Simulation-Based Inference via Regression Projection and Batched Discrepancies

We analyze a lightweight simulation-based inference method that infers simulator parameters using only a regression-based projection of the observed data. After fitting a surrogate linear regression once, the procedure simulates small batches at the proposed parameter values and assigns kernel weights based on the resulting batch-residual discrepancy, producing a self-normalized pseudo-posterior that is simple, parallelizable, and requires access only to the fitted regression coefficients rather than raw observations. We formalize the construction as an importance-sampling approximation to a population target that averages over simulator randomness, prove consistency as the number of parameter draws grows, and establish stability in estimating the surrogate regression from finite samples. We then characterize the asymptotic concentration as the batch size increases and the bandwidth shrinks, showing that the pseudo-posterior concentrates on an identified set determined by the chosen projection, thereby clarifying when the method yields point versus set identification. Experiments on a tractable nonlinear model and on a cosmological calibration task using the DREAMS simulation suite illustrate the computational advantages of regression-based projections and the identifiability limitations arising from low-information summaries.

💡 Research Summary

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This paper investigates a lightweight simulation‑based inference (SBI) technique that relies solely on a regression‑based projection of observed data. The method proceeds in three steps. First, a simple ordinary‑least‑squares (OLS) regression of the response variable (Y) on covariates (X) is fitted once to the real data, yielding regression coefficients (\hat\beta) (or its probability limit (\beta^\circ)). These coefficients define a low‑dimensional linear summary—essentially a “projection” of the data onto a one‑dimensional subspace.

Second, for each candidate parameter vector (\theta) drawn from the prior, a small batch of size (M) of simulated covariate–response pairs ((X_{\text{sim}},Y_{\text{sim}})) is generated from the forward simulator. The batch residual mean
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