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Posted on August 10, by Scott Alexander There is an apocryphal story about the visit of the great atheist philosopher Diderot to the Russian court. Diderot was quite the clever debater, and soon this scandalous new atheism thing was the talk of St.
Euler said, in a tone of absolute conviction: What is your response to that? Thus was he publicly humiliated, all the Russian Christians got an excuse to believe what they had wanted to believe anyway, and Diderot left in a huff. I feel like I am a lot better at the sorts of things Diderot was good at — philosophy, history, social science, et cetera — than at math.
Sometimes, I will have a belief that seems pretty well-founded based on the sort of arguments Diderot would have been able to come up with — and someone will spout a bunch of very complicated math at me and tells me it disproves my belief.
Otherwise, short of going back to school for ten years and getting a math Ph. So I think about Diderot a lot because I want to know what to do in this sort of situation.
One of my go-to examples here is health insurance and the idea that it is wrong to ever deny someone coverage for anything, no matter how low the probability it will help and how expensive the intervention. I try to make an argument against that herebut it requires a little math and it would have been very hard to express clearly without it.
This is an obvious trade-off. Permament easily-fixable lack of rigor, versus letting anyone with a BA in Mathematics push you around. The latest people to make a serious academic attempt to prove the existence of God with math, Tim and Lisa McGrew, used Bayesian probabilitya field of math which thanks to the excellent explanations on yudkowsky.
As a result I was able to avoid getting Eulered and write what I think was a pretty devastating rebuttal. But there are other mathematical arguments I find much less tractable. And by far the most dangerous is statistics. With apologies to Rutherford, all science is statistics or stamp-collecting.
I have tried very hard to outperform most of my famously statistically illiterate profession, but there will always be people far better than I. There will always be people making extremely detailed and Byzantine methodological critiques. And those people will always be able to present me with arguments that are either ultra-important debunkings of things I believed religiously, or else shameless attempts to Euler me.
And I will always have trouble figuring out which ones are which. His basic argument was that proving causation was very very hard which it is and that none of the appropriate statistical work had been displayed in cancer research.
He uses a device to magnify the difference and its importance in the case-control studies by transforming the percentages into observed versus expected figures using a chi-square analysis.
He then suggested that, if the cases had inhaled, 45 lives could have been saved. But you know, on a good day I remember my chi-square analyses, I get the difference between case control and cohort studies right, and then I can read an R.
On the other hand, Glymour seems to be well respected and intelligent, and he says things like: Factor models assume that observed variables that do not influence one another are independent conditional on all of their common causes, an assumption that is a special case of what Terry Speed has called the Markov condition for directed graphical models.
The rank constraints — of which vanishing tetrads are a special case — used in factor analysis are implied by conditional independencies in factor models, conditional independencies guaranteed by the topological structure of the graph of the model, no matter what values the linear coefficients or factor loadings may have.
To exclude more latent variables when fewer will do, Spearman needed only to assume that the vanishing tetrads do not depend on the constraints on the numerical values of the linear coefficients of factor loadings, but are implied by the underlying causal structure.
It is known that the set of values of linear parameters coefficients and variances that generate probability distributions unfaithful to a directed graph is measure zero in the natural measure on parameter space.
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So I have to ask — am I being informed of deep methodological truths that are being neglected? Or am I being Eulered? The way I try to deal with it in practice is seeing if I can route around the objection.
My reaction to the Glymour paper was to try to figure out what it was trying to prove with all its statistics. I will come out and say it: You are adjusting for an imperfect measurement of the confounders you can think of. My particular argument was:Count is a San Francisco based producer who has been involved in just about every aspect of the music business.
He has worked for indie and major labels, scored films, and has worked as producer, engineer, mixer, and remixer for artists such as DJ Shadow, Frank Sinatra, Radiohead, John Cale [Velvet.
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