I further assert that one cannot establish that it IS MORE LIKELY that at least one god exists than that no gods exist using logic, reason, math, or science. — Frank Apisa
A person tells you there are blue pigs everywhere in Australia and another tells you that, if you're lucky, you might spot an orange echidna. You spend a year travelling in Australia and see no blue pigs and no orange echidnas. The quote above is equivalent to saying that blue pigs and orange echidnas are still equally likely, i.e. if you did not see a blue pig, there is a 50/50 chance of them being in Australia, and if you did not see an orange echidna there is a 50/50 chance of them being in Australia.
This is neither logical, reasonable, mathematical or scientific. If blue pigs are supposed to be abundant and orange echidnas rare, the probability of encountering a blue pig is much higher than encountering an orange echidna, thus the probability of
not encountering a blue pig much lower than the probability of
not encountering an orange echidna.
Neither actually exist, to my knowledge and experience (I was lucky enough to spot a few normal echidnas), and neither have been disproven by my experience (it's still possible that Australia is teeming with blue pigs and I was just unlucky), however: the claim that Australia is teeming with blue pigs is now less likely than the claim about the rare orange echidna.
This is, in fact, how science works. We calculate the probability of a null hypothesis being true given the experimental data. Probability theory being a logical, reasonable field of logical, reasonable mathematics.
If God A is omnipresent, eternal, and interacts with matter and electromagnetic radiation, it has a much higher probability of being detected scientifically than God B who was very tiny, billions of light years away, lived only for one second, and had the scattering cross-section of a neutrino. That is, the probability of
not detecting God A ever is much lower than the probability of
not detecting God B. Given that neither God A nor God B have been detected ever, God A is a less likely proposition than God B.
And the notion that God A is omnipresent, eternal, interacts with matter and electromagnetic radiation, but is
not detectable unless He so chooses is non-scientific, and can be dismissed by scientists on those grounds.
If God A can be said to be less likely than God B, then it cannot be said that, unless proven or disproven, God cannot be said to be more likely to exist or not exist on scientific grounds (or indeed mathematical grounds), whatever characteristics God might have.
As an extra: any monotheistic God has a vanishingly small probability of existence if undetected, since there are an infinite number of possible monotheistic Gods and, by definition, at most one can exist, making the monotheistic God's probability of existence infinitesimal on mathematical grounds, again, no matter His characteristics beyond His monotheism.