# Optimization in Stan¶

PyStan provides an interface to Stan’s optimization methods. These methods obtain a point estimate by maximizing the posterior function defined for a model. The following example estimates the mean from samples assumed to be drawn from normal distribution with known standard deviation:

Specifying an improper prior for $$\mu$$ of $$p(\mu) \propto 1$$, the posterior obtains a maximum at the sample mean. The following Python code illustrates how to use Stan’s optimizer methods via a call to optimizing:

import pystan
import numpy as np

ocode = """
data {
int<lower=1> N;
real y[N];
}
parameters {
real mu;
}
model {
y ~ normal(mu, 1);
}
"""
sm = pystan.StanModel(model_code=ocode)
y2 = np.random.normal(size=20)
np.mean(y2)

op = sm.optimizing(data=dict(y=y2, N=len(y2)))

op