Determining if a model is fully specified by given information

Question

I have a zero-parameter model $M_1$ which predicts a parameter $x = 0$ and a model $M_2$ with one parameter $b$ which predicts $x=b$. Then, the sampling distribution of the data $d$ is

$$P(d|x,σ) = N=(d;x,σ^2) = \frac{1}{\sqrt2\sqrtπσ }* exp[\frac{-1}{2} (\frac{d-x}{σ})^2]$$

How can I determine if the models are fully specified by the given information?

Answer 1

M1 is fully specified but M2 isn’t (because we don’t know the distribution of b)