Why not deism?

[chimp3]

In the court room setting I would hope that "authoritative" is a synonym for "expert". So, that includes something like science based.

Well, I guess it depends on the topic. If it's something amenable to scientific study, then sure, an expert is someone who knows about scientific study. 

  In the court setting their testimony is not evidence, they are presenting evidence. 

I'm not sure I understand the difference. Are you wanting to differentiate between the authority of the person speaking and the persuasiveness of the facts he gives? If so, I agree with you that the witness's personal clout is not what's important. 

On the other hand, it turns out that in a lot of cases the facts are not conclusive, and different experts can reach different conclusions from the same facts. In real life, science-type approaches aren't definitive, sad to say. 

Ballistics, Pathology, etc. Regarding a religious claim authorities have a much higher hurdle. If someone claims they are an authority on exorcisms I could just as easily claim I am an authority on talking, flying frogs. They have to support their claim with the evidence for demon possession, not just anecdotes.

Right. I'm fine with that. Ballistics et.al. have lots of empirical backup. Exorcisms not so much. 

The case I've been watching on YouTube is a sad little high school cheerleader who didn't want to be pregnant so much that she ignored it and finally gave birth on her own in the bathroom. The expert testimony comes down to whether the baby was stillborn or whether the cheerleader killed it through neglect after a few minutes. This turns out to require a surprising amount of personal interpretation among the expert doctors. 

What I want to say about evidence, though, is broader. To me, it is dangerous and a bit arbitrary to say that any and all evidence must only be science. (And by science I mean: empirical, repeatable, quantifiable, theory-embedded.) To me, evidence is anything that gives added believability to a proposition. Depending on the proposition in question, I think this could include the personal opinion of someone experienced. It could include common sense. Other things too, depending on the topic.

I am not saying that I want to put spooky ghost stories on an equal basis with science. I am only saying that in the real day-to-day world, where we have to decide things, we should value all input. And I acknowledge that this puts a higher burden on us, because I am not drawing clear boundaries on what I'll accept. It's case-by-case, you-have-to-use-your-brain type situations. 

Basically, in my day to day life, I do not demand evidence from believers. I just don't believe them or their magic books. On line I may get into these debates or I may not. I live in a very religious community and I just glide through my day ignoring that nonsense. But, I am not willing to give personal anecdotes the same credence as physical evidence. If a believer states that their god can alter physical reality (water into wine, weather patterns,etc.) then they are making a claim about physical reality. The burden of proof is far greater for them since they have to demonstrate which property of their god altered the chemistry of water for instance. This is not a case by case situation. This is saying that reality is consistent.