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Baez' series on network theory and information geometry answer a couple of your questions in a very accessible way.
Here Baez and Fong prove a version of Noether's theorem for Markov processes.
http://math.ucr.edu/home/baez/networks/networks_11.html
Earlier Baez talked about conservation of total probability.
http://johncarlosbaez.wordpress.com/2011/09/09/network-theory-part-8/
Here he relates the distribution of existing species to a prior and how Bayes' rule says how the number of each species changes over time.
http://johncarlosbaez.wordpress.com/2011/05/26/information-geometry-part-8/
AI Ballistics Lab? You're trying to direct the explosion that's already underway.
Lukeprog: how has this transition affected your relationship with your parents, siblings, and extended family? Have any readers had similar transitions later in life, with spouse and children?
I think the reason I don't use statistics more often is the difficulty of getting good data sets; and even when there is good data, there are often ethical problems with following it. For example: Bob lives in America, and is seeking to maximize his happiness. Americans who report high levels of spiritual conviction are twice as likely to report being "very happy" than the least religious. Should he become a devout Christian? There's evidence that the happiness comes from holding the majority opinion; should he then strive to believe whatever the polls say is the most common belief in his area?
Another example: Bob has three kids; he knows his wife is cheating on him, but he also knows the effect size of divorce on child outcomes (depression, grades, income, stability of future relationships, etc.) is larger than smoking on lung cancer, aspirin on heart attacks, or cyclosporine on organ transplants. When do the bad effects of staying in the marriage outweigh the bad effects of splitting up?
I grew up as a Mormon; they have a very different view of God than most Christians.
God is an "exalted man", essentially a human that passed through a singularity. Also, regarding spirits: "There is no such thing as immaterial matter. All spirit is matter, but it is more fine or pure, and can only be discerned by purer eyes. We cannot see it; but when our bodies are purified we shall see that it is all matter." Spirits are "children" of God, literally progeny in some sense. Spirits are attached to human bodies, live life as mortal beings, and then separate, retaining the memories of that time; the promise of the resurrection is a permanent fusing of spirit matter to undying bodies made of normal matter, and exaltation, reserved for those who prove worthy, is the ability to create spirit beings. It is the spirit that is conscious. "Eternity" just means "far longer than you have the ability to properly conceive of". "Sin" means "addictive substances or behaviors".
This sort of story is pretty decent sci-fi for early 1800s.
Mormons fully expect spirit matter to show up in the correct theory of physics, whether it's dark matter or supersymmetric particles, or whatever.
As a missionary, I encouraged people to pray and ask God if the Book of Mormon was true; many who did so had an experience that was so unusual that they took us very seriously after that. Those that didn't couldn't be held accountable for not believing us, since that kind of experience was up to God to provide.
I now think there are simpler explanations for most of what I once believed. It took me a long time to come to the conclusion that I was wrong because of the "no conflict between science and religion" tenet, and I was raised as a Mormon in a very loving, functional family, and had particularly clever parents who were very good apologists, and I'm not a very good rationalist yet.
The "critical thinking" paper has changed location; it's now at http://www.aft.org/pdfs/americaneducator/summer2007/Crit_Thinking.pdf
I think most people would say that there's a high probability Bill is an accountant and a low probability that he plays jazz. If Bill is an accountant that does not play jazz, then E is "half right" whereas C is completely wrong. They may be judging the statements on "how true they are" rather than "how probable they are", which seems an easy mistake to make.