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Sep 18, 2021, 8:51:55 PM9/18/21

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I've been reading "Ten great ideas about chance", by Persi Diaconis.

It includes a chapter which utilizes the idea of deriving

probability from statistics, rather than the usual, other

way round. Apparently, invented by Bruno de Finitti, whom

the author idolizes.

Anyhow, he discusses how means can imply probabilities.

And repeatedly refers to "the structure of probability", as explanation.

He never defines this phrase. I have no idea what it means.

Can anyone here elaborate?

--

Rich

It includes a chapter which utilizes the idea of deriving

probability from statistics, rather than the usual, other

way round. Apparently, invented by Bruno de Finitti, whom

the author idolizes.

Anyhow, he discusses how means can imply probabilities.

And repeatedly refers to "the structure of probability", as explanation.

He never defines this phrase. I have no idea what it means.

Can anyone here elaborate?

--

Rich

Sep 18, 2021, 9:58:40 PM9/18/21

to

axioms of probability. It might be that de Finitti works with ideas

about how probabilities or uncertainties (personal probabilities)

derived from data should behave (consistency as new data are added,

etc.) and can then derive the usual axioms of probability on that

basis, for his idea of what a personal probability should behave like.

Sep 19, 2021, 1:37:06 PM9/19/21

to

up at calculus?

--

Rich Ulrich

Sep 20, 2021, 8:15:35 PM9/20/21

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RichD <r_dela...@yahoo.com> wrote:

> I've been reading "Ten great ideas about chance", by Persi Diaconis.

>

> It includes a chapter which utilizes the idea of deriving

> probability from statistics, rather than the usual, other

> way round. Apparently, invented by Bruno de Finitti, whom

> the author idolizes.

>

> Anyhow, he discusses how means can imply probabilities.

Whittle, P. (2005). Probability via Expectation, 4th ed. Springer.
> I've been reading "Ten great ideas about chance", by Persi Diaconis.

>

> It includes a chapter which utilizes the idea of deriving

> probability from statistics, rather than the usual, other

> way round. Apparently, invented by Bruno de Finitti, whom

> the author idolizes.

>

> Anyhow, he discusses how means can imply probabilities.

"We assume a sample space W, setting a level of description of the

realization of the system under study. In addition, we postulate that

to each numerical-valued observable X(w) can be attached a number E(X),

the expected value or expectation of X. The description of the variation

of w over W implied by the specification of these expectations will

be termed a probability process"

> And repeatedly refers to "the structure of probability", as explanation.

part of mathematics within the modern theory of measure and integral",

with "a real-valued random variable [being] a measurable function from

the basic set to the real numbers" [as above].

I enjoyed Charlie Geyer's reworking of Nelson 1987:

https://conservancy.umn.edu/bitstream/handle/11299/199667/Technical%20Report%20657%20Radically%20Elementary%20Probability%20and%20Statistics.pdf?sequence=1

Sep 21, 2021, 8:28:06 PM9/21/21

to

On September 20, David Duffy wrote:

>> I've been reading "Ten great ideas about chance", by Persi Diaconis.

>> It includes a chapter which utilizes the idea of deriving

>> probability from statistics, rather than the usual, other

>> way round. Apparently, invented by Bruno de Finitti, whom

>> the author idolizes.

>> Anyhow, he discusses how means can imply probabilities.

>

> Whittle, P. (2005). Probability via Expectation, 4th ed.

>> I've been reading "Ten great ideas about chance", by Persi Diaconis.

>> It includes a chapter which utilizes the idea of deriving

>> probability from statistics, rather than the usual, other

>> way round. Apparently, invented by Bruno de Finitti, whom

>> the author idolizes.

>> Anyhow, he discusses how means can imply probabilities.

>

> Whittle, P. (2005). Probability via Expectation, 4th ed.

> "We assume a sample space W, setting a level of description of the

> realization of the system under study. In addition, we postulate that

> to each numerical-valued observable X(w) can be attached a number E(X),

> the expected value or expectation of X. The description of the variation

> of w over W implied by the specification of these expectations will

> be termed a probability process"

That sounds about right.
> realization of the system under study. In addition, we postulate that

> to each numerical-valued observable X(w) can be attached a number E(X),

> the expected value or expectation of X. The description of the variation

> of w over W implied by the specification of these expectations will

> be termed a probability process"

"the variation of w over W" must be a probability density.

The text presents it as, if you wager $1, with an expectation +.06,

you're a 53% favorite. Which doesn't bowl me over with profundity.

>> And repeatedly refers to "the structure of probability", as explanation.

>

> Pretty sure we are talking about Kolmogorov's "probability theory as

> part of mathematics within the modern theory of measure and integral",

> with "a real-valued random variable [being] a measurable function from

> the basic set to the real numbers" [as above].

a classic, this is it"

--

Rich

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