Tag: Bayesian analysis

Measuring Belief and Quackery

Mark Davis1 Comment

While reviewing reporting on the RNC this afternoon, I found myself curious about the protocols at news organizations with respect to their editorial boards. For instance, does the Washington Post editorial board require that claimed facts within all opinion pieces are not clearly disputed? Does the New York Times? I suspect yes, which is what we see in the lawsuit filed by Sarah Palin against the New York Times concerning the suggestion that Palin’s campaign was relevant to the shooting of Gabby Giffords. There was at least a debate that rose to the level of the Opinion Editor, if not the board.

I was investigating this because I am curious how WaPo handles Trumpy columnists like Mark Thiessen and Hugh Hewitt, who are mostly cheerleaders without baggage for the current president, with only occasional whataboutisms and other distracting suggestions about Biden’s candidacy. They don’t defend lies and cons. They just cheer. Meanwhile, the board itself came down hard on the repeated falsehoods of Pamela Bondi and the ongoing slaughter of truth in the service of the Trump 2020 campaign.

The mainstream press represents Trump and cronies as conmen and women, manipulative, self-serving, corrupt, cruel, ignorant, ineffectual, morally questionable, and out-and-out liars. And the press uses facts to do so. Yet Trump maintains a remarkable following despite this evidence, with many quizzical onlookers at a loss as to the psychology of Trump’s followers.

In this modern example, there are many, many resources that can be used to fact check and form opinions. Yet people choose to rely on only a few and discount others as being biased.

I was recently reading some fairly detailed Bayesian analysis by philosophers concerning Hume’s argument against miracles.… Read the rest

Bayesianism and Properly Basic Belief

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Kircher-Diagram_of_the_names_of_GodXu and Tenebaum, in Word Learning as Bayesian Inference (Psychological Review, 2007), develop a very simple Bayesian model of how children (and even adults) build semantic associations based on accumulated evidence. In short, they find contrastive elimination approaches as well as connectionist methods unable to explain the patterns that are observed. Specifically, the most salient problem with these other methods is that they lack the rapid transition that is seen when three exemplars are presented for a class of objects associated with a word versus one exemplar. Adults and kids (the former even more so) just get word meanings faster than those other models can easily show. Moreover, a space of contending hypotheses that are weighted according to their Bayesian statistics, provides an escape from the all-or-nothing of hypothesis elimination and some of the “soft” commitment properties that connectionist models provide.

The mathematical trick for the rapid transition is rather interesting. They formulate a “size principle” that weights the likelihood of a given hypothesis (this object is most similar to a “feb,” for instance, rather than the many other object sets that are available) according to a scaling that is exponential in the number of exposures. Hence the rapid transition:

Hypotheses with smaller extensions assign greater probability than do larger hypotheses to the same data, and they assign exponentially greater probability as the number of consistent examples increases.

It should be noted that they don’t claim that the psychological or brain machinery implements exactly this algorithm. As is usual in these matters, it is instead likely that whatever machinery is involved, it simply has at least these properties. It may very well be that connectionist architectures can do the same but that existing approaches to connectionism simply don’t do it quite the right way.… Read the rest

The Rise and Triumph of the Bayesian Toolshed

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Bayes LawIn Asimov’s Foundation, psychohistory is the mathematical treatment of history, sociology, and psychology to predict the future of human populations. Asimov was inspired by Gibbon’s Decline and Fall of the Roman Empire that postulated that Roman society was weakened by Christianity’s focus on the afterlife and lacked the pagan attachment to Rome as an ideal that needed defending. Psychohistory detects seeds of ideas and social movements that are predictive of the end of the galactic empire, creating foundations to preserve human knowledge against a coming Dark Age.

Applying statistics and mathematical analysis to human choices is a core feature of economics, but Richard Carrier’s massive tome, On the Historicity of Jesus: Why We Might Have Reason for Doubt, may be one of the first comprehensive applications to historical analysis (following his other related work). Amusingly, Carrier’s thesis dovetails with Gibbon’s own suggestion, though there is a certain irony to a civilization dying because of a fictional being.

Carrier’s methods use Bayesian analysis to approach a complex historical problem that has a remarkably impoverished collection of source material. First century A.D. (C.E. if you like; I agree with Carrier that any baggage about the convention is irrelevant) sources are simply non-existent or sufficiently contradictory that the background knowledge of paradoxography (tall tales), rampant messianism, and general political happenings at the time lead to a likelihood that Jesus was made up. Carrier constructs the argument around equivalence classes of prior events that then reduce or strengthen the evidential materials (a posteriori). And he does this without ablating the richness of the background information. Indeed, his presentation and analysis of works like Inanna’s Descent into the Underworld and its relationship to the Ascension of Isaiah are both didactic and beautiful in capturing the way ancient minds seem to have worked.… Read the rest