Bayes Theorem & Joseph Smith's Seer Stone

[Analytics]

From my perspective, the value of Bayes' Theorem is that it provides a coherent and logically valid framework for inductive reasoning. The a priori in the formula is intuitively disturbing, whether you label it a prejudice or anything else. Not liking the concept of an a priori doesn't mitigate the fact that logical coherence demands that it must be there.

Aristotle Smith's comment about extraordinary evidence reminds me of when I worked at McDonald's in 1987 during the Monopoly promotion. I was working the front counter, and a mother with a son of about 10-years came to the counter, and the kid asked if he could have a couple of extra game pieces. He had been dutifully collecting the little cards and thought he was close to getting a monopoly somewhere on his board. I thought his naïvété was cute, so I put a handful of game pieces on his tray. He got so excited!

I then thought of the chances of him winning anything because of my generosity. I had a box under the counter with tens of thousands of little Monopoly scratch cards. From my experience, I knew it contained perhaps a few hundred winning cards for a free small fry or small drink, several dozen free Big Macs, and perhaps five winners of $5 cash. But if I stole that entire box of coupons and took it home, would there be a single big prize in it? In all likelihood, no.

I then thought of where these cards were printed. Billions of little cards were rolling off of printers, being stuffed into tens of thousands of giant boxes of game pieces that were being sent across the country. These mass-produced cards were all losers. Of the tens of thousands of boxes, each containing tens of thousands of little cards, exactly one had the winning "Boardwalk" game piece. How was that single card printed? How was it inserted into a box in this giant warehouse? The logistics of creating and distributing a winning card was mindboggling.

Channeling Carl Sagan, actually having a valid winning lotto ticket or a valid McDonald's "Boardwalk" scratch-off card is extraordinary.

[Philo Sofee]

I appreciate all the comments and ideas guys n gals! I am not offended in any way, and wish no offense in any way as I am interested in learning, not arguing. I am among friends and family here. I am working up a paper on my own journey from belief to disbelief, within the parameters of Bayesian thinking as I see, and will enjoy the discussion it generates. It is also a heads up to Mormon apologists and what they are going to have to accomplish in order to turn around disbelief back into belief, with me. It is not for everyone in general, just my own personal assessment of my own personal journey from apologist to skeptic in the Book of Abraham, which was supposedly my apologetic forté. I am going to explore just how I came to disbelieve my very own evidence! In other words, I am going to bear my untestimony...

[Shulem]

It is not for everyone in general, just my own personal assessment of my own personal journey from apologist to skeptic in the Book of Abraham, which was supposedly my apologetic forté. I am going to explore just how I came to disbelieve my very own evidence! In other words, I am going to bear my untestimony...

But we don't have all the papyrus, some of it is missing and so we can't say what's on the missing papyrus, perhaps the Book of Abraham! And, you gots to keep up with the new scholarly stuff coming out of BYU....

[Analytics]

I appreciate all the comments and ideas guys n gals! I am not offended in any way, and wish no offense in any way as I am interested in learning, not arguing. I am among friends and family here. I am working up a paper on my own journey from belief to disbelief, within the parameters of Bayesian thinking as I see, and will enjoy the discussion it generates. It is also a heads up to Mormon apologists and what they are going to have to accomplish in order to turn around disbelief back into belief, with me. It is not for everyone in general, just my own personal assessment of my own personal journey from apologist to skeptic in the Book of Abraham, which was supposedly my apologetic forté. I am going to explore just how I came to disbelieve my very own evidence! In other words, I am going to bear my untestimony...

For what it's worth, I think you are on the right track using Bayesian thinking in this context. Two of my favorite thinkers, Sean Carroll and Nate Silver, are fans of Bayesian thinking in the way you are applying it. In Carroll's The Big Picture, chapters 9 and 10 are about Bayes Theorem. Here are a couple of quotes I have highlighted (pages 72-83):

Bayes’s Theorem can be thought of as a quantitative version of the method of inference we previously called “abduction.” (Abduction places emphasis on finding the “best explanation,” rather than just fitting the data, but methodologically the ideas are quite similar.) It’s the basis of all science and other forms of empirical reasoning....

Bayes’s Theorem is one of those insights that can change the way we go through life. Each of us comes equipped with a rich variety of beliefs, for or against all sorts of propositions. Bayes teaches us (1) never to assign perfect certainty to any such belief; (2) always to be prepared to update our credences when new evidence comes along; and (3) how exactly such evidence alters the credences we assign. It’s a road map for coming closer and closer to the truth.

Bayesian thinking is one of the main themes of one of my favorite books of all time, Nate Silver's The Signal and the Noise. If you happened to have taken a statistics course in college, in all likelihood the mainstream statistics you were taught is more properly called frequentism. Here are some quotes from Silver about this (pages 251-261):

[R.A.] Fisher is probably more responsible than any other individual for the statistical methods that remain in wide use today. He developed the terminology of the statistical significance test and much of the methodology behind it. He was also no fan of Bayes and Laplace—Fisher was the first person to use the term “Bayesian” in a published article, and he used it in a derogatory way, at another point asserting that the theory “must be wholly rejected.”

Fisher and his contemporaries had no problem with the formula called Bayes’s theorem per se, which is just a simple mathematical identity. Instead, they were worried about how it might be applied. In particular, they took issue with the notion of the Bayesian prior. It all seemed too subjective: we have to stipulate, in advance, how likely we think something is before embarking on an experiment about it? Doesn’t that cut against the notion of objective science?

