This page says

In statistics, the likelihood function (often simply called the likelihood) expresses the plausibilities of different parameter values for a given sample of data. While not to be interpreted as a probability, it is equal to the joint probability distribution of a random sample. However, whereas the latter is a density function defined on the sample space for a particular choice of parameter values, the likelihood function is defined on the parameter space while the random variable is fixed at the given observations.

What does "While not to be interpreted as a probability" mean here? Especially "not to be".

Does it imply this meaning (my own version)?

although mathematician/statistician does interpret this object as a probability...

  • It just says that we shouldn't interpret the likelihood as probability.
    – Cardinal
    Oct 12, 2019 at 2:57
  • Although inferential statistics is definitely not my strong suit, this definitely says that the likelihood is not a probability. If you want this explicated further, I suggest you try at a math site specializing in inferential statistics. Oct 13, 2019 at 1:41

1 Answer 1


Here "not to be" means "ought not to be". It is not appropriate to so interpret it. It would be an error to interpret it is a probability.

The part you are asking about could be rephrased thus:

Yes, it would be wrong to interpret it as a probability, however...

  • Thanks for your answer. Is "ought not to be" and "should not to be" safely exchangeable in this case?
    – user97526
    Oct 13, 2019 at 2:52
  • Yes, in this case either will do.
    – David42
    Oct 13, 2019 at 21:10

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