Extension of the blocking argument to space-time lattices

Establish whether the blocking argument generalizes to space-time lattices with anisotropic spatial and temporal mixing ranges, and, if so, prove that the effective sample size scales as n^2T/(r_s^2r_t).

Background

The paper derives spatial generalization bounds for two-dimensional random fields and shows that an n × n image with spatial correlation range r has an effective sample size of order n2/r2, up to logarithmic factors. It also extends the analysis to anisotropic spatial dependence, where the effective sample size is governed by the product of the directional correlation ranges.

The authors conjecture that the same blocking strategy applies when observations are indexed by both two-dimensional spatial coordinates and time. The proposed space-time setting has spatial mixing range r_s, temporal mixing range r_t, and T temporal observations; the conjectured scaling would quantify the marginal information contributed by repeated satellite revisits.

References

We conjecture the blocking argument generalizes to space-time lattices $\Lambda_n \times {1,\dots,T}$ with anisotropic mixing spatial range~$r_s$ and temporal range~$r_t$. Applying 3D blocking gives an effective sample size $n_{\mathrm{eff} \sim n2 T / (r_s2 r_t)$, quantifying the marginal value of each additional revisit.

— How Many Independent Samples Does a Satellite Image Contain? Generalization Bounds for Spatially Dependent Data  (2610.08227 - Young, 6 Oct 2026) in Section Discussion