# Information Threshold, Bayesian Inference and Decision-Making

arXiv: https://arxiv.org/abs/2206.02266 · HTML: https://mlsanity.com/paper/2206.02266/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 5 Jun 2022.

## Builds on (most cited first, 5 of 5)

- [Prevalence Threshold and the Geometry of Screening Curves](https://mlsanity.com/paper/2006.00398/) (2020)
- [Bayesian Updating and Sequential Testing: Overcoming Inferential Limitations of Screening Tests](https://mlsanity.com/paper/2006.11641/) (2020)
- [On the Formalism of The Screening Paradox](https://mlsanity.com/paper/2011.06032/) (2020)
- [Feasibility of Supervised Machine Learning for Cloud Security](https://mlsanity.com/paper/1810.09878/) (2018)
- [Prevalence Threshold and bounds in the Accuracy of Binary Classification Systems](https://mlsanity.com/paper/2112.13289/) (2021)

## Built on by (most cited first, 1 of 1)

- [A Priori Determination of the Pretest Probability](https://mlsanity.com/paper/2401.04086/) (2024)

## Abstract (arXiv)

We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The nature of the threshold is such that for sufficiently adequate binary classification systems, retrieving excess information beyond the threshold does not significantly alter the reliability of our classification assessment. We hereby introduce the "marital status thought experiment" to illustrate this idea and report a previously undefined mathematical relationship between the Bayesian prior and posterior, which may have significant philosophical and epistemological implications in decision theory. Where the prior probability is a scalar between 0 and 1 given by φ and the posterior is a scalar between 0 and 1 given by ρ, then at the information threshold, φe: φe + ρe = 1 Otherwise stated, given some degree of prior belief, we may assert its persuasiveness when sufficient quality evidence yields a posterior so that their combined sum equals 1. Retrieving further evidence beyond this point does not significantly improve the posterior probability, and may serve as a benchmark for confidence in decision-making.