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# Essay talk:Bayesian Inference and the Power of Skepticism

Can't wait for more of this - it's all new to me but it's fascinating so far Keep me in the DARK 14:31, 9 August 2007 (CDT)

## How to present the introduction

I've been asked to comment on this; probability is (with probability 0.845392) the area of math that I am weakest on. I don't really speak the language. I finally (sort of) understood what was going on when I realized the following principle: Probability theory can only go from fundamental (usually unseen) reality to observations that we make. I guess what I call "fundamental reality" what you call "hypothesis", or "h", and what I call "observation" you call "data", or "d". The similarity of "observation" and "data" is trivial, but the I think the notion of "fundamental reality" is, well, fundamental. Neither the observation that someone is drunk nor the observation that they had 10 beers is fundamental reality.

Here's what I mean. We can't see the fundamental reality; we just know that it controls the observations. The math that we study is about manipulating various combinations of reality, and seeing how it affects the observations, but you can never really go the other way. Example: If we know (fundamental reality; don't ask how we know it) that a coin has a 1/2 probability of coming up heads, and we know that a die has a 1/6 probability of coming up "3", we can work out, on solid mathematical grounds, what the probabilities are, of such things as getting 7 consecutive heads, or tails+3 when we flip the coin and roll the die, etc. And we can work out all the Pascal's triangle stuff about binomial distributions etc. etc. when we flip the coin or roll the die many times. But, in most cases, we don't really know the probability. In the case of the coin or the die, we can use physical symmetry to argue that we really do know the probability, and hence use that to illustrate the things we want to illustrate, but in the real world, we don't know the probability, say, that drug X will cure disease Y. And, if we don't know the shape of the die (it's just someone behind a curtain calling out numbers), figuring out its probability is a tricky, but important, task.

The thing we want to do, of course, is to go the other way, observation to underlying reality, but we can't. All we can do is calculate "If the probability that drug X cures disease Y is P or less, what is the probability of the outcome we observed in our clinical trial?" And we find a value of P such that, based on sound mathematics, the probability of observing what we observed is very low. When it is low enough, we use our human intuition to say that "It follows that the probability that X cures Y must be 70% plus or minus whatever."

Anyway, I hope my insights can be helpful, though you clearly know a lot about the subject. SJIHAS 15:18, 19 August 2007 (CDT)

I think you have described the standard statistical model fairly clearly. The idea that we calculate the likelihood of our data given our hypothesis (sorry I only speak probability language in the science dialect) and if its sufficiently high while the "null" hypothesis is sufficiently low we can make some sort of intuitive claim about the our hypothesis. Or in the popperian sense we have failed to falsify our alternative hypothesis.
But Bayesian inference attempts to link the likelihood probability directly with the probability of our hypothesis with out having to make a link to "intuition" or "significance" cut offs. Bayes equation is:
With P(Ai | A) being our posterior or our probability of our hypothesis given our data (our goal) and P(Ai) being a prior probability and then P(A | Ai) being the likelihood.
So the likelihood probability is what you just described and its where frequentist stop the proccess. And you are right that we can't really move much further with just the likelihood probability, but if we have a prior we can mathematically relate that likelihood probability to a posterior probability or our "gold standard" of an actual probability for our hypothesis.
Makes sense right? tmtoulouse provoke 15:37, 19 August 2007 (CDT)

## Very difficult (for liberal arts types, maybe)

 “”This is often a very difficult subject for statistical novices to grasp intuitively.

Not really. It is difficult for people who are not good in math. Everybody that was in my probability class "got" this the day it was explained. They were mostly physics, computer science, and math majors though. Quick Comment 15:06, 27 August 2007 (CDT)

*shrug* it depends how its presented, but I couldn't keep track of the number of undergrads I have had in lab classes that can't figure this stuff out, but thats psychology and biology. Also I am attempting to write this for an audience with very little statistics at all, not sure how that working out. tmtoulouse provoke 15:10, 27 August 2007 (CDT)
Simply describe it as "initially counterintuitive". Most intuitively fail to predict the Monty Hall Problem (and the Birthday paradox) until these are specifically taught. Quick Comment 15:13, 27 August 2007 (CDT)
Works for me. tmtoulouse provoke 15:22, 27 August 2007 (CDT)

## Ugh

 “”Essentially this axiom stats that the probability for X and the probability for not X must sum to 1. If this axiom is obeyed the hypothesis that predicts everything is prima facie in violation and is not considered a valid hypothesis.

