Tag Archives: Bayes Theorem

The Questions We Permit Ourselves to Ask

In historical research, we evaluate the plausibility of hypotheses that aim to explain the occurrence of a specific event. The explanations we develop for this purpose have to be considered in light of the historical evidence that is available to us. Data functions as evidence that supports or contradicts a hypothesis in two different ways, corresponding to two different questions that need to be answered with regard to a hypothesis:

1. How well does the event fit into the explanation given for its occurrence?

2. How plausible are the basic parameters presupposed by the hypothesis?

. . . . .

[A]lthough this basic structure of historical arguments is so immensely important and its disregard inevitably leads to wrong, or at least insufficiently reasoned, conclusions, it is not a sufficient condition for valid inferences. Historical data does not come with tags attached to it, informing us about (a) how – or whether at all – it relates to one of the two categories we have mentioned and (b) how much plausibility it contributes to the overall picture. The historian will never be replaced by the mathematician.23

23 This becomes painfully clear when one considers that one of the few adaptations of Bayes’s theorem in biblical studies, namely Richard Carrier, On the Historicity of Jesus: Why We Might Have Reason for Doubt (Sheffield: Sheffield Phoenix, 2014), aims to demonstrate that Jesus was not a historical figure.

Heilig, Christoph. 2015. Hidden Criticism?: The Methodology and Plausibility of the Search for a Counter-Imperial Subtext in Paul. Tübingen: Mohr Siebeck. pp. 26f

Bayes’ theorem explained by Lily Serna

Last night I chanced to turn on the TV half way through a program trying to show viewers how interesting maths was. Yeh, okay. But I watched a little as they demonstrated how they do searches at sea for missing persons. Then it suddenly got interesting. Bayes’ theorem was introduced as their way of handling new information that came to them as they conducted their search. And the presenter, a maths wiz (I have seen her magical maths brain at work on another show), Lily Serner, explained it all without the maths. Move the red button forward to the 44:54 mark:

Or a more truncated version is also on youtube

Another simple introduction on The Conversation:

Bayes’ Theorem: the maths tool we probably use every day, but what is it?

Even a Bayesian Historian Can Slip Up! (once)

I argue that the interpretation of Bayesianism that I present here is the best explanation of the actual practices of historians.

— Tucker, Aviezer. 2009. Our Knowledge of the Past: A Philosophy of Historiography. Reissue edition. Cambridge University Press. p. 134

Aviezer Tucker

I have posted aspects of Aviezer Tucker’s discussion of how Bayesian reasoning best represents the way historians conduct their research but here I want to post a few details in Tucker’s chapter that I have not covered so far.

(Interjection: it is not strictly fair to call Aviezer Tucker a “Bayesian historian” because, as is clear from the opening quote, what he argues is that all historians, at least at their best and overall, employ Bayesian logic without perhaps realizing it.)

Tucker includes discussion of biblical criticism in his book but in his chapter on Bayesian methods he unfortunately contradicts himself. The contradiction can best be explained, I think, by appealing to the power of the Christian story to implant unquestioned assumptions into even the best of scholars. I could call that my hypothesis and suggest that the prior probability for it being so in many historians is quite high.

No doubt readers will recall my recent quotation from Tucker:

There have been attempts to use the full Bayesian formula to evaluate hypotheses about the past, for example, whether miracles happened or not (Earman, 2000, pp. 53–9). Despite Earman’s correct criticism of Hume (1988), both ask the same full Bayesian question:

“What is the probability that a certain miracle happened, given the testimonies to that effect and our scientific background knowledge?”

But this is not the kind of question biblical critics and historians ask. They ask,

“What is the best explanation of this set of documents that tells of a miracle of a certain kind?”

The center of research is the explanation of the evidence, not whether or not a literal interpretation of the evidence corresponds with what took place.

(Tucker, p. 99)

One explanation for the documents relating the miracles is that the miracles happened and were recorded. Other explanations can also come to mind.

No doubt because the question focused on miracles it was very easy for Tucker and countless others before and since to think of alternative hypotheses to explain the stories of miracles that have survived for our reading entertainment today.

