Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a simulator posing the need for simulation-based inference (SBI).

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.

This paper, which is Part 1 of a two-part paper series, considers a simulation-based inference with learned summary statistics, in which such a learned summary statistic serves as an empirical-likelihood with ameliorative effects in the Bayesian setting, when the exact likelihood function associated with the observation data and the simulation model is difficult to obtain in a closed form or computationally intractable. In particular, a transformation technique which leverages the Cressie-Read discrepancy criterion under moment restrictions is used for summarizing the learned statistics between the observation data and the simulation outputs, while preserving the statistical power of the inference. Here, such a transformation of data-to-learned summary statistics also allows the simulation outputs to be conditioned on the observation data, so that the inference task can be performed over certain sample sets of the observation data that are considered as an empirical relevance or believed to be particular importance. Moreover, the simulation-based inference framework discussed in this paper can be extended further, and thus handling weakly dependent observation data. Finally, we remark that such an inference framework is suitable for implementation in distributed computing, i.e., computational tasks involving both the data-to-learned summary statistics and the Bayesian inferencing problem can be posed as a unified distributed inference problem that will exploit distributed optimization and MCMC algorithms for supporting large datasets associated with complex simulation models.

We introduce \textit{OneFlowSBI}, a unified framework for simulation-based inference that learns a single flow-matching generative model over the joint distribution of parameters and observations. Leveraging a query-aware masking distribution during training, the same model supports multiple inference tasks, including posterior sampling, likelihood estimation, and arbitrary conditional distributions, without task-specific retraining. We evaluate \textit{OneFlowSBI} on ten benchmark inference problems and two high-dimensional real-world inverse problems across multiple simulation budgets. \textit{OneFlowSBI} is shown to deliver competitive performance against state-of-the-art generalized inference solvers and specialized posterior estimators, while enabling efficient sampling with few ODE integration steps and remaining robust under noisy and partially observed data.

We consider problems of parameter estimation where design variables can be actively optimized to maximize information gain. To this end, we introduce JADAI, a framework that jointly amortizes Bayesian adaptive design and inference by training a policy, a history network, and an inference network end-to-end. The networks minimize a generic loss that aggregates incremental reductions in posterior error along experimental sequences. Inference networks are instantiated with diffusion-based posterior estimators that can approximate high-dimensional and multimodal posteriors at every experimental step. Across standard adaptive design benchmarks, JADAI achieves superior or competitive performance.