From Robert Scholes and Robert Kellogg, The Nature of Narrative (1966):
The epic poet is a repository of tradition, fulfilling the functions of entertainer and historian simultaneously. The tradition provides him with his authority. The familiar invocation to the muse of Homeric epic may well represent an attempt on the part of the Greek epic poet to shift the authority from constricting tradition to inspiration, which is freer because personal and creative. The inspired bard must answer to his muse alone, and his muse can only speak through him …. In seems highly likely that the invocation is a sophisticated feature which developed late in Greek oral epic as a manifestation of the creative impulse toward a more fictional kind of narrative ….
The Greek historians in their narratives substitute for the authority of tradition a new kind of authority. The histor as narrator is not a recorder or recounter but an investigator. He examines the past with an eye toward separating out actuality from myth. Herodotas takes his authority not so much from his sources as from the critical spirit with which he means to approach those sources. Where the traditional poet must confine himself to one version of the story, the histor can present conflicting versions in his search for the truth of fact. Thucydides is the perfect type of the ancient histor, basing his authority on the accuracy of conclusions he has drawn from evidence he has gathered.
The principal other source of narrative authority which we would expect to find in empirical narrative is not so readily found there in the ancient world. This is the authority of the eye-witness. We have commented elsewhere on the rarity of first-person narrative in pre-Roman narratives. This absence is nowhere more striking than in such a narrative as Xenophon’s Anabasis. Here the author witnessed the events narrated and took a prominent part in them. Yet he not only narrates in the third person, casually introducing himself (Xenophon, an Athenian) in Chapter 8 of Book I, but originally caused his manuscript to be circulated under someone else’s name. Thucydides also refers to himself bleakly in the third person in Book IV of The Peloponnesian War, striking the personal note of the eye-witness momentarily — in Book V — and even there emphasizing his leisure for investigation rather than any immediacy of observation… The reason for this employment of third-person narrative of historical works may be that the reliability of the histor seemed to the ancients clearly greater than that of the eye-witness…. First-person narrative seems to have been used mainly in the ancient world not for factual or mimetic representation, but for highly unreliable and one-sided apologiae …