Likelihood principle

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Intuitively, the likelihood principle states that all information for inference on parameter $\theta$ should be based on the likelihood ratio. Formally, suppose that $x$ and $y$ arise from distributions indexed by $\theta$. Then if $\ell(\theta;x)=k\ell(\theta;y)$, then any inference based on $x$ or $y$ must be the same.


References

• Vic Barnett (1971). Comparative statistical inference. London: John Wiley & Sons.
  
• James O. Berger and Robert Wolpert (1988). The likelihood principle. IMS Lecture notes - Monograph series.
• G.A. Young and R.L. Smith (2005). Essentials of statistical inference. Cambridge University Press.