Inference problems are ubiquitous across many fields in astrophysics. Different inference methods allow us to determine the probability associated with the parameters of a theoretical model given a set of observational data. Traditional inference methods, such as MCMC, cannot be applied when the error distribution in the measured data is unknown. This is where new alternatives, employing machine learning techniques—often referred to as Simulation-Based Inference (SBI)—can help perform inference without explicitly assuming the likelihood of the data. However, while these techniques are powerful, they also have limitations.
One of the most critical limitations of implicit inference models (as well as traditional methods) is their sensitivity to the model misspecification problem. This occurs when the theoretical model assumed for inference does not match the "true" model that generated the observed data, potentially leading to significantly biased parameter estimates. To illustrate this issue, I will present an example that directly motivates my current work: Suppose we are analyzing data from a hydrodynamical simulation known to have been run within a ΛCDM cosmology. However, we lack knowledge of the specific baryonic physics used in the simulation. Given a set of theoretical models that incorporate different baryonic physics prescriptions (without certainty that they fully cover the baryonic scenario of the simulation), how confident can we be that the recovered cosmological parameters are correct and unbiased? More importantly, is there a technique that can robustly "protect" cosmological parameter inference from this issue?
To find the answers to these questions—especially the second one—don’t miss my talk!