if, at the same time, you know of no way that a particular option is possible, then you have no way of knowing what probability to assign to that option.
You cannot assign an arbitrarily precise probability to that option, but that is usually true of any option. However, you should be able to bracket the probability, e.g. by saying it is less than 1 in a million.
Second, if you believe that you know of only a small fraction of what can be known of the way(s) that that option is possible
That's why you assign a confidence range to your estimates.
H: Parsimony. Without it, you could make up an infinite regress of causes for your causes, none of which add any power or scope to your explanation.

P: I'm not sure what you mean. Are you saying that there are no causes for anything?

Of course not.  Consider the theories:
A) The universe exists and is self-caused or uncaused or has no known cause.
B) The universe was caused by God, who is self-caused or uncaused or has no known cause.
C) The universe was caused by God, who was caused by SuperGod, who is self-caused or uncaused or has no known cause.
I'm saying that B is more parsimonious than C, and A is more parsimonious than B. I'm saying that without parsimony, you have no reason not to believe in SuperGod, and SuperDuperGod, ad infinitum. (I of course here rely on the fact that any attribute of self-causedness or uncausedness that can be imputed to God can be imputed to the universe itself.)
H: That's a valid way to use the terms, but then causation even more obviously vanishes -- just as unmarried maleness does not "cause" bachelorhood.

P: If I light a match in a tank of gasoline fumes and the fumes ignite, is the fact that the fumes have ignited a random fact, or has the flame caused the fumes to ignite?

I didn't ask you whether you thought unmarried maleness causes bachelorhood, so please don't ask me such a specious question as whether a match's flame can cause ignition of gasoline fumes.
If every cause is properly reduced, in our minds, to a description of events, and nothing properly understood as causing anything,
I didn't make the latter claim.  Again: when construing my position, please type a quotation mark, paste something that I wrote, and then type another quotation mark.
H: Supernaturalists usually say God is self-causing and self-explaining.

P: What is 'God'?

See http://humanknowledge.net/Thoughts.html#god.  In general, if you want to know what I mean by 'foo', first look it up in my book by referencing http://humanknowledge.net/Thoughts.html#foo.  If my book doesn't define it, then assume that I intend the relevant sense in Merriam-Webster at http://www.m-w.com.
To see the idea of an 'epistemic vantage point', you need to see the idea of 'foundation'.

There are two main options for a 'foundation', that is, for an entity/entities that has/have 'se existence':

I don't agree that anyone knows any particular options for how an entity could be self-causing, or how a fact could be self-explaining.
A)actual physical infinity, by infinite regress of things that comprise, or are in some sense responsible for, one or more of all other things ('things' here in either case being time, matter, motion, qualia, cognition, quantity, etc.)  or  B)actual physical finity.
C)Apart from the problem of infinity/finity, there is a third main option:  nothing is the foundation for anything (this is with or without any actual physical infinity).
I'll take your 'foundation' to mean the property by which an entity is self-causing or a fact is self-explaining.  On this reading, I don't see that you've given any explanation whatsoever as to how in particular a fact or entity could be foundational.
Now, for the 'epistemic vantage point'. In any one of these cases for a 'foundation', there are two options: 1)you are that 'foundation'  2)you are not that 'foundation'.  If you are not that foundation, then your epistemic vantage point of that 'foundation' is necessarily from 'below' it (sorry for the confusion of terms), looking up at it as you would at a moon that you inherently cannot reach (I have to use some illustration of 'epistemically below').
I agree that I am not self-causing or self-explaining.  So?
H: Why must any thing (event? fact? what?) have a "direct cause"?

P: See option C above.

I did. My question remains unanswered..
H: for our purposes (viz., of answering "why?" questions), the concept of an explanation generalizes the concept of a cause.

P: Not sufficient. See 'epistemic vantage point', above.

I did; I don't see how it addresses my point.  It might help if you could relate your position or point to anything referenced by one of these online philosophy encyclopedias.
If "why" is a valid question, then there must be a valid answer, and, if there is a valid answer, then there must be a true answer.
You once again assume the Principle of Sufficient Reason -- that every circumstance/event/entity has a cause, or that every fact has an explanation.  We don't know that this principle is universally true.
H: I think the fear of uncertainty explains more about religion than it does about naturalism. [..] By 'uncertainty' here I mean lack of  knowledge, especially lack of certain knowledge.

P: See 'foundation' above.