So Fisher and his contemporaries instead sought to develop a set of statistical methods that they hoped would free us from any possible contamination from bias. This brand of statistics is usually called “frequentism” today, although the term “Fisherian” (as opposed to Bayesian) is sometimes applied to it....

Nor is the frequentist method particularly objective, either in theory or in practice. Instead, it relies on a whole host of assumptions. It usually presumes that the underlying uncertainty in a measurement follows a bell-curve or normal distribution. This is often a good assumption, but not in the case of something like the variation in the stock market. The frequentist approach requires defining a sample population, something that is straightforward in the case of a political poll but which is largely arbitrary in many other practical applications. What “sample population” was the September 11 attack drawn from?

The bigger problem, however, is that the frequentist methods—in striving for immaculate statistical procedures that can’t be contaminated by the researcher’s bias—keep him hermetically sealed off from the real world. These methods discourage the researcher from considering the underlying context or plausibility of his hypothesis, something that the Bayesian method demands in the form of a prior probability. Thus, you will see apparently serious papers published on how toads can predict earthquakes, or how big-box stores like Target beget racial hate groups, which apply frequentist tests to produce “statistically significant” (but manifestly ridiculous) findings...

Right now, for instance, we may be undergoing a paradigm shift in the statistical methods that scientists are using. The critique I have made here about the flaws of Fisher’s statistical approach is neither novel nor radical: prominent scholars in fields ranging from clinical psychology to political science to ecology have made similar arguments for years. But so far there has been little fundamental change.

Recently, however, some well-respected statisticians have begun to argue that frequentist statistics should no longer be taught to undergraduates. And some professions have considered banning Fisher’s hypothesis test from their journals. In fact, if you read what’s been written in the past ten years, it’s hard to find anything that doesn’t advocate a Bayesian approach...

It will take some time for textbooks and traditions to change. But Bayes’s theorem holds that we will converge toward the better approach. Bayes’s theorem predicts that the Bayesians will win.

[Morley]

snip.

snip again.

Wow. Thank you, Analytics. I think you just explained my anti-Bayesian bias. I'll at least step back and take another look.
.

[Physics Guy]

From what the linguist in my family says, it used to take a lot less statistical know-how to get a linguistics paper published than it now does, and in particular Bayesian statistics has become a practical necessity.

I even helped a bit to make a graph for a linguistics paper once, showing Bayesian likelihoods of different model parameters, given the data. At least in that case I thought the graph really showed exactly what you really wanted to know, while at the same time clearly indicating the limits of how much you could really learn from the data. The various factors and confidence intervals that were in the old social sciences statistical toolbox were in comparison clumsy. They sounded kind of relevant to what you wanted to know, but you had to do a lot of squinting and arguing to figure out what exactly they meant. From my point of view the advantage of the Bayesian approach was just that it was flexible. You could ask what you really wanted to ask, and find out as much as the data would tell you about it, by going back to the simple first principles of Bayes's theorem and just applying logic and arithmetic from there. There was no need to flip through tomes of statistical policy to find out whether this or that inference was officially legitimate, or to do your best using the wrong tool for the job because you could only choose from among the handful of authorised tools. And at least in that one case there was nothing subjective about our graph. It showed black-and-white facts, except we showed them in pretty colors, and it was quite informative.

But I'm not so sure that the world is inevitably moving towards Bayesian salvation. I expect there'll come a backlash in the social sciences, because it really is a problem that Bayes often tells you that you have no conclusion, and if you don't have a conclusion then you can't write a paper. I doubt people will really try to say that Bayes is wrong but they'll probably be able to carve out some turf on which things besides Bayes can have some kind of legitimacy. Sometimes the strongest piece of logic is the Politician's Syllogism:

We have to do something.
This is something.
Therefore, we have to do this.

[Analytics]

snip.

Wow. Thank you, Analytics. I think you just explained my anti-Bayesian bias. I'll at least step back and take another look.
.

You're welcome! Nate Silver is an amazing thinker and writer.

[Analytics]

But I'm not so sure that the world is inevitably moving towards Bayesian salvation. I expect there'll come a backlash in the social sciences, because it really is a problem that Bayes often tells you that you have no conclusion, and if you don't have a conclusion then you can't write a paper. I doubt people will really try to say that Bayes is wrong but they'll probably be able to carve out some turf on which things besides Bayes can have some kind of legitimacy. Sometimes the strongest piece of logic is the Politician's Syllogism:

We have to do something.
This is something.
Therefore, we have to do this.

LOL.

It reminds me of the academics who were stranded on an island, trying to figure out how to open the cans of food that washed ashore. After the physicists, chemists, and engineers offered various fangled ideas of how to solve this problem, the Economist shouted out, "I got the solution! Let's assume a can opener!"

[Philo Sofee]

Analytics
Bayesian thinking is one of the main themes of one of my favorite books of all time, Nate Silver's The Signal and the Noise. If you happened to have taken a statistics course in college, in all likelihood the mainstream statistics you were taught is more properly called frequentism. Here are some quotes from Silver about this (pages 251-261):

OK, I got the book! We may have to start a new thread after I get it read. I suspect it won't take long, it really does look excellent and intriguing!

[Analytics]

Analytics
Bayesian thinking is one of the main themes of one of my favorite books of all time, Nate Silver's The Signal and the Noise. If you happened to have taken a statistics course in college, in all likelihood the mainstream statistics you were taught is more properly called frequentism. Here are some quotes from Silver about this (pages 251-261):

OK, I got the book! We may have to start a new thread after I get it read. I suspect it won't take long, it really does look excellent and intriguing!

I'm looking forward to it!