The phrase "a brilliant analysis of" is correct and usable in written English.
You can use it when describing a thoughtful and insightful examination of a particular subject or topic.
Example: "The author provides a brilliant analysis of the social implications of technology in modern society."
Alternatives: "an insightful examination of" or "a profound critique of".
For a brilliant analysis of historical writing as a discursive practice, see Hayden White's: Metahistory.
Brown and Linden provide a brilliant analysis of the competitive crisis facing the U.S.
Frank Rich has produced a brilliant analysis of the Karl Rove imbroglio in "Follow the Uranium" (column, July 17).
This was a brilliant analysis of everyman as a way of talking intimately, challengingly and refreshingly about the human condition.
This thin novel begins and ends with a brilliant analysis of an art installation consisting of Alfred Hitchcock's "Psycho" slowed down so that it lasts twenty-four hours.
"One of the book's most telling sections is a brilliant analysis of the looting of Angola," wrote Michael Sheridan in the Sunday Times.
Jehovah's Witnesses don't have a great track record, particularly in regards to their predictions for when Armageddon will arrive, but they once published a brilliant analysis regarding the cause of homosexuality in their book, Your Youth - Getting the Best Out of It.
Technology journalist Danny Sullivan writing at searchengineland.com did a rather brilliant analysis of what the New York Times would look like if produced by Demand Media.
The Ethical Soundscape is a brilliant analysis linking modern media practices of moral self-fashioning to the creation of increasingly powerful religious publics.
"She's doing a brilliant analysis," said Allen Johnson, a supervising professor of anthropology at UCLA. "In Cameroon she was plunged into a moment of enormous drama and as an anthropologist was lucky to be in the right place at the right time". Horton believes she's on the correct path.
Grant provides a brilliant analysis.
