# On the definition of informative vs. ignorable nuisance process

## TL;DR

This paper generalizes the concepts of informative and ignorable processes across various inference types and purposes, providing a broad framework and comparing with existing literature.

## Contribution

It introduces a unified, general framework for defining informative and ignorable processes applicable to Bayesian and frequentist inference.

## Key findings

- Proposes a comprehensive statistical framework for survey sampling.
- Clarifies the distinctions between design and selection processes.
- Provides a comparative analysis with existing definitions in literature.

## Abstract

This paper is an early version. We propose to generalise the notion of "ignoring" a random process as well as the notions of informative and ignorable random processes in a very general setup and for different types of inference (Bayesian or frequentist), and for different purposes (estimation, prediction or testing). We then confront the definitions we propose to mentions or definitions of informative and ignorable processes found in the litterature. To that purpose, we provide a very general statistical framework for survey sampling in order to define precisely the notions of design and selection, and to serve to illustrate and discuss the notions proposed.