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The lecturer states that once the data have been collected, they should be treated as constants because there is no more variability. This fixed-data perspective is what allows the likelihood to be discussed as a function of the parameter alone.

Conditions: The data have already been observed.; The discussion is in the inference stage rather than the sampling stage.

The lecturer states that once the data have been collected, they should be treated as constants because there is no more variability. This fixed-data perspective is what allows the likelihood to be discussed as a function of the parameter alone.

Conditions: The data have already been observed.; The discussion is in the inference stage rather than the sampling stage.

The likelihood function is a function of the unknown parameter $\theta$ after the observed data $x_1, \dots, x_n$ are fixed. It assigns to each candidate parameter value a measure of how likely the observed data are under that parameter.

Conditions: The data $x_1, \dots, x_n$ are treated as fixed observed constants.; The argument being varied is the parameter $\theta$.

The likelihood function is a function of the unknown parameter $\theta$ after the observed data $x_1, \dots, x_n$ are fixed. It assigns to each candidate parameter value a measure of how likely the observed data are under that parameter.

Conditions: The data $x_1, \dots, x_n$ are treated as fixed observed constants.; The argument being varied is the parameter $\theta$.

In likelihood inference, the observed data $x_1, \dots, x_n$ are held fixed, and the parameter $\theta$ is varied to compare different candidate values.

Conditions: The data have already been observed.; One is comparing different candidate values of $\theta$.

In likelihood inference, the observed data $x_1, \dots, x_n$ are held fixed, and the parameter $\theta$ is varied to compare different candidate values.

Conditions: The data have already been observed.; One is comparing different candidate values of $\theta$.