Re: ATTN: George Duncan

Posted by George Duncan-2 on May 25, 2020; 12:14am
URL: http://friam.383.s1.nabble.com/ATTN-George-Duncan-tp7596345p7596358.html

Hey, Nick, glad to see you continuing to address these basic statistical questions. I'll respond from a Bayesian perspective, which I think is mostly compatible with Pierce's writings though I haven't read much at all of his. 

First, most all Bayesians and indeed perhaps a majority of statisticians would consider the posed question, "Is it true that the coin I hold in my hand is a fair coin?", can have no physical meaning as no such coin has "real-world" existence, certainly no one could construct such a coin.

Second, to me and other Bayesians (and perhaps Pierce) a more meaningful question goes something like this: 

I entertain that the coin I hold has a certain probability p of being flipped heads. Prior to ever flipping the coin I have a probability distribution over possible values of p. This is based on everything I know about the coin (who gave it to me, what it looks like, my past experience in flipping other coins, etc.) This probability distribution may well be personal to me. A common way of characterizing such distributions on p is through one of the family of beta distribution, a family chosen because it is plausible for cases where the coin looks ordinary and there is nothing strange in how I came by the coin. The nice thing mathematically is that after flipping the coin, say seven times and getting 2 heads and 5 tails, the posterior distribution, which now reflects your uncertainty given this experience, is again a beta distribution with just different parameters. Beautiful! If I have time tomorrow I'll show you how this works.

Third, there are hints of frequency theory (so non-Bayesian) perspective in what you write, most likely reflective of those statistics courses you took way back when--60 years ago!. As I said, the Bayesian perspective is I believe more compatible with Pierce. Long ago statisticians like Pearson and R.A. Fisher were not Bayesians. Statisticians today are much more likely to be Bayesians. The reason for this is mainly twofold, (1) the wide range of applications in areas like engineering, economics and medicine that are amenable to Bayesian analysis, and (2) the enormous increase in computational power that makes implementation of Bayesian analysis possible (few problems are as easy as the coin toss, and what if the prior distibution is not in beta form?).

On Sun, May 24, 2020 at 12:56 PM <[hidden email]> wrote:

All, particularly, George—

 

In an earlier larding, I argued that Peirce’s idea of truth is essentially a statistical one.   So:

 

Is it true that the coin I hold in my hand is a fair coin? 

 

Let the coin be flipped once, and it comes out heads, what do you think?  No way of telling, right? OK.  Flip it again.  Heads again.  Two heads in a row.  P=0.25.  Sure, I guess so.  It could be fair.  Flip it again. Hmmm. Three heads in a row………Five heads in a row. P= 03125.  You know?  I think that coin is probably not fair.  “Fair” in this formulation means the infinite distribution of H and T coinflips is .5.  “Probably not” means, the chances that this coin’s flips are drawn from a .5 distribution is less than 0.0312 and my threshold of dis belief is 0.05.  Thus, when I  say that the coin is not fair, that inference is in part a statement about me, and the truth of the matter, the limit of the distribution of flips, is prospective.  But the notion that there can be some truths of some matters is absolutely essential to science.  Why else would we flip the coin? 

 

Now George:  why am I bothering you about this.  Three questions:

1. Is this valid statistical logic?  I ask because all psychologists are only amateur statisticians, and many of us bugger up the logic. In particular, we are known to confuse type I and type II error.
2. Is this Peirce’s logic?  If not, what is Peirce’s logic; and
3. Is Peirce’s logic the ORIGIN of the logic of statistical inference that I was taught 60 years ago in graduate school**.  If so, which among the famous statisticians, Pearson, Spearman, Fischer, etc., read Peirce? 

 

[signed]

 

TLOLTT*

 

* The Little Old Lady Tasting Tea

** RIP, Rheem Jarrett

 

Nicholas Thompson

Emeritus Professor of Ethology and Psychology

Clark University

[hidden email]

https://wordpress.clarku.edu/nthompson/

 

 

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