The Interpreter; Bayes Theorem; Nephites and Mayans

[_Gadianton]

That’s really interesting. All of these papers are from real journals, right? It would be interesting if there was an odd duck publication out there that paved the way for that misuse. Sic et non staff do this all the time, wouldn’t quite themselves have made that odd interpretation of godel, or known how to make even that misuse of it, but if someone else who seems credible did then that’s where feeling justified and confident comes in.

[_Lemmie]

Gad gave me an idea so i went back to the Dale's paper to check, and noticed this:

Insights from Basic Statistics

Statistics describes the probability (likelihood) of events occurring within a given population. A population is a set of related items or events of interest for some test we wish to perform.

Immediately followed by:

In this case, the population we wish to test is the factual statements in the Book of Mormon and corresponding factual statements in the book The Maya.

So the 131 + 18 statements, argued to be independent, are drawn from a population of related items.

[_Jersey Girl]

Aside to Physics Guy.

Are you really a physics guy? I need help resolving an issue that involves physics. If you are, may I PM you with the issue? (Any other takers? Please let me know.)

[_Physics Guy]

I'm a physics professor, so yes, I might be able to help with a physics problem. Or maybe not. It's embarrassingly easy to stump even highly trained people with physics questions. I am not qualified to give medical, legal, or financial advice. Feel free to PM me.

[_SteelHead]

Ask me all your medical questions.

I'm not a Dr but I play one on the internet.

[_Res Ipsa]

Lemmie, I understand the significance of independent v. Independent, and I agree that the Dales treated dependent evidence as independent. But I don’t see the Dales’ use of “related” in your first quote as having anything to do with that. Related commonly means members of some group, and populations chosen for statistical study generally are members of some group. I see the usage as being very much like “similar”, which seems to an acceptable substitute.

What am I missing?

[_honorentheos]

I'm sure Kass and Raftery would be thrilled to learn what their work has led to.

That's a thought. There's an outside chance that one of them might be willing to comment. Since the chance can't be less than 2% no matter what, it could be worth a try.

[_Lemmie]

Lemmie, I understand the significance of independent v. Independent, and I agree that the Dales treated dependent evidence as independent. But I don’t see the Dales’ use of “related” in your first quote as having anything to do with that. Related commonly means members of some group, and populations chosen for statistical study generally are members of some group. I see the usage as being very much like “similar”, which seems to an acceptable substitute.

What am I missing?

Their population isn't a space from which they randomly chose "similar" elements for an experiment. If it was, they would have defined them as individual outcomes, randomly chosen as a subset from the full population, and presented their results as a distribution of outcomes of the single experiment, not as independent outcomes to multiply by each other.

The Dales are using each one of these items as an entirely separate experiment. They should have said they have 131+48 subsets of the total population, each of which contains one totally independent event with one and only one outcome. Which no one would ever do in a real study.

[_Lemmie]

That’s really interesting. All of these papers are from real journals, right? It would be interesting if there was an odd duck publication out there that paved the way for that misuse. Sic et non staff do this all the time, wouldn’t quite themselves have made that odd interpretation of godel, or known how to make even that misuse of it, but if someone else who seems credible did then that’s where feeling justified and confident comes in.

Yes, the couple mentioned so far are real: Jeffrey, Kass and Raftery, and a couple of medical ones. But none of them just assign values rather than test, or have sample sizes of ONE, and none advocate mass multiplication. I agree, like the Gödel thing, it must have come from somewhere.

[_Res Ipsa]

Lemmie, I understand the significance of independent v. Independent, and I agree that the Dales treated dependent evidence as independent. But I don’t see the Dales’ use of “related” in your first quote as having anything to do with that. Related commonly means members of some group, and populations chosen for statistical study generally are members of some group. I see the usage as being very much like “similar”, which seems to an acceptable substitute.

What am I missing?

Their population isn't a space from which they randomly chose "similar" elements for an experiment. If it was, they would have defined them as individual outcomes, randomly chosen as a subset from the full population, and presented their results as a distribution of outcomes of the single experiment, not as independent outcomes to multiply by each other.

The Dales are using each one of these items as an entirely separate experiment. They should have said they have 131+48 subsets of the total population, each of which contains one totally independent event with one and only one outcome. Which no one would ever do in a real study.

Addressing your second paragraph, I can understand why no one would ever do it in a study, but isn't that just what is done when folks use Bayesian analysis to evaluate evidence in the real world? For example, in a jury trial, the jury is presented with several pieces of evidence that are not randomly selected from the population of all evidence. They could make their decision by assigning a prior probability to the defendant's guilt, determining a likelihood ratio for each piece of evidence, and then perform an operation that accounts for any dependence of the pieces of evidence, and end up with the probability of the defendant's guilt. Other than the acknowledged subjectivity in determining the prior probability and the numerator and denominator of each LR, is there anything invalid in the methodology?