Judges are meeting to select a victor of the 50,000 pound (USD 77,000) award from six books that include a Jamaican novel about the attempted assassination of Bob Marley, a tale of Nigerian brothers and an American family saga.
The prestigious prize opened entries to English-language writers of all nationalities two years ago. It had previously been restricted to writers from Britain, Ireland and the Commonwealth of former British colonies.
Some British book-lovers expressed fears of an American takeover, but last year's winner was Australia's Richard Flanagan, for "The Narrow Road to the Deep North."
British bookmakers Ladbrokes and William Hill, which offer odds on the prize as if it were a sporting event, made Yanagihara the favorite for her unsparing 700-page tale of childhood trauma and its legacy.
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The other front-runners in betting are British writer Sunjeev Sahota's "The Year of the Runaways," the highly topical story of migrants from India scrabbling to make a living in Britain, and "A Brief History of Seven Killings" by Marlon James, the first Jamaican Booker finalist.
The Booker guarantees a big boost in sales for the winner, and can transform writers' careers. When Hilary Mantel won for Tudor saga "Wolf Hall" in 2009, she went from modestly successful novelist to literary superstar.
Founded in 1969, the award is officially named the Man Booker Prize after its sponsor, financial services firm Man Group PLC.