What in Christian faith lies behind subject of science?

First of all, Ethics is not precisely a science at all. But even if you put that aside, the Christian claim is that a study of ethics without a proper anchor in the absolute truth of God's word will lead to incorrect and flawed ethical judgments.

Sociology is, per Wikipedia, the study of human social behavior and it's origins. Since it is limited to human behavior, it would not cover relationships with the supernatural. Additionally, in studying the origin of human behavior, one would be prompted to look further and further back, tracing the line of causality as far as you can. Christians would argue that, as the root cause of the Universe and Humanity, learning about the nature of God could greatly inform sociologists.

Psychology is, again per Wikipedia, the study of mental functions and behaviors. This is not about "personal experiences", except perhaps in regards to the mind's influence and interpretation of our senses involved in creating those experiences. But even it if were, the Christian claim is that the word of God has much to inform us about proper behavior and nature of man.

Ultimately, Science has a very specific domain. It is the study of our natural physical universe. Science will always be at a disadvantage when studying the super-natural, because the scientific method begins first and foremost with observation, and the supernatural goes beyond what our physical bodies and instruments are able to observe. I hope this is a little clearer or deeper and explanation to you than a simple "don't apply science to my faith." Science, by definition, draws a boundary for itself where it will not go. This is not something Christians have done, but something that Science/Scientists have chosen for themselves. They can look for super-natural effects, but they will not find them.

God is not in competition with any truth-bound field of study. The Christian God is truth. The Christian God is the act of being itself. So, the absolute simplest answer I think we could posit is this: A Christian religion (and most any religion) is a set of devotions, practices, and studies that harmonize us, familiarize us, and bring us into relationship with being itself.

God and religion are therefore not in competition with any branch of science, art, literature, history, trivia, physical fitness, etc.. God and religion are not in competition with any human institution or endeavor that is submissive to or aimed at truth. All truth inherently participates in being, and all things that are participants in being are inherently participants in truth. More down to earth, everything that exists is necessarily described by truth, and truth necessarily describes things that exist. Hence, proper religion -- particularly proper Christianity -- does not impede or conflict with truth-bound endeavors.

Rather, religion magnifies these endeavors. It motivates us to have truthful endeavors to begin with. And it impels us to keep our endeavors submissive to truth. We abandon things like astrology, largely because they tend not to correlate with truth. And we pursue things like science (honest science, in particular) because they tend to correlate with truth. And perhaps most importantly, because our religion prioritizes truth (God) ahead of our science, art, literature, physical fitness, history, and so forth, we tend to avoid treating these lesser things as truths themselves or ends, rather than means.

We pursue God through Christianity because God is truth. We pursue everything else because it sheds light on God. And our pursuit of God keeps everything else in check.

Now, that's not to say people don't go bad, abandon the truth, lie about their data, start dabbling in impressionism or non-rhyming poetry, etc.. (Obviously the last two are just my opinions, not dogma.) In fact, Judaism and Christianity both point out quite explicitly in the first few pages of our scriptures that people go bad. And, religious leaders aren't free from error either. Our scripture points highlights that too. In fact, our religious denominations disagree about things too -- and truthiness would suggest, in some cases, that one be right and the other wrong on some points of disagreement.

But in general, our goal is service to the truth. And barring extensive human corruption, Christianity is neither a competitor to any field you've highlighted. Rather, it transcends all of them. None of them exist without truth. They're all different (but lesser) means of approaching the tentacles truth (God's creation, and therefore God).

Also worth checking out, Fr. Robert Barron (Catholic Priest) talks about "Science v. Religion" a lot, mostly in response to atheistic "science-worship" he comes across.

• Scientism and God's Existence: A Commentary by Fr. Barron
• Fr. Barron comments on Religion & Science
• Father Barron Against The YouTube Heresies

By the word science I understand it as a discipline of studying the physical world, or possible metaphysical world (like the mind) expressed in observable physics. Then by these objective observations, experiments, which must be repeatable, draw logical deductions and inferences. These in turn lead to more study, testing, conclusions until a body of knowledge and beliefs are developed which explain large portions of observed phenomena in the material world.

In what sense does Christian faith fall under this discipline? I would say in a few ways and sense.

First, in analyzing the scriptures and determining which translation is the most accurate of the original is according to a scientific discipline. This naturally brings our faith in some sense under science because the scriptures determine what our faith is.

Secondly, though to a much lesser extent the study of history, where texts outside of scripture are evaluated for trustworthiness by scientific comparison to other know facts of history, influences what many Christians believe. This historical science provides context for how many scriptures might be properly interpreted.

Third, in the same way that philosophy can follow rules about what is logical, what is a fallacy, etc. Christian theology based on its premises can is some sense become more disciplined and rigorous to ensure the thought patters or not illogical and that biblical texts and assumed beliefs are not developed under dishonest forms of reasoning. From this standpoint religious beliefs can spout from observed phenomena, such as for every good design, there is high probability that there is an architect or designer.

However, with all these aspects where Christian faith is influenced or in some sense brought under science, it is probably truer to say that it is brought under science only from the standpoint that it respects reason in whatever valid shape one might find it.

When turning to the scripture itself, science is considered, as a lower form of knowledge and biblical faith is a higher and more certain form of knowledge. In other words the knowledge that we can obtain from observing what is not seen, is greater than what we can achieve from what is seen:

Now faith is the assurance of things hoped for, the conviction of things not seen. (Hebrews 11:1)

The scripture treats knowledge that comes from God through the Bible as a light. It means this in a literal sense, whereby the knowledge we might obtain by light, or the sight which we can obtain, is not possible but by faith. Therefore to simply things, the Bible describes a scientist without faith as more or less a man who is literally blind to higher forms of knowledge. He can see the physical world but not the spiritual. No matter how hard he tries to ‘see’ he can’t because he has no ‘light’.

Naturally the result is that such a blind mind concludes the gospel is just foolishness because he can’t see it:

The natural person does not accept the things of the Spirit of God, for they are folly to him, and he is not able to understand them because they are spiritually discerned. (1 Corinthians 2:14)

The Greek root of the word ‘discerned’ means to investigate, or appraise. In this sense those without faith are not able to judge, evaluate, or discern the meaning of what is certain and true about God because it seems foolish from beginning to end, having no light which alone comes from faith in the gospel.

Conclusion: There are aspects where Christian faith is under science, these occur where physical and logical elements overlap or influence Christian thinking. Christian faith by nature puts itself above reason and science, and what can be seen with the eye altogether, for it fixes itself upon God, who is above all things whatsoever.