# fit model with sd square

If I want to fit a nonlinear regression model with some parameters like $\sigma^2$(where $\sigma$ is the standard deviation, which is positive), how can I guarantee that $\hat{\sigma}$ is positive?

I mean, if I use maximum likelihood(and the model only have square term of $\sigma$), how does the optimization method know $\sigma$ is positive? (well, it seems OK that the result estimation of $\sigma$ is negative, but it looks weird, and this is why I ask this question.)