Bayesian Brain & Dopamine Belief Updating Simulator Cognitive Neuroscience Lab

🧠 Gaussian Probability Density Updating (Prior vs Evidence → Posterior)
Prior $P(\theta)$ Likelihood $P(x|\theta)$ Posterior $P(\theta|x)$
Prior Mean ($\mu_0$) 0.300
Evidence Mean ($\mu_e$) 0.800
Posterior Mean ($\mu_p$) 0.600
Posterior Precision ($\tau_p$) 25.00
Dopamine RPE +0.500
KL Divergence 0.6081 nats
⚡ Dopaminergic VTA / PFC Spike Firing Trajectories (RPE/IPE Burst Dynamics)
VTA Rate: 42 Hz

📌 Simulation State & Verification Proof VALIDATED

Calculated conjugate Bayesian parameters: Prior $\mathcal{N}(0.30, 10.0)$, Evidence $\mathcal{N}(0.80, 15.0)$ yield Posterior Mean = 0.600, Precision = 25.00, RPE = +0.500, KL = 0.6081.

🎛️ Parameters & Drag Handles
Prior Mean ($\mu_0$) 0.30
Prior Precision ($\tau_0 = 1/\sigma_0^2$) 10.0
Evidence Mean ($\mu_e$) 0.80
Evidence Precision ($\tau_e$) 15.0
📚 Cognitive Bias & Belief Pathways
📋 Simulation Trial History Log
Trial $\mu_0$ $\mu_e$ $\mu_p$ RPE KL
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