A simple and conservative empirical likelihood function


Multiple measurements with an unknown Gaussian likelihood function are treated probabilistically. The likelihood function

L(\mu)\propto \left( (n-1)\sigma_x^2 +n(\mu-\overline{x})^2 \right)^{-n/4} is derived

where \mu is the true value, \overline{x} is the mean,

and \sigma_x^2 is the variance obtained from the n measurements.

DOI Code: 10.1285/i20705948v7n2p432

Keywords: likelihood function, empirical, data analysis, lognormal, probabilistic, Bayesian.


Sivia, D. S. with Skilling, J. (2006). Data Analysis--A Bayesian Tutorial, 2nd Ed. Oxford Science Publications.

Guthrie Miller. (2013) Probabilistic Interpretation of Data--A Physicist's Approach. Lulu Publications.

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