If P(X)=1, and P(~X)=0, P(X)+P(~X)=1. In any event, the wording here is awkward (and the idea you're trying to convey may be incorrect--but I can't say I understand the idea you're trying to convey). I would use "premise" "condition is met" and show how P(X)+P(~X) /= 1 in your example. Quick Comment 15:25, 27 August 2007 (CDT)

I agree i muddled several ideas into one here, I will think about how to make it clearer. tmtoulouse provoke 15:59, 27 August 2007 (CDT)

## Karl Popper's bright line

You should be careful here; Popper considered the theory of evolution as non-scientific under falsifiability criteria (though he said many of the underlying theories were scientific). In any event, my understanding is the anti-Darwinians quoted Popper first, and argued that ToE alternatives are equally non-scientific (specifically, metaphysical). Popper of course was used against them in some trial. And other philosophers of science disagree with Popper and his bright line (to the advantage of ToE proponents). Quick Comment 15:50, 27 August 2007 (CDT)

Well, Popper of course later retracted that statement completely, and one can accept Popper's ideas about demarcation without needing Popper to say where individual theories fall under the demarcation. tmtoulouse provoke 16:01, 27 August 2007 (CDT)
Also I am not really putting forth Popper as the sole authority on demarcation, only bringing in how his ideas fit into Bayesian inference and side on the skeptic and scientist perspective. There are other themes in the philosophy of science I have worked in here too. tmtoulouse provoke 16:06, 27 August 2007 (CDT)
I would like to see where "Popper...later retracted that statement completely". In my recollection of a reading of the retraction, he hedged. Maybe there was another retraction that was "complete." Quick Comment 16:16, 27 August 2007 (CDT)
Skeptical Inquire addressed this a few years back tmtoulouse provoke 16:27, 27 August 2007 (CDT)
The (without quote marks in your link) "quite a bit more to the theory than he had understood from a cursory examination of the subject" is a more accurate portrayal of what Karl Popper wrote, if my memory is correct. In 1980 he wrote "their hypotheses can in many cases be tested"--Popper, Karl (1980), "Letter to the Editor", New Scientist 87, page 611--as cited by Numbers, Ronald L. (1992), Creationists: The Evolution of Scientific Creationism page 247. Ronald Numbers does not seem to take the stance of "complete" retraction, and the creationists do not either (with some merit, it seems). I'll have to get the Dialectica 32:344-346 to see if evolutionists are quote mining again. Primary sources are better in my opinion. Quick Comment 17:09, 27 August 2007 (CDT)

### Context

Here it is in as much context as need I believe:

I do not see how any of that can remotely support the creationist position. And again I stand by the point that regardless of what Popper says the tautological nature of natural selection or the scientific status thereof is not defined by his approval or disapproval. tmtoulouse provoke 17:37, 27 August 2007 (CDT)

That evolutionism is metaphysics? Quick Comment 11:12, 28 August 2007 (CDT)
Uh, no it's not. tmtoulouse provoke 13:16, 28 August 2007 (CDT)
My comment was an explanation of how ID/creationists might use what Popper wrote against the scientific status of theory of evolution (ism). When you say "it's not," I assume you mean that evolutionism is not metaphysics, and not that Popper did not classify it as such. Quick Comment 13:40, 28 August 2007 (CDT)
I don't think Popper says that no. tmtoulouse provoke 00:48, 29 August 2007 (CDT)

## Another recommendation.

Assume some prior knowledge on the part of your readers, and/or point them to other peviously written articles for primers on probability. Then delete the tutorial, and focus on the point of your paper. Quick Comment 15:52, 27 August 2007 (CDT)

I will think about it, but want to finish the essay first. tmtoulouse provoke 16:02, 27 August 2007 (CDT)
Yeah, I was guessing it might help you finish to essay faster. But then again, if it helps organize your thoughts, it's probably worthwhile. Quick Comment 16:17, 27 August 2007 (CDT)