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I am reading "Probabilistic Machine Learning" by K. Murphy. In it, he defines the likelihood of a dataset as

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However, this dataset $D$ is defined as:

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So if all $x_n, y_n$ are random variables, it would seem that one needs to account for $p(x_n|\theta)$ via conditional probability? I assume this would factor out if assumed to be a constant, but I didn't see this explicitly stated.

Please excuse this potentially naive question.

kjetil b halvorsen
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    Please type your question as text, do not just post a photograph or screenshot (see here). When you retype the question, add the [tag:self-study] tag & read its wiki. – kjetil b halvorsen Oct 13 '22 at 02:51
  • Have a look at https://stats.stackexchange.com/questions/144826/what-is-the-difference-between-conditioning-on-regressors-vs-treating-them-as-f/192746#192746 and https://stats.stackexchange.com/questions/215230/what-are-the-differences-between-stochastic-and-fixed-regressors-in-linear-regre/417324#417324 – kjetil b halvorsen Oct 13 '22 at 03:12

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