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Interactive 3D/MLE & MAP Explorer
Sample Size
n = 20
550
New Sample
Prior (MAP)
Estimates
MLE μ̂:0.000
MLE σ̂:1.000
Log-L:0.00
MLE finds the parameters that make the observed data most probable. The ★ marks the peak of the likelihood surface. MAP pulls the estimate toward a prior belief.
Try: Enable Prior with high strength - watch MAP (green dot) drift toward μ=0 away from the MLE star. More data weakens the prior's pull.

MLE & MAP Explorer - Interactive Visualization

Maximum Likelihood Estimation (MLE) finds parameters that make observed data most probable: θ̂_MLE = argmax P(data|θ). Maximum A Posteriori (MAP) adds a prior: θ̂_MAP = argmax P(data|θ)·P(θ). This visualization shows data points, the likelihood surface as contours, the MLE as a star, and how adding a prior shifts the estimate toward the prior mean (regularization).

  • See likelihood contours and MLE star on a 2D parameter space
  • Click Add Prior to shift from MLE to MAP estimation
  • Watch MAP estimate move toward prior as prior strength increases
  • Understand that L2 regularization = Gaussian prior (MAP)
  • Generate new data samples to see estimate variability (bias-variance)

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.