On the back cover of the Bloomsbury edition of Harry Potter and the Goblet of Fire is this picture:
Who is the ghost?
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The costume definitely reminds me of Nearly Headless Nick.
The picture on the cover definitely resembles the description of his costume on Wikia:
He would usually sport a ruff, which would ensure his partially severed head stayed in place, as well as tights, a pair of breeches, a doublet or, occasionally, a tunic. ... He also sported a small moustache and goatee.
As for other House Ghosts, I don't remember anyone else ever been described as wearing the costume on the book cover.
Also, check the costume he wears on Harry's first day at Hogwarts.
Given the costume I would assume that it is Sir Nicholas de Mimsy-Porpington aka Nearly Headless Nick
I would have to say it is the Fat Friar. I can't recall any other ghost described as "round and jolly to all." He's the Hufflepuff house ghost.
Giles Greenfield was the illustrator of the UK Bloomsbury edition of Goblet of Fire. He sent a sketchbook of his early conceptual artwork to a YouTuber called The Potter Collector. Here's the video featuring the book.
The sketchbook features an early version of his rendering of the back cover.
It's not entirely clear what Greenfield wrote next to his drawing. But it's something like the following:
the main door p353
An article on the Harry Potter Lexicon allows us to track p353 to chapter 23 (The Yule Ball). There was a typo on this page which was corrected in a subsequent edition.
Around the start of the chapter we find this excerpt:
"You know, they’re dentists, they just don’t think teeth and magic should - look! Pigwidgeon’s back!”
Ron’s tiny owl was twittering madly on the top of the icicle-laden banisters, a scroll of parchment tied to his leg. People passing him were pointing and laughing, and a group of third-year girls paused and said, “Oh look at the weeny owl! Isn’t he cute?”
“Stupid little feathery git!” Ron hissed, hurrying up the stairs and snatching up Pigwidgeon. “You bring letters to the addressee! You don’t hang around showing off!”
(Goblet of Fire, Chapter 23, The Yule Ball).
Clearly, this passage was only a very loose inspiration for Greenfield's final drawing. The stairs and banisters are entirely ice-free and there aren't any students about (I always assumed it was a Hogwarts staircase at night when only the ghosts are about).
The context of the original passage does at least clarify who the owl is on the back cover.
Nevertheless, it doesn't help us identify the ghost. Greenfield's initial sketch didn't feature a ghost, or a suit of armour. These are added in at a later date, so can be put down to artist licence. Here's a more finished sketch featuring the ghost.
As for which ghost Greenfield wanted to depict, we simply can't say. It may not have been any particular named ghost; it could've been just a background filler ghost. Personally, I think his portly demeanour suggests the Fat Friar, but that really is just a guess.
I always thought it was Peeves. He’s the trouble-making ghost at Hogwarts who got cut out of the movies.