Neural Conditional Simulation for Complex Spatial Processes

Thomas M. Menino Convention & Exhibition Center 

A key objective in spatial statistics is to simulate from predictive distributions--the distributions of a spatial process at select unobserved locations conditional on observations--to enable spatial prediction and uncertainty quantification. However, exact conditional simulation from predictive distributions is intractable or inefficient for many spatial process models. In this talk, we present Neural Conditional Simulation (NCS)--a method which utilizes neural diffusion models for conditional simulation from predictive distributions of complex spatial processes. Using a masking approach, we train a score-based diffusion model within a stochastic differential equation (SDE) framework to learn the conditional reverse process--a process which reverse-diffuses Gaussian noise into samples from conditional distributions. Importantly, the diffusion model only requires unconditional samples from the spatial process during training and is amortized with respect to the mask, provided the mask pattern is similar to those used during training. We conclude with a data application in which we use NCS to model spatial extremes data with max-stable processes.

approximate simulation

simulation-based inference

diffusion model

spatial extremes

likelihood-free inference

generative model 

Section on Statistics and the Environment