I see it; I don't see what point you're trying to make here.
You yourself must be operating according to some foundation in this debate, otherwise your position is untenable by definition.
By my understanding (above) of what you mean by 'foundation', this statement makes no sense.  Again: I might better understand you if you related what you're saying to something referenced by one of these online philosophy encyclopedias.
I think your definition of faith (and thus religion) is arbitrary.
Then so is Merriam-Webster's.  I'm using roughly their 2a and 2b2 definitions of 'faith', as they reference their 1a definition of 'religion'.
What is your definition of worship?
See Merriam-Webster.
I wish to know how, or whether, and if not, why, you would revise [Holtz's comments on science and religion, skepticism and faith] in light of all of my new replies above.
Not. Why?  Because your new replies are either irrelevant (or are opaque to me).
Thus, any belief based on revelation and exempt from doubt = x  The question now is, does x exist? To answer this, we must first know what we mean by 'revelation', 'exempt' and 'doubt'. Please define your usage of these terms so as to allow no epistemic, heuristic, etc., loopholes by which everyone would be defined as having x.
Again, see Merriam-Webster. Specious ways of defining everyone as having 'faith' are always available. In my book I catalogued four examples, and I thank you for giving me a fifth.  You made no reply to my diagnosis of its speciousness, so I'll repeat that diagnosis: It's specious to define 'faith' as any occasion in which not all evidence about X is univocal and paradigm considerations (i.e. evidence about evidence) play a role in ultimately deciding between X and not-X. This is yet another facile attempt to make 'faith' into a meaningless label that makes no practical distinctions whatsoever.
H: I don't know what you mean by "solid" here, and I don't know what "denial" you have in mind.

P: For what I mean by 'solid', see 'foundation', above. For what I mean by 'denial', see my first new reply about probability, above, 'foundation', above, and cause/description/explanation, above

Sorry, I still don't understand.
H: I'm sorry, but I don't understand your point here.

P: Same as above.

Sorry, I still don't understand.
H: I don't know what you mean by "power"

P: Synonymous with 'foundation'

Sorry, I still don't understand.
H: I still don't know what you mean by "power", but you're obviously using some in-principle qualitative similarity to wish away an obvious quantitative difference in probability.

P: Do you wish to revise, or retract, that?

H: The supposed irony you identified does not obtain for atheists.

P: If, by 'irony', you mean a subjective sense of irony, then you are incorrect.

I mean that there is no irony in rationality not being used for rationality's intended purpose X if one does not think there exists any intender behind the existence of rationality. Do you dispute this?
If an A or B 'foundation' exists, then there is no true error of 'the God of the Gaps'. [..]
I've seen no convincing demonstration of this from you.
The atheist simply has to follow the heirarchy of physics downward as each more basic level of it is uncovered. The error that does occur is actually symmetric between theists and atheists.
It's laughable to say that because atheists posit certain brute facts, it's not unparsimonious for theists to posit god(s) merely for the purpose of "explaining" those facts.
 H: Be especially more careful about using the word 'all'.

P: I'm sorry, but that's an invalid request.

I'm sorry, but yours is an invalid observation.  You should use 'all' when you mean 'all', otherwise use 'almost all'.  If you can't do that, then we shouldn't be having this discussion.
There is no objective boundary in communication. We are ever dancing over the phone to each other, each with an indefinite number of arms.
Your phone/arm analogy wasn't very useful before, and it doesn't help me here either. :-)
All forms of semantic communication between mutually undefined agents can proceed only by way of reciprocal confirmation of meaning.
See, it's not so hard to use 'all' correctly.
H: Again: Anyone who thinks of science as an alternative to religion is making a basic mistake. Science is not a worldview, and any "conflict" between science and religion is actually an epistemological conflict between skepticism and faith.

P: It seems to me that either there is an inherent conflict between what you are calling 'religion', and 'science',

Only insofar as science is based on skepticism, which is incompatible with the faith on which so much religion is based.
If what you are calling 'religion' and 'science' are not alternatives to each other
Recall from my definition of 'religion' that it does not necessarily require faith. However, for probably 99% of religionists, it involves faith or mysticism, which are antithetical to skepticism.
H: The fact that we might be wrong about our causal relationships is not a good reason to say that arbitrary hypothetical entities exist.

P: Please explain what you mean by 'arbitrary'.

See Merriam-Webster.
If you do not further define your use of the term 'religion' to include the notion that religion is simple-minded, then I concede that I am incorrect in my impression.
Faith and mysticism are usually (but not always) more simple-minded than skepticism, and religion at any rate need not be based on either faith or mysticism.
P: how are you not as an algorithm to its axiom? Can an algorithm prove its own axiom as such?
H: I don't understand what you're saying.
P: See 'foundation', above.
Sorry, I still don't understand.

OK, that's ten cases (just this time) of me totally not understanding your point, along with four cases of you asking me to define words when I intend their plain dictionary definitions. This is not enough signal to noise to justify this cadence of responses, so mine will probably start slowing down.