ROME — Several of this city’s finest museums bear the names of the aristocratic families who once built majestic palazzi and stuffed them full of priceless art: the Borghese, the Barberini, the Doria Pamphilj, and more still.

But one of the world’s most precious private collections — that of the Torlonia family — has remained out of bounds, unseen by the public and known to most scholars only through its catalog, published in the late 19th century. It includes scores of busts and a veritable who’s who of classical mythology, dating from the fifth century B.C. to the fourth century A.D. Eventually the collection would swell to 620 statues depicting Greek and Roman gods, goddesses and mythical heroes, as well as portraits of Roman emperors. The catalog’s author, Pietro Ercole Visconti, described the sculptures as “an immense treasure of erudition and art, amassed in silence over the course of many, many years.”