# Accuracy Requirements for Empirically-Measured Selection Functions

## TL;DR

This paper derives formulas to determine the required measurement accuracy of selection functions using Monte-Carlo injections, ensuring unbiased population inference, with the number of injections scaling linearly with population size.

## Contribution

It provides a mathematical framework linking injection measurement accuracy to unbiased population inference in selection functions.

## Key findings

- Number of injections scales linearly with population size
- Coefficient depends on injection and population distributions
- Formulas enable planning of injection campaigns for unbiased results

## Abstract

I give formulas for the accuracy to which a selection function must be measured via Monte-Carlo injections in order to have un-biased population inference. The number of found injections scales linearly with the number of objects in the population; the coefficient in front of the linear term depends on both the distribution of injections and the inferred population distribution.