Good science should do eliminate influences, but it cannot eliminate the senses themselves without inevitably crippling the whole enterprise. One inevitably has to pass observations through one’s senses that he or she has to presume are working correctly a priori.

What I can appreciate about noumenology is the fact that entities exist and have an essence apart from those observing them, (i.e. logic), but as I have said this has more to do with ontology then epistemology. But as far as an epistemic framework is concerned, it never produced one or was it intended to be used as one because noumenology was concerned with ontology. Nietzsche concerns were over the issues of causation, and if I understand it right, "thing-in-itself" falls apart because so much of a thing's identity is caught up in its causal relationships to other things, but this is hardly a critique of any sort of epistemology.

This may be the case if one asserts that the supernatural does not interact with the natural world, but I think this is probably a minority rather than a majority of particular beliefs. You'd be right in saying that by definition one cannot empirically test the supernatural per se, but that's not a problem with the supernatural...it's a limitation of empirical tests. But the point of the tests is not to establish something’s ontology, but to empirically verify the belief in the existence of some being, which can be tested empirically such as the example I have I gave concerning belief in Santa Claus.

I suppose so, but I don't think we can say that noumenonology is opposed to phenomenology as philosophical system, Phenomenology is a more, rather in depth philosophical frame work while noumenology is principally a concept in ontology.

I'd agree, you can’t have it both ways. The question is then, how does one test such things? Intelligent design proponents do on teleological grounds. Others attempt to do so using historical methods to test the authenticity of miracles.

I'm concerned about justifying  beliefs, not so much in the actual ontology of the object of belief. Granted, the ontology of the object of belief should actually exist for the belief to be valid, but as I've said before, I am, at minimal level asking for an empirical test to justify beliefs.

Phenomenology is tp noumenology as apples are to Valencia oranges. By this I mean that noumenology's concern was more or less with ontology. Phenomenology addressed practically every major branch of philosophy. Noumenology could be a part of another philosophical framework such as Kantian transcendentalism or the like.

Then it's not a question of empirical observations existing, but a question of whether or not the empirical observations are valid.

The original inquiry for a test would be the difference between to two statements, "I believe Santa Claus exists" and "Santa Claus exists". The test I'd ask for is to test the former, not the latter.

A hypothesis to satisfy something like "supernatural" depends on what would attributes to the supernatural. A Humean definition defines it as, "a transgression of a law of nature by a particular volition of the Deity, or by the interposition of some invisible agent" while some are broader such as miracles of circumstance that have a perfectly natural explanation but nevertheless seem miraculous. One example given says a boy is stuck on a train tracks, his mother hears a train and prays for the boy's life. Sure enough, the train stops inches in from of the boy. It happened that at the moment the woman prayed, the engineer tripped and hit his head on the break causing the train to stop. Some attribute things like design. Numerous proposals have been offered on how to empirically test such things. The tests exist, but the question again comes back to the validity of the tests.

Transcendentalism did at least get at something, and I think it is basically the same conversation we had to start with: something cannot validate itself. This was Kant's biggest critique of Hume, and I think a sound one.

For many people, dealing with the phenomenon this is enough. But for others, myself included, it's not and why I sympathize with Kant's critique of Hume.

Some things do not have the luxury of being rigorously observed. For example, unless one can repeat the assassination of JFK, one cannot rigorously test whether or not Oswald actually killed him. What one does in that case is work from what has been observed. The nexus of observations can actually prove to be quite reliable. Suppose 6 people independently report an event. These six people have a habit of lying with every other statement he or she makes (that is they only tell the truth half the time). The probability of them all reporting the same event would be less than 2%. This of course does not guarantee that the observation is true, but at the same time, neither does all the rigorous empirical observations in the world guarantee something is true either.

I'm not asking for truth per se, but justification (i.e. and empirical test if one is claiming to be empirical about his or her beliefs) for such a belief. If knowledge is justified true belief, then I'm looking for the justification for such knowledge.

I tossed that out there to because some consider such things to be miracles. Even if it is purely hypothetical, I have had such stories cited to me as examples of "miracles". The discussion here is whether or not this is a post hoc ergo propter hoc fallacy or not. But to the one who is the benefactor of such things, convincing them it was not a miracle would seem miraculous in and of itself. 

I'd agree noumenon argument results in infinite regress if the idea of the noumenon is treated as a "thing-in-itself" and really counter-productive if left alone. Everything becomes a tautology if Kant is right. This can be avoided (and probably where I'd part company with Kant) if one one grounds the ontology of a "thing-in-itself" and limit the number of things that get the "thing-in-itself" status. This is the basic strategy employed by Sartre, Husserl, and Merleau-Ponty, but they differ one what they appointed  as a "thing-in-itself". I do think some things have ontology in and of themselves but not all things. In other words, their are necessary and contingent entities --  a sort of cosmological necessity but not nccessarily a god.

I would be testing the belief, not the ontological status of the object of belief. I'm not leading to a "empiricism can't test itself". I'm basically asking, "If you claim to be empirical about your beleifs, show how you are empirical about your beliefs". It's a test of credulity, not a test of ontology.

True, beliefs do not necessarily have to be empirical, but If I am not claiming to be empirical about the belief, then I should be able to demonstrate how I am empirical.

One does not necessarily need a personal test. Reading and accepting the results from empirical tests performed by others without actually performing the tests would at some level be empirical, albeit it is not a personal test, therefore would be belief founded upon empirical tests, although these of course are contingent upon the reliability of the original testers.

I don't think one would have to perform a test here either, because there are plenty of tests that verify molecules do not retain imprints. Based upon these empirical tests, I can eliminate other ad hoc hypothesis in a Popperian sense.

Sure...You know what you believe, you say it's empirical, and cite how its empirical.

It does however bother me when people cite the amount of evidence for one thing compared to the amount of evidence for another thing as justification for a belief. The argument goes, "there is more evidence for belief x than belief y, therefore belief x must be true"  --  an ad populum fallacy of sort.

The "weight of evidence" is a better way to put it. Simple number of items of evidence is inadequate, yes - you need to evaluate each item.

If the arguments on one side include one or more very 'strong' ones, and the other side has only equivocal ones at best, it's a 'no-brainer'.

If it is less clear, we may resort to Bayesian analysis, which provides a more rigorous way to combine individual assessment of the strength of each argument or item of evidence.

Saying "therefore belief x must be true" is still not the way one should express the conclusion, even after more careful evaluation - more appropriately "therefore it is likely/very likely/almost certain that A is true, depending on the cumulative weight on each side.