The Slip Up

But look what happened to Tucker’s argument when he was faced with something that sounded more “historically plausible”: read more »

Analysis of the McGrath and Carrier debate on a Bayesian approach to history

The latest contest started when James McGrath made a mockery of his understanding of Carrier’s mehod: Jesus Mythicism: Two Truths and a Lie

I have run the to and fro posts through a Linguistic Inquiry and Word Count (LIWC) analysis. Here are the interesting results:

VARIABLE MCGRATH 1
Two Truths
(449 words)
CARRIER
Wrong Again
(2485 words)
MCGRATH 2
Mythicist Math
(680 words)
Analytic thinking:
(the degree to which people use words that suggest formal, logical, and hierarchical thinking patterns)
82.22% 32.85% 55.17%
Authenticity:
(when people reveal themselves in an authentic or honest way)
49.57% 34.39% 39.55%
Clout:
(the relative social status, confidence, or leadership that people display through their writing)
38.59% 47.75% 48.82%
Tone:
(the higher the number, the more positive the tone)
92.86% 16.55% 13.75%
Anger: 0.22% 0.56% 0.88%

.

Tone

Unfortunately when one reads McGrath’s Two Truths post one soon sees that his very positive tone (over 92% positive) is in fact an indication of overconfidence with the straw-man take-down.

But but but….. Please, Richard, please, please, please! Don’t fall into McGrath’s trap. Sure he sets up a straw man and says all sorts of fallacious things but he also surely loves it when he riles you. It puts him on the moral high ground (at least with respect to appearances, and in the real world, despite all our wishes it were otherwise, appearances do seriously count).

But see how McGrath then followed with a lower tone — and that’s how it so easily can go in any debate on mythicism with a scholar who has more than an academic interest in the question.

Anger

Ditto for anger.

This variable was measured by the following words:

MCGRATH1 CARRIER MCGRATH2
lying destroyed
argued
argument
liar
arguments
argues
lied
lies
damned
insults
criticized
argument

Clearly a more thorough and serious analysis would need to sort words like “argument” between their hostile and academic uses.

Analytic thinking style

James McGrath began the discussion in a style that conveyed a serious analytical analysis of Carrier’s argument. Of course anyone who has read Carrier’s works knows McGrath’s target was a straw man and not the actual argument Carrier makes at all. (Interestingly when Carrier pointed out that it appeared McGrath had not read his actual arguments McGrath at best made inferences that he had read Carrier’s books but fell short of saying that he had actually read them or any of the pages where Carrier in fact argued the very opposite of what McGrath believed he had.) Nonetheless, McGrath’s opening gambit conveyed a positive approach for anyone unfamiliar with Carrier’s arguments.

But look what happened to McGrath’s analytical style after meeting Carrier’s less analytical style: he followed Carrier’s lead.

Carrier has chosen to write in natural language style which is fine for informal conversation but the first impression of an outsider unfamiliar with Carrier’s arguments would probably be that McGrath was the more serious analyst of the question. (I understand why Carrier writes this way but an overly casual style, I suspect, would appeal more to the friendly converted (who are happy to listen rather than actively share the reasoning process) than an outsider being introduced to the ideas.

In actual fact, Carrier uses far more words that do indeed point to analytic thinking than does McGrath. Carrier uses cognitive process words significantly more frequently than does McGrath (24% to 16%/19%). But his sentences are far less complex and shorter.

Other

There are many other little datasets that a full LIWC analysis reveals. One is a comparative use of the personal singular pronoun. A frequent use of “I” can indicate a self-awareness as one speaks and this can sometimes be a measure of some lack of confidence. Certainly the avoidance of “I” is often a measure of the opposite, of strong confidence and serious engagement in the task at hand. Carrier’s use of I is significantly less than McGrath’s.

Another progression one sees is the use of “he”. As the debate progressed it became increasingly focused on what “he” said: e.g. McGrath1: 0.45%; Carrier 1.65%; McGrath2 2.06%.

McGrath sometimes complains about the length of Carrier’s posts. But more words are linked to cognitive complexity and honesty.

—o—

Of course I could not resist comparing my own side-line contribution:

VARIABLE NEIL
Reply
(1077 words)
Analytic thinking:
(the degree to which people use words that suggest formal, logical, and hierarchical thinking patterns)
86.42%
Authenticity:
(when people reveal themselves in an authentic or honest way)
44.36%
Clout:
(the relative social status, confidence, or leadership that people display through their writing)
56.27%
Tone:
(the higher the number, the more positive the tone)
32.13%
Anger:
(measured by my use of “criticism”, “argument” and “critical”)
0.93%

.


