Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters yield identical observations. This arises in many practical situations, such as when inferring the distance and power of a radio source (is the source close and weak or far and strong?) or when estimating the amplifier gain and underlying brain activity of an electrophysiological experiment. In this work, we present hierarchical neural posterior estimation (HNPE), a novel method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters. Our method extends recent developments in simulation-based inference (SBI) based on normalizing flows to Bayesian hierarchical models. We validate quantitatively our proposal on a motivating example amenable to analytical solutions and then apply it to invert a well known non-linear model from computational neuroscience, using both simulated and real EEG data.

Recent advances in neural density estimation have enabled powerful simulation-based inference (SBI) methods that can flexibly approximate Bayesian inference for intractable stochastic models. Although these methods have demonstrated reliable posterior estimation when the simulator accurately represents the underlying data generative process (GDP), recent work has shown that they perform poorly in the presence of model misspecification. This poses a significant problem for their use on real-world problems, due to simulators always misrepresenting the true DGP to a certain degree. In this paper, we introduce robust variational neural posterior estimation (R VNP), a method which addresses the problem of misspecification in amortised SBI by bridging the simulation-to-reality gap using variational inference and error modelling. We test R VNP on multiple benchmark tasks, including using real data from astronomy, and show that it can recover robust posterior inference in a data-driven manner without adopting tunable hyperparameters or priors governing the misspecification.

To overcome these issues, we present Truncated Sequential Neural Posterior Estimation (TSNPE).

Modeling strong gravitational lenses is prohibitively expensive for modern and next-generation cosmic survey data. Neural posterior estimation (NPE), a simulation-based inference (SBI) approach, has been studied as an avenue for efficient analysis of strong lensing data. However, NPE has not been demonstrated to perform well on out-of-domain target data -- e.g., when trained on simulated data and then applied to real, observational data. In this work, we perform the first study of the efficacy of NPE in combination with unsupervised domain adaptation (UDA). The source domain is noiseless, and the target domain has noise mimicking modern cosmology surveys. We find that combining UDA and NPE improves the accuracy of the inference by 1-2 orders of magnitude and significantly improves the posterior coverage over an NPE model without UDA. We anticipate that this combination of approaches will help enable future applications of NPE models to real observational data.

Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters yield identical observations. This arises in many practical situations, such as when inferring the distance and power of a radio source (is the source close and weak or far and strong?) or when estimating the amplifier gain and underlying brain activity of an electrophysiological experiment. In this work, we present hierarchical neural posterior estimation (HNPE), a novel method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters. Our method extends recent developments in simulation-based inference (SBI) based on normalizing flows to Bayesian hierarchical models.

Despite the promise of Neural Posterior Estimation (NPE) methods in astronomy, the adaptation of NPE into the routine inference workflow has been slow. We identify three critical issues: the need for custom featurizer networks tailored to the observed data, the inference inexactness, and the under-specification of physical forward models. To address the first two issues, we introduce a new framework and open-source software nbi (Neural Bayesian Inference), which supports both amortized and sequential NPE. First, nbi provides built-in "featurizer" networks with demonstrated efficacy on sequential data, such as light curve and spectra, thus obviating the need for this customization on the user end. Second, we introduce a modified algorithm SNPE-IS, which facilities asymptotically exact inference by using the surrogate posterior under NPE only as a proposal distribution for importance sampling. These features allow nbi to be applied off-the-shelf to astronomical inference problems involving light curves and spectra. We discuss how nbi may serve as an effective alternative to existing methods such as Nested Sampling. Our package is at https://github.com/kmzzhang/nbi.

Atmospheric retrievals (AR) characterize exoplanets by estimating atmospheric parameters from observed light spectra, typically by framing the task as a Bayesian inference problem. However, traditional approaches such as nested sampling are computationally expensive, thus sparking an interest in solutions based on machine learning (ML). In this ongoing work, we first explore flow matching posterior estimation (FMPE) as a new ML-based method for AR and find that, in our case, it is more accurate than neural posterior estimation (NPE), but less accurate than nested sampling. We then combine both FMPE and NPE with importance sampling, in which case both methods outperform nested sampling in terms of accuracy and simulation efficiency. Going forward, our analysis suggests that simulation-based inference with likelihood-based importance sampling provides a framework for accurate and efficient AR that may become a valuable tool not only for the analysis of observational data from existing telescopes, but also for the development of new missions and instruments.

Modern surveys often deliver hundreds of thousands of stellar spectra at once, which are fit to spectral models to derive stellar parameters/labels. Therefore, the technique of Amortized Neural Posterior Estimation (ANPE) stands out as a suitable approach, which enables the inference of large number of targets as sub-linear/constant computational costs. Leveraging our new nbi software package, we train an ANPE model for the APOGEE survey and demonstrate its efficacy on both mock and real APOGEE stellar spectra. Unique to the nbi package is its out-of-the-box functionality on astronomical inverse problems with sequential data. As such, we have been able to acquire the trained model with minimal effort. We introduce an effective approach to handling the measurement noise properties inherent in spectral data, which utilizes the actual uncertainties in the observed data. This allows training data to resemble observed data, an aspect that is crucial for ANPE applications. Given the association of spectral data properties with the observing instrument, we discuss the utility of an ANPE "model zoo," where models are trained for specific instruments and distributed under the nbi framework to facilitate real-time stellar parameter inference.

Simulation-Based Inference (SBI) is a promising Bayesian inference framework that alleviates the need for analytic likelihoods to estimate posterior distributions. Recent advances using neural density estimators in SBI algorithms have demonstrated the ability to achieve high-fidelity posteriors, at the expense of a large number of simulations ; which makes their application potentially very time-consuming when using complex physical simulations. In this work we focus on boosting the sample-efficiency of posterior density estimation using the gradients of the simulator. We present a new method to perform Neural Posterior Estimation (NPE) with a differentiable simulator. We demonstrate how gradient information helps constrain the shape of the posterior and improves sample-efficiency.