Path: ...!Xl.tags.giganews.com!local-4.nntp.ord.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 02 Sep 2024 17:09:18 +0000
Subject: Re: Bayes in your Luggage
Newsgroups: sci.math
References: <uv7b5v$dtk9$2@solani.org>
 <aihf1j51mbm2t7rhhin61hl57rhh25l1nt@4ax.com> <uv9i5r$etdh$1@solani.org>
 <cf19c394-082c-4861-8bd7-17ee34286781@att.net>
 <4aWcnaCNrYb3dd37nZ2dnZfqn_GdnZ2d@giganews.com>
From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Mon, 2 Sep 2024 10:09:21 -0700
User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:38.0) Gecko/20100101
 Thunderbird/38.6.0
MIME-Version: 1.0
In-Reply-To: <4aWcnaCNrYb3dd37nZ2dnZfqn_GdnZ2d@giganews.com>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 7bit
Message-ID: <53Sdnd43Y8ajbEj7nZ2dnZfqn_UAAAAA@giganews.com>
Lines: 79
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-dHsVa69ijLSvu6tao6nSMLG80HqqLOiwH5G3lv+OFXmHm84WwenLKY8W4icyYYylqz6xKsb1hc1ez+q!OqHGud2LNRrE8YBDxSwq/SnY3IgaNkHrsqdM5ReUdu5/stA0JP2o/dcA37ETC2UE4584gZ85Tfat!YA==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
Bytes: 4690

On 05/12/2024 09:03 AM, Ross Finlayson wrote:
> On 04/11/2024 03:12 PM, Jim Burns wrote:
>> On 4/11/2024 4:45 PM, Mild Shock wrote:
>>> John wrote:
>>
>>>> But if pushed, I'd go for both.
>>>
>>> What about a non-reflexive preference relation
>>> between the two. Which one would you read first?
>>>
>>> I also undecided in this matter. :-(
>>
>> Don't mimic Buridan's ass, and
>> starve to death instead of choosing.
>>
>> Could it ever be more appropriate to flip a coin
>> than to choose between books on Bayes' theorem?
>>
>>
>
> Bayes' rule for conditional probabilities is so de rigeur
> that most people haven't even heard of anything else.
>
> Bayes-ically there's also Jeffries, and Knight, into what
> is called uncertainty, and Bayesian, Jeffries, and Knightian
> un-certainty. This gets into things like "the long tail"
> and "outliers" and "the error record" and "anomalies" with
> regards to "the Central Limit Theorem" and some "Uniformization
> Limit Theorem" about "classical law(s) of probabilities" from
> "law(s) of large numbers" from counting arguments and combinatorial
> argument from counting arguments for classical, discrete probabilities,
> which of course all have an implicit coordinate in "time".
>
> So, flipping a coin as a source of random samples from {0,1}
> is also called Bernoulli trials.
>
> Now, you might wonder that sampling a real number from [0,1],
> the interval, has that the real nubmers are equi-distributed all
> through that as sequences of 0's and 1's in binary, so that,
> sampling a real number from the uniform distribution, involves
> infinitely-many Bernoulli trials, to get one sample, while at
> the same time, each 0 or 1, both starts a new sample, and,
> refines all previous examples.
>
> Well, one would usually just figure to partition [0,1] into
> a given number of equal-sized partitions, a power-of-two many, say,
> then just flip a coin enough times to make one sample then bucket
> it there, as far as it's been "quantized" this way, the discrete
> distribution, uniform, of the continuous distribution, uniform.
>
> Well that gets into that there are multiple law(s) of large numbers,
> and multiple kinds of "Cantor space", which here is the space of
> all the sequences of 0's and 1's and not necessarily so defined
> as by the "Cantor function", which is associated with "Standard
> Cantor Space" or "Sparse Cantor Space" in contrast to these other
> notions of Cantor space that go along with these other law(s) of
> large numbers, "Square Cantor Space", which is countable because
> of line-continuity and "Signal Cantor Space" which is having a
> greater cardinal up into signal-continuity.
>
>
> That is, it's simple that the "law(s) of large numbers" are
> related to these "definitions of continuity" the line-reals,
> the standard field-reals of course, and signal-reals, they
> each make for a law of large numbers, they each make for a
> space of all possible values, and they each make for those
> by their own definitions of completeness, making a repleteness
> together, remaining consistent in their cardinals with not
> being connected their Cartesian functions, this way making
> a great super-standard model of mathematical continua.
>
>
> Bayes and his baggage, ....
>
>

Bayes and his bummage, ....