# In "A statistical model is a family of probability distributions of a random variable which is…" does "which" refer to "a statistical model"?

I have a few questions about the use of the pronoun which.

In the sentence:

A statistical model is a family of probability distributions of a random variable which is smoothly parametrized by a finite number of real parameters.

1. Is the pronoun which referring to the noun "statistical model" or the noun "variable"?

2. How could I rewrite the sentence above to make the pronoun which refer to the noun "statistical model"?

• Caveat: This is not an area I know but here is the rewrite: A statistical model, smoothly parametrized by a finite number of real parameters, is a family of probability distributions of a random variable. It's an apposition. Nov 19, 2021 at 21:07

Disclaimer- I am a non native speaker. So just for the reference sake.

1 --> Neither of them. which is referring to "a family of probability distributions of a random variable"

2 --> You don't need to do. Because "A statistical model" is the subject so that it should be explained by the clause (in this case "a family of probability distributions of a random variable which is smoothly parametrized by a finite number of real parameters.").

Just FYI.

1. Is the pronoun which referring to the noun "statistical model" or the noun "variable"?

It is almost certainly not referring to "a statistical model". It would be very unusual for a relative clause ("which is smoothly . . .") that appears after a clause's finite verb ("is") to modify a subject that appears before the finite verb. (Modifiers are usually placed as close to their heads as possible. Some features of English syntax, such as "extraposition", allow movement to the right, but those features don't seem to apply here.)

The relative clause is adjacent to the nominal phrase "a random variable", and that is what it most likely modifies. It is also possible for it to modify the entire nominal phrase "a family of probability distributions of a random variable", but that seems less likely to me (because we don't usually refer to a "family" as "smoothly parametrized").

2. How could I rewrite the sentence above to make the pronoun which refer to the noun "statistical model"?

The simplest rewrite would involve moving the relative clause to a position adjacent to what it modifies:

A statistical model which is smoothly parametrized by a finite number of real parameters is a family of probability distributions of a random variable.

Other versions are also possible. For example, in a comment above Lambie offers a nice version that changes the relative clause into a past participle phrase (via "whiz deletion"):

A statistical model smoothly parametrized by a finite number of real parameters is a family of probability distributions of a random variable.

(She added commas, which would often be considered to make the past participle phrase nonrestrictive or parenthetical. You didn't include any commas in your original sentence, so I left them out.)