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Likelihood

Definition​

Definition

We assume that we observe the realisations x1,…,xnx_1, \dots, x_n of the random variables X1,…,XnX_1, \dots, X_n. The function

θ→∏i=1nPθ(Xi=xi)\theta \rightarrow \prod_{i=1}^{n} \mathbb P_\theta(X_i = x_i)

is called the likelihood of θ\theta for the realisation (x1,…,xn)(x_1, \dots, x_n) and is denoted L(θ;x1,…,xn)L(\theta; x_1, \dots, x_n ) or simply L(θ)L(\theta) if there is no ambiguity.

Results​

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