# Show Thoughts

Empirical Bayes methods estimate the prior from the data.

More formally, they choose some parametric form for the prior, and estimate an optimal set of parameters $\theta_{opt}$ by optimizaton: $$\theta_{opt} = \mathrm{arg\;max}_\theta\prod_n\int P_\theta(x)P(m_n\mid x)\;dx,$$ for measurements $m_n$ and possible latent variable values $x$.