Re: Bayes in your Luggage

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, ....