Bayesian Update for A Normal Distribution
with Known and Unknown Variance
J. Jack Lee and Ying-Wei Kuo
PID:865; v1.0.6.0 ; Last Updated: 03/26/2026
Unknown Variance: Data Update
Credible Interval Coverage (%)
Prior Parameters
Mean of Mean ( \(\mu_0\))
Size of Mean ( \(n_0\))
Inv-gamma of Var, Shape \(a\)
Inv-gamma of Var, Scale \(b\)
Calculate Prior
Sample Values:
Data Point
Summary
Sample Mean
Sample Std Dev
Sample Size
Display Confidence Interval Coverage (%) for Sample Mean
Sample
(separate by a comma)
Calculate Posterior
Edit
Start Over
Unknown Variance: Vary Prior
Credible Interval Coverage (%)
Prior Parameters
Mean of Mean ( \(\mu_0\))
Size of Mean ( \(n_0\))
Inv-gamma of Var, Shape \(a\)
Inv-gamma of Var, Scale \(b\)
Calculate Prior
Sample Values:
Data Point
Summary
Sample Mean
Sample Std Dev
Sample Size
Display Confidence Interval Coverage (%) for Sample Mean
Sample
(separate by a comma)
Calculate Posterior
Edit
Start Over
Known Variance: Data Update
Credible Interval Coverage (%)
Prior Parameters
Mean of Mean ( \(\mu_0\))
Var of Mean ( \(\sigma_0^2\))
Sample True Var ( \(\sigma^2\))
Calculate Prior
Sample Values:
Data Point
Summary
Sample Mean
Sample Size
Display Confidence Interval Coverage (%) for Sample Mean
Sample
(separate by a comma)
Calculate Posterior
Edit
Start Over
Known Variance: Vary Prior
Credible Interval Coverage (%)
Prior Parameters
Mean of Mean ( \(\mu_0\))
Var of Mean ( \(\sigma_0^2\))
Sample True Var ( \(\sigma^2\))
Calculate Prior
Sample Values:
Data Point
Summary
Sample Mean
Sample Size
Display Confidence Interval Coverage (%) for Sample Mean
Sample
(separate by a comma)
Calculate Posterior
Edit
Start Over
Support Document
Known Variance
Unknown Variance
Support Document
Known Variance: Data Update
Known Variance: Vary Prior
Unknown Variance: Data Update
Unknown Variance: Vary Prior
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