How does Gaussian Naïve Bayes handle continuous variables mathematically?

Updated May 17, 2026

Short answer

Gaussian Naïve Bayes assumes features follow a normal distribution within each class.

Deep explanation

Gaussian NB models likelihood as P(x|C) using Gaussian density: (1 / √(2πσ²)) exp(-(x-μ)² / 2σ²). It estimates mean and variance per class for each feature. During prediction, it multiplies probabilities across features under independence assumption.

Real-world example

Medical diagnosis using patient vitals like blood pressure and temperature.

Common mistakes

  • Assuming real-world data strictly follows normal distribution.

Follow-up questions

  • What if data is not Gaussian?
  • Can we mix distributions?

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