From Wikipedia:
Care of the dead and the loving duty toward one's ancestors (pietas) were fundamental aspects of ancient Roman culture.[52] A clear manifestation of this is Roman Republican era portrait busts which may have originated in the practice of making death masks of ancestors which were displayed in the home and during funerary rites and on the anniversary of the ancestor's death.
And further down:
Ancient Rome
Detail from an early second-century Roman sarcophagus depicting the death of Meleager
See also: Roman funerals and burial
The Romans, like many Mediterranean societies, regarded the bodies of the dead as polluting.[66] During Rome's Classical period, the body was most often cremated, and the ashes placed in a tomb outside the city walls. Much of the month of February was devoted to purifications, propitiation, and veneration of the dead, especially at the nine-day festival of the Parentalia during which a family honored its ancestors. The family visited the cemetery and shared cake and wine, both in the form of offerings to the dead and as a meal among themselves. The Parentalia drew to a close on February 21 with the more somber Feralia, a public festival of sacrifices and offerings to the Manes, the potentially malevolent spirits of the dead who required propitiation.[67] One of the most common inscriptional phrases on Latin epitaphs is Dis Manibus, abbreviated D.M, "for the Manes gods", which appears even on some Christian tombstones. The Caristia on February 22 was a celebration of the family line as it continued into the present.[68]
A noble Roman family displayed ancestral images (imagines) in the tablinum of their home (domus). Some sources indicate these portraits were busts, while others suggest that funeral masks were also displayed. The masks, probably modeled of wax from the face of the deceased, were part of the funeral procession when an elite Roman died. Professional mourners wore the masks and regalia of the dead person's ancestors as the body was carried from the home, through the streets, and to its final resting place.[69]
You can read about various cultures and veneration of the dead at this wikipedia entry. (It doesn't say anything about ancient Greece).
My guess is that Epicurus would participated only because it was so widely practiced and seemed necessary to those who were not Epicureans.
Since we don't have an American annual ritual of ancestor veneration, then I think it would feel awkwar to try to start doing that, especially if as Epicureans we don't believe that a spirit survives death.
