Fudbucker does a nice balanced summary of fine tuning and its opposing multiverse hypothesis.
The "observation" I was referring to is that fact that many people claim to have experienced events that appear to have a supernatural explanation. My statement is a fact as I have crafted it.
It is not scientific proof, and is attacked on the basis that every single one of them has a "natural" explanation, no matter how difficult it may be to explain.
The "natural explanations" go so far as to to say that a person who is not on drugs, not disposed to mental aberrations, is not in an unusual or stressful situation, must have hallucinated. This is the ultimate denial.
As to deduction, I am referring to the fact that mankind is struggling to find a logical (not necessarily scientific) explanation for the origin of the universe and for the existence of intelligent life.
The theists claim that God is the prime cause on the basis of divine (supernatural) revelations, and claim that without God the world could not have survived the naturally hostile environment, and that it would not have had the propensity to form life. Prime cause comes down to "it just is".
The atheists claim that the laws of physics and the quantum field are the prime cause and have always existed and "just are". They suspend their wonder at how some energy field forms matter, then galaxies, then planets capable of forming life, and serendipitously has a "geologically quiet" period to maximize the evolution of human beings to the point we are today.
If I had only a few unremarkable supernatural events I would be rather conflicted as to which hypothesis to chose. However, I have had a number of them, and some are hard to explain without God (created by a Cosmic Intelligence).
The deductions I talk about are also a matter of applying logic to the many claims others have of the supernatural. There is much fraud and mistake. But once those are discounted then one has to look at a hypothesis of what is allowed and what is not allowed. This is not a scientific law or rule. It is figuring out the thought processes of the Cosmic Intelligence using observations of claims.
And to predict the response to my post by most atheists? "Bah - Humbug." Or, "if I do not experience a remarkable event, I refuse to acknowledge the possible existence of the supernatural. I can get by on the fact that 99.9999% or better for physical laws to take precedence is good enough for me."