Standard deviation of the posterior

I am trying to replicate Code 2.6 from Statistical Rethinking by Richard McElreath.

def model():
    p = pyro.sample("p", dist.Uniform(0, 1.0))
    return pyro.sample("w", dist.Binomial(9, p))

def guide():
    p_param = pyro.param("p_param", torch.tensor(0.1), constraint=constraints.unit_interval)
    return pyro.sample("p", dist.Delta(p_param))

conditioned = pyro.condition(model, data={"w": tensor(6.)})
svi = pyro.infer.SVI(model=conditioned,
                                optim=pyro.optim.SGD({"lr": 0.001, "momentum":0.1}),
losses = []
num_steps = 5000
for t in range(num_steps):

I would also like to get the standard deviation and the 89% percentile interval for p. Looking at other examples of pyro on this thread and tutorials, here is my attempt (with incorrect stdev of 0.28 instead of 0.16):

pred = Predictive(model, posterior_samples={"w": tensor([6.]*5000)})
> 0.2856

How can I get the stdev of the posterior?

@spad I think you need to use AutoLaplaceApproximation.

guide = pyro.infer.autoguide.AutoLaplaceApproximation(conditioned)
# then train svi
laplace_guide = guide.laplace_approximation()
pred = pyro.infer.Predictive(laplace_guide, num_samples=1000)

otherwise, p is just the constant MAP point. You can also use other autoguides, but LaplaceApproximation is what the author of SR book used.

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