Pennebaker, James W. 2013. The Secret Life of Pronouns: What Our Words Say About Us. Reprint edition. New York: Bloomsbury Press.


How Historical Research Works (and does not work) — even with Bayes’

A Roman Catholic historian who thinks he’s a Bayesian walks into the secret Vatican archives. There he discovers a document that might have significance for rewriting the origins of Christianity. I have reproduced a facsimile:

The historian is stunned. His faith has taught him that James was only a cousin or half-brother. If he was wrong about that, he wonders, how can he even be sure Jesus existed at all?

Reeling in doubts, the historian is nonetheless conscientious and no fool. He knows he has to test this document for its authenticity. So he snips off a corner of it and sends it to the laboratory to determine the age and provenance of the material. As an extra check he sends a high definition copy to a paleographer.

The results come back. The material is dated between 40 AD and 60 AD and the paleographic analysis confirms that the style to what was typical of the year 50 AD.

Next, he asks if the letter is genuinely by Paul. His colleagues tell him it sounds just like the Paul they know so that is confirmed.

Since this is evidently an autograph questions of the contents of the letter being altered during the process of copying do not arise.

But how reliable are its contents as historical evidence? Our historian asks if we can verify that this particular James really was known to be the literal brother of Jesus.

He consults the latest scholarship on the book of Acts and discovers that it is now established “beyond doubt” that the first chapters, 1-15, were written in the year 45 AD and that the original text said that James was not only the head of the church but was also the junior brother of Jesus, one year younger to be precise. The contents of Paul’s letter are confirmed!

But our historian is more thorough still. Did anyone else in the early church know anything of this letter and its contents? He pores through Tertullian’s writings and sees that Tertullian quotes the passage about meeting James to refute Marcion’s heresy that Jesus was not really a flesh and blood human being born of a woman on earth.

That clinched it! The letter and its contents sure seemed to be genuine and known to be genuine by the venerable Fathers.

But our historian is a Bayesian. At least he thinks he is. He read half of a blurb on the back cover of a book that had Bayes written on its front cover and is confident that he got the hang of it from that.

If he was wrong about Jesus having brothers how can he be sure Jesus even existed? The historian pauses to think of all the unbelievable stories about Jesus. Could such a person really have existed in the first place? So he puts on what he thinks is his Bayesian cap that looks very much like one of those conical dunce caps and sets to work.

He weighed the evidence. He took all the stories that were mythical and set them against the evidence for the reality of Jesus and here’s what he found:

The weight of numbers proved it. Jesus did not exist after all. He was entirely mythical. The claims of the letter were all bogus. read more »

Clarification needed for my reply to McGrath’s criticism of the use of Bayesian reasoning

McGrath does not tell his readers in the post we are addressing what he has in mind as the “clear-cut” evidence for the historicity of Jesus but from previous posts and comments I am convinced that it is the “brother of the Lord” passage in Galatians 1:19 that he has in mind. If I am wrong then someone will no doubt inform me.

I ought to have made that point clearer in my original post.

If someone can direct me to where McGrath recently made the point about that Galatians passage (was it in response to the reddit discussion about Vridar?) I would much appreciate it.

 

 

Reply to James McGrath’s Criticism of Bayes’s Theorem in the Jesus Mythicism Debate

Aviezer Tucker

James McGrath in a recent post, Jesus Mythicism: Two Truths and a Lie, made the following criticism of the use of Bayes’s theorem in the Jesus Mythicism debate:

. . . . as I was reminded of the problematic case that Richard Carrier has made for incorporating mathematical probability (and more specifically a Bayesian approach) into historical methods. . . .

If one followed Carrier’s logic, each bit of evidence of untruth would diminish the evidence for truth, and each bit of evidence that is compatible with the non-historicity of Jesus diminishes the case for his historicity.

The logic of this argument is based on a misunderstanding of the nature of historical inquiry and how a historian is expected to apply Bayesian logic. (It also misconstrues Carrier’s argument but that is another question. I want only to focus on a correct understanding of how a historian validly applies Bayesian reasoning.)

