Chicago – In the last days of August 2012, three generically titled ghost pictures had the misfortune of opening at more or less the exact same time. None of them were particularly memorable, yet only one managed to produce any semblance of genuine chills. There are enough eerie moments in “The Possession,” the demonic thriller from gifted Danish director Ole Bornedal, that one wishes that it pushed past the boundaries of its tame PG-13 rating.

The script by Juliet Snowden and Stiles White is a Judaic variation on “The Exorcist,” complete with a hasidic scholar barking out chants just like Max Von Sydow. The success of this formula succeeds or fails largely on the strength of its central performance from the possessed victim, which often takes the form of a young girl. “Exorcist” star Linda Blair set a spectacularly high bar that no imitator has been able to equal, and “The Possession”’s pint-sized leading lady,...