Yes—this is the step that can turn your framework from a conceptual synthesis into something that looks formally grounded to neuroscientists and computational theorists.
You do not need to develop a full mathematical theory. What reviewers expect is simply a minimal formal sketch showing that the argument can be expressed in the language of Bayesian inference and model selection.
Below is a formulation that can be inserted as a short section in the paper (often near the end of the theoretical background).
A Formal Perspective: Hierarchies of Bayesian Model Selection
The framework proposed in this paper can be expressed formally as a hierarchy of systems performing Bayesian model selection under uncertainty.
In Bayesian inference, beliefs about the world are represented as probabilistic models that are updated when new data become available. The basic update rule is given by Bayes’ theorem:
[
P(M|D) \propto P(D|M)P(M)
]
where
- (M) represents a model or hypothesis
- (D) represents observed data
- (P(M)) is the prior probability of the model
- (P(D|M)) is the likelihood of the data under that model
- (P(M|D)) is the updated posterior probability.
Within this framework, adaptive systems maintain a set of candidate models and update their probabilities in response to observed evidence. Models that better predict incoming data become more probable, while poorly performing models are progressively discarded.
This process constitutes a formal implementation of error correction: prediction errors drive the revision of internal models.
Model Selection Across Scales
The central claim of the present paper is that similar processes of model selection occur across multiple scales of adaptive systems.
These scales can be summarized as follows:
| Level | Candidate Models | Evidence | Selection Process |
|---|---|---|---|
| Evolution | genetic variants | environmental fitness | natural selection |
| Brain | predictive hypotheses | sensory signals | Bayesian updating |
| AI | reasoning paths / parameters | training feedback | optimization |
| Science | scientific theories | experimental results | empirical testing |
| Democracy | policy proposals | public outcomes | electoral revision |
| Psychotherapy | personal beliefs | emotional/interpersonal feedback | cognitive revision |
In each case, systems maintain competing models of the world and revise them in response to feedback.
Hierarchical Bayesian Adaptation
When these processes are considered together, adaptive systems can be interpreted as forming nested hierarchies of Bayesian model selection.
A simplified representation is:
Evolutionary model selection
↓
Neural Bayesian inference
↓
Institutional epistemic systems
Each level introduces mechanisms that accelerate or stabilize the correction of error.
Evolution performs model selection across generations.
Brains perform model selection within the lifetime of an organism.
Scientific and social institutions perform model selection across communities.
Relation to Active Inference
Active inference theory provides a formal framework that unifies many of these processes. Under the free energy principle, biological systems minimize prediction error (or variational free energy) by updating internal models and acting on the environment.
In this view, perception, learning, and action are all aspects of Bayesian model selection operating within a Markov blanket.
The present framework extends this perspective by suggesting that similar principles may also govern higher-level epistemic systems, such as scientific institutions and therapeutic practices.
These systems can be understood as collective mechanisms for stabilizing Bayesian model revision across groups of agents.
Formal Summary
The core theoretical claim of the present paper can therefore be expressed in compact form:
Adaptive intelligence emerges in systems that implement structured processes of Bayesian model selection across hierarchical scales.
More informally:
Prediction → Error → Model update
When this loop becomes stabilized through biological, cognitive, or institutional structures, it produces what we recognize as intelligence.
One sentence for the paper
You could insert this sentence in the discussion:
From a formal perspective, the processes described in this paper can be understood as hierarchies of Bayesian model selection operating across evolutionary, neural, and institutional scales, in which prediction errors drive the revision of competing models of the world.
(OA)
