It’s dated 2007, but Google thinks its only just appeared on the web. A new Ph.D. thesis — The Case of the Psychic Detective : progress, professionalism and the occult in psychic detective fiction from the 1880s to the 1920s (PDF link).
“This thesis examines a little-known hybrid genre popular in the late nineteenth and early twentieth centuries: psychic detective fiction. The stories that comprise this hybrid genre involve the rational investigation of supernatural phenomena. They have received relatively little critical attention due, in part, to their inability to fit comfortably in either the traditional ‘detective’ or ‘ghost story’ categories, in addition to the comparative obscurity of many of the writers.”
Relevant to Inspector Thomas Malone in “The Horror at Red Hook”, a Lovecraft story that seems to have been aimed at publication in Detective Tales…
“He had the Celt’s far vision of weird and hidden things, but the logician’s quick eye for the outwardly unconvincing”