# Biological Basis of the Code The code provided is a part of the Hierarchical Gaussian Filter (HGF) toolbox, specifically designed to model learning and inference processes in the brain. The HGF is a computational model used to understand how humans update their beliefs about the world in the face of new or uncertain information. It provides a framework for simulating the dynamic learning processes that occur within an individual when they are confronted with probabilistic stimuli. ## Key Biological Concepts Modeled ### Hierarchical Structure - **Hierarchical Levels:** The HGF framework is based on a hierarchy of levels that represent different levels of abstraction in belief updating. The number of levels in this model is determined by the length of the parameter vector `pvec`. Each level may correspond to different aspects of the belief updating process, such as perceptual states, beliefs about environmental states, or even higher-order beliefs about the stability of these states. ### Parameters The following key parameters have direct biological relevance: - **Mu (μ):** Represents the prior mean of beliefs at each hierarchical level. It models the expectations about the environment before encountering new evidence. - **Sigma (sa_0):** Represents the prior variance (uncertainty) associated with each level's beliefs. This can be thought of as capturing the brain's uncertainty about its own beliefs or predictions. - **Rho (ρ):** Relates to the drift parameter, representing volatility or changes in the environment over time. It captures the notion that the environment is not static, and the brain must adapt to it. - **Kappa (ka):** Modulates the coupling between levels. In biological terms, this can be interpreted as the influence that belief updates at one level have on the levels above or below it. - **Omega (ω):** Represents biases or tendencies in the belief updating process. It might be related to specific neurotransmitter effects that bias certain perceptions or outcomes. - **Alpha (α):** Represents learning rate, dictating how quickly beliefs are updated with new evidence. This reflects synaptic plasticity properties or the speed at which new information is integrated. - **Eta (η0, η1):** These parameters could model additional biases or modulatory effects on the learning rate, possibly reflecting adaptive mechanisms like attention or arousal that influence the learning process. ### Biological Interpretation The biological foundation of the HGF model lies in the neurobiological processes of learning and adaptation. It mirrors concepts in neuroscience where the brain is continuously updating its internal models of the world based on sensory inputs and prior experiences. The hierarchical nature maps onto the brain's ability to abstract and integrate information across multiple scales, from sensory processing to complex decision-making. Parameters like learning rate, volatility, and biases can be linked to neural substrates and neuromodulators, providing insights into the cognitive and neural mechanisms of belief updating and inference.