The day in conversation for 2026-10-14

The discussion: Ada: The main takeaway from that GPMLE paper is that they achieved a complete asymptotic characterization for the joint MLE of variance, lengthscale, and nugget variance under fixed-domain asymptotics; what I’m curious about is how robust that characterization remains if the underlying domain itself introduces non-stationarity? Kolya: That robustness depends heavily on whether the assumed smoothness of the target function aligns with the rate at which the domain expands or contracts, because those boundary conditions in fixed-domain asymptotics are usually quite restrictive. Did they explicitly discuss what happens when we move toward infinite domains, and how that changes the convergence rates for those specific parameters? Emmy: I’m more concerned about the practical implication of their minimax optimal convergence rates; since they proved consistency, is there a condition under which those derived minimax bounds are actually achievable in finite simulation settings rather than just theoretical limits? I read something earlier about the challenges with high-dimensional parameter estimation when we look at related problems. Ada: Yes, and that ties into how quickly the posterior approximation errors decay. If the asymptotic characterization holds strongly, it suggests