Asimov, everything a person believes is based on some authority. This gets tricky when dealing with historical evidence because all we have is archeology and early testimony. It doesn't matter what the historical event was, we only know about it because of those two things. We know from Suetonius, Tacitus, Pliney, and Josephus (all pagan sources) that there were persecuted Christians in the first century. This doesn't take into consideration all of the "biased" Christian sources.
So what questions arise from this information? The two biggest questions that jump out at me are.... who were these people and why were they persecuted? It must have been a large group if the Roman Caesars took notice of them (according to pagan sources). They were also willing to die instead of flee, which means they held strong beliefs about non-resistance.
If you, Asimov, told me you saw a pink elephant in your room last night I'd say you're either lying or delusional. But if I perceive you to be a rational person (which I do, based on your writings) and you were also willing to be tortured and beheaded for this claim... I'd take you more seriously. In fact, I'd be persuaded that you had indeed witnessed something. Now, if you also brought me a few hundred other people, who were all willing to undergo tortue and death, who also saw the pink elephant I'd have a lot of trouble writing off this experience as a mass conspiracy.... especially if you stood to gain nothing by it.
Why would you care if I believe your testimony about the pink elephant unless you were convinced of it yourself? To take this a step further, let's say the elephant had instructed you to give up all your possessions, live in poverty, love those who hate you, and serve others the rest of your life? Very few people (if any) would consider this a good reason to lie. Did you see the videos of those Iraqi Muslims sawing off the heads of contract workers? Would they have endured the same treatment to advance a lie? I think it's very naive to think so.
So we come back to authority. The apostle Paul, from his writings, seemed to be a very rational man. Even liberal scholars date his epistles to the mid-first century. So we now have early testimony of a man claiming he met a resurrected savior that a bunch of other Jews had seen as well. Paul travels around proclaiming the message and gets thrown in jail and beheaded by Nero for his troubles. Did Paul do these things because he wanted to advance some new mythology? My knowledge of human nature says his testimony holds more weight than, say, a chair-holder at Cambridge, 2000 years later, who stands only to gain by his assertions, claiming Paul was spreading a myth.
Thank you for your time.