# Accounting for selection bias using simulations: A general method and an application to millimeter-wavelength surveys

## TL;DR

This paper introduces a Bayesian correction method for astronomical source flux densities that uses simulations to model complex survey selection effects and an analytic prior for flexible source count modeling, demonstrated on ACT data.

## Contribution

A novel hybrid Bayesian approach combining simulated likelihoods with analytic priors to correct for selection bias in astronomical surveys.

## Key findings

- Effectively models complex selection processes.
- Allows flexible source count assumptions without re-simulation.
- Applied successfully to ACT millimeter-wavelength survey data.

## Abstract

We have developed a new Bayesian method to correct the flux densities of astronomical sources. The hybrid method combines a simulated likelihood to model survey selection together with an analytic source-count-based prior. The simulated likelihood captures the effect of complicated selection methods, such as multi-frequency filtering or imposed restrictions on recovered sample properties (e.g., color cuts). Simulations are also able to capture unanticipated sources of uncertainty. In this way, the method enables a broader application of Bayesian techniques. Use of an analytic prior allows variation of assumed source count models without re-simulating the likelihood. We present the method along with a detailed description of an application to real survey data from the Atacama Cosmology Telescope.