In support of my assertion that James McGrath’s criticism is misinformed I turn to a historian and philosopher of history, Aviezer Tucker (see also here and here), author of Our Knowledge of the Past: A Philosophy of Historiography. He treats Bayesian reasoning by historical researchers in depth in chapter three. I quote a section from that chapter (with my own formatting):

There have been attempts to use the full Bayesian formula to evaluate hypotheses about the past, for example, whether miracles happened or not (Earman, 2000, pp. 53–9).

We may compare McGrath’s criticism. He is of the impression that the Bayesian formula is used to evaluate the hypothesis that Jesus did exist. This is a common misunderstanding. If you are confused, continue to read.

Despite Earman’s correct criticism of Hume (1988), both ask the same full Bayesian question:

“What is the probability that a certain miracle happened, given the testimonies to that effect and our scientific background knowledge?”

We may compare McGrath’s criticism again. He is of the impression that the historian using Bayesian logic is asking what is the probability that Jesus existed, given the testimonies to that effect and our background knowledge. If you are still confused then you share McGrath’s misunderstanding of the nature of historical inquiry. So continue with Tucker:

But this is not the kind of question biblical critics and historians ask. They ask,

“What is the best explanation of this set of documents that tells of a miracle of a certain kind?”

The center of research is the explanation of the evidence, not whether or not a literal interpretation of the evidence corresponds with what took place.

(Tucker, p. 99)

In other words, biblical critics and historians ask (Tucker is assuming the biblical critic and historian is using Bayesian logic validly and with a correct understand of the true nature of historical research) what is the best explanation for a document that, say, purports to be by Paul saying he met the James, “the brother of the Lord”.

I use that particular example because — and someone correct me if I am mistaken — Jame McGrath and others believe that passage (Galatians 1:19) makes any questioning of the historicity of Jesus an act of “denialism”. (McGrath does not tell his readers in the post we are addressing what he has in mind as the “clear-cut” evidence for the historicity of Jesus but from previous posts and comments I am convinced that it is the “brother of the Lord” passage in Galatians 1:19 that he has in mind. If I am wrong then someone will no doubt inform me.)

No one, I am sure, would mean to infer that the late and highly respected Philip R. Davies was guilty of denialism when he suggested that the historical methods he applied to the Old Testament should also be applied to the New — a method I have sought to apply to the study of Christian origins ever since I read Davies’ groundbreaking book.

Back to the question. It is the question of what is the best explanation for the passage in our version of Galatians that I have attempted to address several times now.

That is the question that the historian needs to ask. Every decent book I have read for students about to undertake advanced historical studies has stressed, among many other duties, the necessity for the researcher to question the provenance, the authenticity, of the documents he or she is using, and to know all the questions related to such questions from a thorough investigation of the entire field. My several posts have attempted to introduce such questions that should be basic to any historical study.

Tucker, from my reading of his book, would not consider such an exercise to be “denialism”, but sound and fundamental historical method — and even sound biblical criticism. read more »

How Bayes’ Theorem Proves the Resurrection (Gullotta on Carrier once more)

Yet I cannot help but compare Carrier’s approach to the work of Richard Swinburne, who likewise uses Bayes’ theorem to demonstrate the high probability of Jesus’ resurrection, and wonder if it is not fatally telling that Bayes’ theorem can be used to both prove the reality of Jesus’ physical resurrection and prove that he had no existence as a historical person.49

49 Richard Swinburne, The Resurrection of God Incarnate (Oxford: Oxford University Press, 2003).

The above quotation is from page 16 of Daniel Gullotta’s 37 page review of Richard Carrier’s On the Historicity of Jesus [OHJ].

To make such a comparison one would expect the author to be familiar with how the Bayes’ rule is used by both Carrier and Swinburne. Unfortunately Gullotta nowhere indicates that he consulted the prequel to OHJ, Proving History, in which Carrier explained Bayes on a “for dummies” level and which was referenced repeatedly in OHJ. Gullotta moreover indicated that he found all of the Bayesian references in OHJ way over his head — even though the numbers used were nothing more than statements of probability of evidence leaning one way or the other, such as when we say there is a 50-50 chance of rain or we are 90% sure we know who’s been pinching our coffee at work. Robert M. Price has expressed similar mathemaphobia so Gullotta is not alone.

