This interactive figure illustrates a simple BayesianA mathematical framework for updating beliefs based on new evidence. Named after Thomas Bayes, it describes how to combine prior knowledge with new observations. model of perceptual inference in which bodily state modulates how strongly sensory evidence is weighted.
The plot shows three probability distributions along a one-dimensional perceptual estimate axis:
Prior expectationWhat we expect to perceive before receiving sensory input, based on past experience and context. Represented as a probability distribution over possible perceptual states. (orange dashed)
Sensory evidence (likelihood)Information arriving from the senses (e.g., vision, touch, hearing). Also called the "likelihood" in Bayesian terms. Represented as a probability distribution reflecting sensory uncertainty. (cyan dashed)
PosteriorThe updated belief after combining prior expectations with sensory evidence. This is the brain's best estimate of what's actually out there. Computed via Bayes' rule. estimate (purple solid, filled)
The prior and likelihood have fixed means at different locations. The posterior is computed via the standard Gaussian conjugate update, combining the two sources according to their relative precisionStatistical reliability or certainty of information. Higher precision = narrower distribution = more confident. In Bayesian inference, precision determines how much weight each source of information receives. Mathematically: precision = 1/variance. (reliability).
Interoceptive signal strength (I)A model parameter representing internal bodily signals (like heartbeats or breathing) that modulate the relative precision of prior expectations vs. sensory evidence. Higher I = trust priors more; lower I = trust sensory input more.: interpretation
The slider I represents a simplified proxy for cardiorespiratory interoceptive signalling, modelled here as a factor that reallocates precision between internal expectations and incoming sensory evidence.
I → +1: Prior precision increases and sensory precision decreases. The posterior shifts toward the prior.
I → −1: Sensory precision increases and prior precision decreases. The posterior shifts toward sensory evidence.
I ≈ 0: Prior and sensory precision are balanced. The posterior lies between them, reflecting similar weighting.
Key message: rhythmic changes in interoceptive signalling may bias perception by shifting the balance between evidence-driven and expectation-driven inference, even when the external input is unchanged.
Manual Control
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Sensory dominantBalancedPrior dominant
Current I:0.00
Prior precision:How certain/reliable the prior expectation is. Higher values = narrower distribution = more confident. Formula: 1/σ²_prior—
Likelihood precision:How certain/reliable the sensory evidence is. Higher values = narrower distribution = more confident measurement. Formula: 1/σ²_likelihood—
Prior weight:The percentage contribution of the prior to the posterior. Computed as: prior_precision / (prior_precision + likelihood_precision). When this is high, the posterior is pulled toward the prior.—
Likelihood weight:The percentage contribution of sensory evidence to the posterior. Computed as: likelihood_precision / (prior_precision + likelihood_precision). When this is high, the posterior is pulled toward the sensory input.—
Posterior mean:The center of the posterior distribution—the brain's best estimate. It's a precision-weighted average of the prior mean and likelihood mean: μ_post = (w_prior × μ_prior) + (w_lik × μ_lik)—
Posterior SD:Standard deviation of the posterior—how uncertain the final estimate is. Lower values = more confident estimate. Formula: σ_post = 1/√(precision_prior + precision_likelihood)—
Balanced precision weighting — posterior reflects roughly equal influence from prior expectations and sensory evidence.
Dynamic Oscillation
Oscillate the interoceptive signal to simulate rhythmic physiological modulation (e.g., cardiac or respiratory cycles).
Presets
Signal-to-Signal Ratio (SSR)A framework for understanding how different physiological signals compete for influence over perception and action. Here, interoceptive (internal bodily) signals modulate the balance between prior expectations and exteroceptive (external sensory) precision. — Precision Dynamics
This panel shows how interoceptive (orange) and exteroceptive (light blue) precision vary over time as interoceptive signal strength changes. In this toy model, the two traces trade off: when interoceptive precision increases, exteroceptive precision decreases, and vice versa.