# What are the optimized “data” given parameter? Use of “symmetry” of Bayesian theorem

I am interested in "reverse" way.
Suppose you already managed to get the model parameter$\theta$, given data $D$ through optimization. What you did is exactly below.

$p(\theta|D)=\frac{p(D|\theta)p(\theta)}{p(D)}$ What are the likely "model parameter $\theta$ " given data $D$?

Now, by using "Symmetry of Bayesian theorem", one can also say,

$p(D|\theta)=\frac{p(\theta|D)p(D)}{p(\theta)}$ What are the likely "data $D$ " given model parameter $\theta$ ?

So, after calculated parameter $\theta$, now you are in search for Data $D$,... better data,.. data that explains a given parameter/Model best.
I am wondering if there is any research or paper talking about this by using the symmetry of Bayesian theorem.

Thank you

Specification of a model for the sample data $x \in \mathscr{X}$ involves direct specification of a family of density functions $\{ p_\theta(x) | \theta \in \Theta \}$ conditional on a parameter $\theta$. The data that "fits" this model best is the mode of the sampling distribution, which is given by:
$$\text{mode}(\theta) = \underset{x \in \mathscr{X}}{\arg \max} \text{ } p_\theta(x).$$