{\sc ampere}: A tool to fit heterogeneous observations consistently

TL;DR

ampere tackles the problem of Bayesian inference with expensive and potentially misspecified forward models in astronomy by introducing a flexible likelihood framework that absorbs structured residuals into a kernel-based covariance, enabling self-consistent inference from heterogeneous data. Its modular architecture separates models, data, and inference, and wraps multiple backends including MCMC, nested sampling, and likelihood-free methods (SBI/NPE) to balance exactness and efficiency; it also supports amortized inference to accelerate analysis over large samples. The paper demonstrates ampere on diverse problems—modified blackbody fitting, stellar parameter inference from photometry and spectroscopy, star-plus-dust systems, mineralogy of carbon-star envelopes, and carbonate detection in NGC 6302—showing accurate parameter recovery and often more realistic uncertainty estimates than prior analyses. This framework is positioned to scale to large surveys (e.g., JWST, SPHEREx) and can be extended to additional data types and accelerated with JAX, enabling widespread, robust interpretation of complex astronomical observations.

Abstract

As astronomy advances and data becomes more complex, models and inference also become more expensive and complex. In this paper we present {\sc ampere}, which aims to solve this problem using modern inference techniques such as flexible likelihood functions and likelihood-free inference. {\sc ampere}\ can be used to do Bayesian inference even with very expensive models (hours of CPU time per model) that do not include all the features of the observations (e.g. missing lines, incomplete descriptions of PSFs, etc). We demonstrate the power of \ampere\ using a number of simple models, including inferring the posterior mineralogy of circumstellar dust using a Monte Carlo Radiative Transfer model. {\sc ampere}\ reproduces the input parameters well in all cases, and shows that some past studies have tended to underestimate the uncertainties that should be attached to the parameters. {\sc ampere}\ can be applied to a wide range of problems, and is particularly well-suited to using expensive models to interpret data.

Figures (9)

• Figure 1: Demonstration of concepts of model misspecification and flexible likelihoods. If we start from a spectrum that contains emission and absorption lines but is contaminated by fringing, we can attempt to interpret it by modelling the lines and the fringing simultaneously (a, top). When using this model, the residuals (red points, a, bottom) follow the expected i.i.d. Gaussian distribution (three samples from which are shown as pink dotted lines). However, if we take a misspecified model which does not include the fringing (b, top), the resulting residuals (b, bottom) show quasi-periodic structure, which is inconsistent with the samples from the i.i.d. Gaussians we would normally expect (pink dotted lines), resulting in a dramatic misunderstanding of the uncertainty and potentially the parameters as well. However, when we change the likelihood function (c, top), the uncertainty distribution becomes more representative. Indeed, the simplified uncertainty band is overly pessimistic, since it neglects the dependence between points that has been introduced (c, bottom. The samples from the correlated distribution in this case show not just similar amplitude to the observed residuals, but also oscillations of similar quasi-period and amplitude. This highlights the equivalence between model misspecification and correlated noise.
• Figure 2: ampere architecture. See text for details.
• Figure 3: Composite figure showing the values recovered by the different inference approaches for the modified blackbody example. The black dashed line in each panel denotes the 'true' values of the input blackbody function, whilst the coloured dots denote the output for the four inference methods implemented in ampere.
• Figure 4: Posterior samples from models fitted to synthetic photometry and a synthetic Gaia spectrum for inferring astrophysical parameters. The parameters are so tightly constrained by this combination that the model samples form a single band.
• Figure 5: Plot of wavelength vs flux density for the star with circumstellar dust example. Photometric data points are denoted by the circular data points with 1-$\sigma$ uncertainties, the Spitzer/IRS spectrum is denoted by the blue line and its 1-$\sigma$ uncertainty as the shaded region. Realisations of the stellar photosphere and dust modified blackbody model are shown by the black lines, with the maximum amplitude probability model denoted by the magenta line.