Let's try one in cosmology. The universe contains at least 3 and perhaps 4 very different kinds of matter, whose origins probably are physically completely different. There is the Cosmic Background Radiation (CBR) which is photons from the later parts of the Big Bang but is actually the residue of all the kinds of radiation that were in the Bang, like flavored hadrons and mesons which have annihilated and become photons. You can count them and they tell you pretty well how many quanta of radiation there were in the beginning; and observation tells us that they were pretty uniformly distributed, in fact very, and still are.

Next is radiant matter — protons, mostly, and electrons. There are only a billionth as many of them as quanta of CBR, but as radiation in the Big Bang there were pretty much the same number, so all but one out of a billion combined with an antiparticle and annihilated. Nonetheless they are much heavier than the quanta of CBR, so they have, all told, much more mass, and have some cosmological effect on slowing down the Hubble expansion. There was an imbalance — but what caused that? That imbalance was generated by some totally independent process, possibly during the very turbulent inflationary era.

In fact out to a tenth of the Hubble radius, which is as far as we can see, the protons are very non-uniformly distributed, in a fractal hierarchical clustering with things called "Great Walls" and giant near-voids. The conventional idea is that this is all caused by gravitational instability acting on tiny primeval fluctuations, and it barely could be, but in order to justify that you have to have another kind of matter.

So you need — and actually see, but indirectly — Dark Matter, which is 30 times as massive, overall, as protons but you can't see anything but its gravitational effects. No one has much clue as to what it is but it seems to have to be assumed it is hadronic, otherwise why would it be anything as close as a factor 30 to the protons? But really, there is no reason at all to suppose its origin was related to the other two, you know only that if it's massive quanta of any kind it is nowhere near as many as the CBR, and so most of them annihilated in the early stages. Again, we have no excuse for assuming that the imbalance in the Dark Matter was uniformly distributed primevally, even if the protons were, because we don't know what it is.

Finally, of course there is Dark Energy, that is if there is. On that we can't even guess if it is quanta at all, but again we note that if it is it probably doesn't add up in numbers to the CBR. The very strange coincidence is that when we add this in there isn't any total gravitation at all, and the universe as a whole is flat, as it would be, incidentally, if all of the heavy parts were distributed everywhere according to some random, fractal distribution like that of the matter we can see — because on the largest scale, a fractal's density extrapolates to zero. That suggestion, implying that Dark Energy might not exist, is considered very dangerously radical.

The posterior probability of any particular God is pretty small

Here's another, which compared to many other peoples' propositions isn't so radical. Isn't God very improbable? You can't in any logical system I can understand disprove the existence of God, or prove it for that matter. But I think that in the probability calculus I use He is very improbable.

There are a number of ways of making a formal probability theory which incorporate Ockham's razor, the principle that one must not multiply hypotheses unnecessarily. Two are called Bayesian probability theory, and Minimum Entropy. If you have been taking data on something, and the data are reasonably close to a straight line, these methods give us a definable procedure by which you can estimate the probability that the straight line is correct, not the polynomial which has as many parameters as there are points, or some intermediate complex curve. Ockham's razor is expressed mathematically as the fact that there is a factor in the probability derived for a given hypothesis that decreases exponentially in the number N of parameters that describe your hypothesis — it is the inverse of the volume of parameter space. People who are trying to prove the existence of ESP abominate Bayesianism and this factor because it strongly favors the "Null hypothesis" and beats them every time.

Well, now, imagine how big the parameter space is for God. He could have a long gray beard or not, be benevolent or malicious in a lot of different ways and over a wide range of values, he can have a variety of views on abortion, contraception, like or abominate human images, like or abominate music, and the range of dietary prejudices He has been credited with is as long as your arm. There is the heaven-hell dimension, the one vs three question, and I haven't even mentioned polytheism. I think there are certainly as many parameters as sects, or more. If there is even a sliver of prior probability for the null hypothesis, the posterior probability of any particular God is pretty small.