Analytical proof first requires a definition so we know what we are looking for. The most accepted basic definition of God is "the originator and ruler of the universe (Websters). Focusing on only a tiny piece of the universe (the first living cell), we can analytically prove no need for a Creator God if some natural mechanism could be shown to be able to bring "first life" into existence. On the other hand, an "originator" would have to exist if I can prove that the only other alternative, random chance (aka naturalistic evolution) was impossible.
So, to disprove or prove God analytically, I wanted to use hard science if at all possible (yes I've studied this stuff for many years). And no, I'm not just talking about a bunch of dead bones, such as the lack of transitional fossil species.
Statistical proof is simply proof by statistic or probability. Looking at the laws of physics, we know that gravity exists and I doubt that even you would be able to refute or be willing to challenge this. Many other laws of physics have also been proven, based on tests that indicate the probability of a law is so high (regarding cause and effect) that any other explanation is deemed virtually impossible.
Do we know for absolute certainty that these laws are true? No! But as a result of massive experimentation, we know that the odds of denying the laws of physics are absurdly small. None are proven to 100 percent certainty. Yet all key laws of physics are proven to a degree of certainty exceeding 1 chance of non-occurrence in 10^50 That means that there is less than 1 chance in 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 of any of them not being right. In other words, the odds of gravity not existing are absurdly small. Gravity is essentially a fact.
It seamed to me that a God of the universe would provide some statistical "proof" that He exists, if He in fact existed. I could test the probability of His existence by testing for something that only God could so, I could test for His ability to foretell the future with perfect precision and accuracy.
Legal proof is the third commonly accepted type of proof, and that is proof beyond a reasonable doubt. Courts have defined this standard, judgment by peers based on evidence, the best that is available. Hence there is often uncertainty with legal proof because an event can't be repeated. Legal evidence includes eyewitness testimony, hostile-witness testimony, corroborative reports and circumstantial evidence.
I think it is fairly apparent that if analytical and statistical proof didn't support the existence of God, then legal proof won't carry must weight. On the other hand, if they do prove that God exists, then we are faced with another issue, who God is. This is where the legal evidence comes in.
This will be the starting point for my next series of posts. I'll do my best to keep them short, but make no promises. Evidence, I believe needs to be explored fully to the best of my ability. If you are a truth seeker and not just a rabid anti-theist you will read along at your own pace.