Nonlinear Aggregation of Local Likelihood Scores for Simulation-Based Inference

Many scientific simulators have intractable joint likelihoods but tractable marginal, pairwise, or block likelihoods. We introduce nonlinear local-score ag- gregation (NLSA), which transforms local likelihood scores before groupwise in- variant pooling to learn a surrogate Fisher score. Score matching trains this score over the joint surface of generating and evaluation parameters, after which neu- ral posterior estimation conditions on a pilot–score pair. Across two controlled models and a challenging Smith max-stable spatial-extremes simulator, NLSA improves score and posterior accuracy over an identity composite-score baseline and other benchmark Fisher-score surrogate architectures.