Likelihood Function Likelihood principle Data Statistical Model Sample x 1 . . . x n {\displaystyle x_{1}...x_{n}} Random variable X is discrete: x ∼ f θ ( x ) {\displaystyle x\sim {f}_{\theta }(x)} f θ ( s ) {\displaystyle f_{\theta }(s)} L : Ω → R {\displaystyle L:\Omega \rightarrow {R}} L ( θ | s ) = f θ ( s ) {\displaystyle L(\theta |s)=f_{\theta }(s)} Likelihood ratio L ( θ 1 | s ) L ( θ 2 | s ) {\displaystyle {L(\theta _{1}|s)} \over {L(\theta _{2}|s)}} Equivalent Likelihood function L * ( θ | s ) = c L ( θ | s ) {\displaystyle L{\text{*}}(\theta |s)=cL(\theta |s)} L ∗ ( θ 1 | s ) L ∗ ( θ 2 | s ) {\displaystyle {L^{*}(\theta _{1}|s)} \over {L^{*}({\theta }_{2}|s)}} = c L ( θ 1 | s ) c L ( θ 2 | s ) {\displaystyle {cL({\theta }_{1}|s)} \over {cL(\theta _{2}|s)}}
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