Anyway, we have a right to expect that the reviewer is familiar with the way Bayes is used in at least one of the works he is comparing, and since he skipped the Bayesian discussion in OHJ he is presumably aware of how Swinburne used Bayes to effectively prove the resurrection of Jesus.

Bayes’ theorem is about bringing to bear all background knowledge and evidence for a particular hypothesis, assessing it against alternative hypotheses, and updating one’s assessments in the light of new information as it comes along.

If that sounds no different from the common sense way we ought to approach any problem, that’s because it is no different from common sense methods. That’s why Bayes “cracked the enigma code, hunted down Russian submarines and emerged triumphant [even in historical studies!] from two centuries of controversy“.

Anyway, scholars who ought to know better have indicated that they can safely dismiss Bayes because Richard Swinburne used it to prove the resurrection of Jesus. Never mind that that’s like saying we should never use syllogisms in argument because some joker used one to prove everything with two legs was a man.

Richard Swinburne

So let’s see exactly how Swinburne used a tool that some of the smartest people in the world use for all sorts of good things in order to prove Jesus is alive today and about to come and judge us all.

Bayes works with facts. Hard data. Real evidence. Stuff.

For Swinburne, anything in the Bible is a definite fact that requires us to believe it if there is nothing else in the Bible to contradict it. That’s the “hard data” that Swinburne feeds into his Bayesian equation!

Notice some of Swinburne’s gems found in The Resurrection of God Incarnate (with my own bolding as usual):

Most of St Paul’s epistles are totally reliable historical sources. The synoptic gospels are basically historical works, though they do sometimes seek to make theological points (especially in the Infancy narratives) by adding details to the historical account. St John’s Gospel is also basically reliable, at any rate on the later events of the story of Jesus . . . . (p 69)

I argued earlier that, in the absence of counter-evidence, apparent testimony should be taken as real testimony and so apparent historical claims as real historical claims. (p. 70)

It seems fairly clear that the main body of the Acts of the Apostles is intended to be taken as literal history. It reads like any other contemporary work of history, and the later parts (which contain no reports of anything miraculous) are so detailed and matter-of-fact as to have a diary-like quality to them. (p. 71)

Hence there is no justification for thinking that Mark is trying to do anything else than record history when he writes about these events . . . (p. 73)

I conclude that the three synoptic Gospels purport to be history (history of cosmic significance, but I repeat, history all the same). (p. 74)

Just as apparent testimony must be read as real testimony, so real testimony must be believed, in the absence of counter-evidence.  (p. 76) read more »

What’s the Difference Between Frequentism and Bayesianism? (Part 2)

Witch of Endor by Nikolay Ge
Witch of Endor by Nikolay Ge

In the previous post we began to discuss the fundamental difference between the Bayesian and frequentist approaches to probability. A Bayesian defines probability as a subjective belief about the world, often expressed as a wagering proposition. “How much am I willing to bet that the next card will give me a flush?”

To a frequentist, however, probability exists in the physical world. It doesn’t change, and it isn’t subjective. Probability is the hard reality that over the long haul, if you flip a fair coin it will land heads up half the time and tails up the other half. We call them “frequentists,” because they maintain they can prove that the unchanging parameter is fixed and objectively true by measuring the frequency of repeated runs of the same event over and over.

Fairies and witches

But does objective probability really exist? After reading several books focused on subjective probability published in the past few decades, I couldn’t help noticing that Bruno de Finetti‘s Theory of Probability stands as a kind of watershed. In the preface he says that objective probability, the very foundation of frequentism, is a superstition. If he’s correct, that means it isn’t just bad science; it’s anti-science. He writes: read more »

What’s the Difference Between Frequentism and Bayesianism? (Part 1)

English: Picturing 50 realisations of a 95%-co...
English: Picturing 50 realisations of a 95%-confidence interval (Photo credit: Wikipedia)

As my thesis partner and I gathered up the evidence we had collected, it began to dawn on us — as well as on our thesis advisers — that we didn’t have enough for ordinary, “normal” statistics. Our chief adviser, an Air Force colonel, and his captain assistant were on the faculty at the Air Force Institute of Technology (AFIT), where my partner and I were both seeking a master’s degree in logistics management.

