🚀 Key Finding: In high-dimensional spaces, amortized point estimation significantly outperforms full posterior approaches!

For point estimation, we use:
🔹 Maximum Likelihood (MLE)
🔹 Maximum-a-Posteriori (MAP)

But what about posterior estimation?

🔍 Parametric Inference: Point vs Full Posterior Estimation

Two approaches:
📌 Point Estimation (MLE/MAP) – Optimizes for a single parameter value
📊 Full Posterior Estimation – Approximates the full distribution (MCMC, VI)

Which is best for amortized inference? We find out! 👇

We provide a rigorous comparison of different architecture choices, parameterizations of densities, and training objectives for learning this amortized in-context posterior estimator. Further studies on high-dimensional problems, cases of misspecification, etc. in the paper!