# A Unifying Perspective on Probabilities as Model Predictions

arXiv: https://arxiv.org/abs/2609.09855 · HTML: https://mlsanity.com/paper/2609.09855/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 79 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration](https://mlsanity.com/paper/2107.05719/) (2021)
- [Forecast Hedging and Calibration](https://mlsanity.com/paper/2210.07169/) (2022)
- [On the Richness of Calibration](https://mlsanity.com/paper/2302.04118/) (2023)
- [The Objective Function: Science and Society in the Age of Machine Intelligence](https://mlsanity.com/paper/2209.10418/) (2022)
- [Three Types of Calibration with Properties and their Semantic and Formal Relationships](https://mlsanity.com/paper/2504.18395/) (2025)
- [In Defense of Defensive Forecasting](https://mlsanity.com/paper/2506.11848/) (2025)
- [The Costs of Pretending That There Are Data-Generating Probability Distributions in the Social World](https://mlsanity.com/paper/2407.17395/) (2024)
- [Insights From Insurance for Fair Machine Learning](https://mlsanity.com/paper/2306.14624/) (2023)
- [Formalising causal inference as prediction on a target population](https://mlsanity.com/paper/2407.17385/) (2024)

## Abstract (arXiv)

Although probabilistic statements are ubiquitous, foundational disagreements persist about their understanding, as exemplified by debates between Bayesians and frequentists; moreover, it is unclear when and why acting on them actually leads to desirable outcomes. Here, we argue that every probability is the output of a prediction method, that is, it depends on both a particular way of constructing abstractions and a way of transforming them into predictions. Through this, we provide a unifying perspective on supposedly different kinds of probabilities and show that even supposedly objective ones are model-dependent. We demonstrate that when a finite calibration criterion is met, one can anticipate the distribution of utilities for a given policy and inform successful decision-making on finite sets of events. Based on the notion of prediction methods, inductive arguments, and the probability calculus, we explain the feasibility of the calibration criterion in many settings. Overall, we develop a coherent perspective on probabilities and their use, connecting key intuitions behind other interpretations along the way.