We had traveled to the Warner Robins Air Logistics Center in Georgia to talk with a group of supply-chain managers and to administer a survey. We were trying to find out if they adapted their behavior based on what the Air Force expected of them. Our problem, we later came to understand, was a paucity of data. Not a problem, said our advisers. We could instead use non-parametric statistics; we just had to take care in how we framed our conclusions and to state clearly our level of confidence in the results.

Shopping for Stats

In the end, I think our thesis held up pretty well. Most of the conclusions we reached rang true and matched both common sense and the emerging consensus in logistics management based on Goldratt’s Theory of Constraints. But the work we did to prove our claims mathematically, with page after page of computer output, sometimes felt like voodoo. To be sure, we were careful not to put too much faith in them, not to “put too much weight on the saw,” but in some ways it seemed as though we were shopping for equations that proved our point.

I bring up this story from the previous century only to let you know that I am in no way a mathematician or a statistician. However, I still use statistics in my work. Oddly enough, when I left AFIT I simultaneously left the military (because of the “draw-down” of the early ’90s) and never worked in the logistics field again. I spent the next 24 years working in information technology. Still, my statistical background from AFIT has come in handy in things like data correlation, troubleshooting, reporting, data mining, etc.

We spent little, if any, time at AFIT learning about Bayes’ Theorem (BT). I think looking back on it, we might have done better in our thesis, chucking our esoteric non-parametric voodoo and replacing it with Bayesian statistics. I first had exposure to BT back around the turn of the century when I was spending a great deal of time both managing a mail server and maintaining an email interface program written in the most hideous dialect of C the world has ever produced. read more »

Bayes, Schizophrenia, Autism and Brain Chemistry

A fascinating essay, even if speculative, by Scott Alexander on the brain chemistry behind Bayesian, deductive and inductive reasoning, and light it possibly sheds on conditions like schizophrenia, autism, and being stoned.

It’s Bayes All The Way Up

What Does “Probably” Mean to Historians and Forecasters?

We often hear it said that historians deal with probabilities, not certainties. Thus Bart Ehrman explains in his latest book:

Historians, of course, can ask what probably happened in the past, for example, in the earthly ministry of Jesus with his disciples. And historians can establish with relative levels of probability that this, that, or the other tradition is likely something that happened or didn’t happen. But history is all a matter of such greater or lesser probabilities. When dealing with a figure such as Jesus, these probabilities are established only by critically examining the memories that were recorded by later authors.

Ehrman, Bart D. (2016-03-01). Jesus Before the Gospels: How the Earliest Christians Remembered, Changed, and Invented Their Stories of the Savior (p. 31). HarperCollins. Kindle Edition. [My bolded emphasis in all quotations.]

Interestingly Ehrman assumes as a certainty (not probability) that the gospel narratives were sourced from “memories” of Jesus (whether personally experienced or fabricated memories) and sidesteps an entire area of biblical scholarship that argues the evangelists themselves imaginatively created the narratives of Jesus inspired by analogous tales in the Jewish Scriptures and other writings. He also uses the language — e.g. “that were recorded by” — we associate with historical “reports” or “records” thus further entrenching his bias in the mind of the reader. But we’ll leave Ehrman’s own contradictions aside for now and focus on the more general principle.

Anyone who has read scholarly works relating to Christian origins is familiar with the language of probability, possibility, maybe, likelihood, etc. Too often, however, this same language magically transforms itself as the argument proceeds into certainty. As Jacob Neusner in Rabbinic Literature and the New Testament complained of “pseudocritical” scholarship, it is commonly characterized a number of faults including

the use of “presumably,” “must” or “may have been,” and “perhaps,” a few sentences later magically converted into “was” and “certainly.” (p. 88)

A serious possibility

tetlsLet’s start with the reverse of history: forecasting the future. The past is past and gone but reverse our perspective for a moment and problems with vague and loose language become immediately obvious. The following cases are taken from Superforecasting: The Art and Science of Prediction by Philip E. Tetlock and Dan Gardner. In early 1951 the CIA published a National Intelligence Estimate warning that a Soviet Union attack on Yugoslavia “should be considered a serious possibility.” What does that phrase mean to you?

