([marginal(guess).data[0] for _ in range(10000)])
print("Mean")
print(res_importance.mean())
print(res_importance_guide.mean())
print(res_importance_guide_weird.mean())
print("Std")
print(res_importance.std())
print(res_importance_guide.std())
print(res_importance_guide_weird.std())
```

would output something like:

```
Mean
8.49218823838
8.44276266947
8.46633415203
Std
0.703899055717 # <<<<<<< here's what's strange
0.983066442502
1.01712713134
```

I inspected Pyro source code to check what’s the default guide for `pyro.infer.Importance`

and it seems to be the model itself for this simple model with data:

```
import pyro.poutine as poutine
guide = poutine.block(scale, hide_types=["observe"])
res_model = np.array([scale(guess).data[0] for _ in range(10000)])
res_guide = np.array([guide(guess).data[0] for _ in range(10000)])
print(res_model.mean())
print(res_guide.mean())
print(res_model.std())
print(res_guide.std())
```

would output something like:

```
8.47813085794
8.49829654074
1.00555316964
0.998794367065
```