But a few days later, Kent was chatting with a senior State Department official who casually asked, “By the way, what did you people mean by the expression ‘serious possibility’? What kind of odds did you have in mind?” Kent said he was pessimistic. He felt the odds were about 65 to 35 in favor of an attack. The official was startled. He and his colleagues had taken “serious possibility” to mean much lower odds. Disturbed, Kent went back to his team. They had all agreed to use “serious possibility” in the NIE so Kent asked each person, in turn, what he thought it meant. One analyst said it meant odds of about 80 to 20, or four times more likely than not that there would be an invasion. Another thought it meant odds of 20 to 80— exactly the opposite. Other answers were scattered between those extremes.

Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 858-864). Random House. Kindle Edition.

A fair chance

When in 1961 President Kennedy sought to know the chance a small army of Cuban expatriates landing at the Bay of Pigs would have in toppling Fidel Castro his Chiefs of Staff concluded that the plan had a “fair chance” of success.

The man who wrote the words “fair chance” later said he had in mind odds of 3 to 1 against success. But Kennedy was never told precisely what “fair chance” meant and, not unreasonably, he took it to be a much more positive assessment.

Tetlock, Philip; Gardner, Dan (2015-09-24). Superforecasting: The Art and Science of Prediction (Kindle Locations 872-873). Random House. Kindle Edition.

Sherman Kent of the CIA’s Office of National Estimates sought a remedy by setting out more precise meanings: read more »

A Historian Reviews Carrier: “The Bayesian perspective on historiography is commonsensical”

dr_tucker
Aviezer Tucker

Thanks to a reader who has alerted me to an article by a philosopher of history, Aviezer Tucker, on Richard Carrier’s Proving History in the prestigious peer-reviewed journal History and Theory. I have since seen an rss feed alerting me to Carrier’s own comments on the review. I look forward to reading it but meantime I’d like to remind readers of a post I did a few years ago on the author:

Real Historians Do Bayes!

I also see that Tucker’s review has been made open access. (The journal’s policy is to make a work open access if the author or their supporting institution pays a fee of $3000. So do appreciate the access you have to this article. It’s free to you but the publisher is not giving it away free.)

The Reverend Bayes vs Jesus Christ.

See also Carrier’s comments. No doubt I’ll write something once I have had a chance to read it, too.

 

More Thoughts on Minimal Historicity: When Bigger Isn’t Better

U-2 over California
U-2 over California

Many years ago, I had what I still consider the best job in the world. A second lieutenant in my twenties, I found myself in charge of operational maintenance on the swing shift for the entire “black side” of the flightline at Beale Air Force Base. Back then, the tankers were on the north side of the flightline, while the U-2s (including their TR-1 cousins) and SR-71s sat on the south side.

Of course, the real work depended on experienced NCOs. As the old joke goes, the job of an OIC (Officer in Charge) is to listen to the NCOIC, then nod and say, “Oh, I See.” But I did serve at least one crucial function. Only an officer could sign off on a “Red X” and clear a plane to fly.

One night we were driving around in the little blue pickup truck assigned to the maintenance officer on duty, when we stopped at one of the U-2 shelters. The senior NCO and I were checking on the status of some repair; I forget exactly what it was now. At any rate, we got to talking and one of the guys asked the crew chief about a car he’d been looking at. The young buck sergeant told us that he did almost buy one vehicle. It looked nice, he said, and the payments seemed reasonable. But then he noticed something fishy.

“When I added up all the payments,” he said, “it was more than the price of the car!”

I felt compelled to explain. “If . . . I mean . . . Suppose . . . Hmm.” And then I realized there wasn’t enough time to explain how interest works, and it wasn’t clear it would do much good anyway. I gave a wide-eyed look at the senior NCO, offered some excuse about needing to get over to the SR-71s, and we quickly departed.

I had a similar feeling of helplessness reading Dr. Matthew Baldwin’sA Short Note on Carrier’s ‘Minimal Historicism.'” One’s first inclination is to want to help someone who’s thrashing about wildly, but where to start? Baldwin writes in his post, “This game is more than somewhat suspect: it is rigged from the start.” And he followed up with the same sentiments in his comment on Neil’s recent post, where he wrote: read more »