We learned about Bayes (expectations and priors) after
classical probability, then also about Jeffreys, in
courses in statistics and probability. The usual notions
of the probability density and cumulative distribution functions,
and moment generating functions, as identifying distributions,
were presented with the results as about the uniqueness of a
pdf and a CDF and an MGF for a given distribution. This is much
then about the Central Limit Theorem, and then for results in
the standardization about z usually besides such usual
notions of the various statistics as so computed from sample
data, then as about estimators and usually with the goal of
finding the unbiased maximum likelihood estimators.
(A usual notion of model fitting and over families of distributions
by their scale and shape parameters finding relevant distributions
as match data wasn't much discussed in these usual courses
in statistics and probability theory.) Things like least squares,
then about computation of variance and mean for normal
distributions, then ANOVA/ANCOVA/MANCOVA, Student's
and Fisher's and t-tests, these are usual introductory applications
of statistics.

The parastatistics are about the Bose-Einstein and Fermi-Dirac
statistics, then about more parastatistics, as what in various
statistical ensembles of particle physics, where QM is probabilistic,
these are methods as what seem to add up.

https://en.wikipedia.org/wiki/Parastatistics

Paraconsistency in statistical hypotheses would seem to involve
mostly being built into the hypothesis itself, though it's mostly
where in statistics "it isn't not so", or, "it isn't so", not, "it is so".
Simply building in parastatistics as a reasonable notion of
"it could be wrong" seems a bit removed from some theory
with "ex falso nihilum" not "ex falso quodlibet", then besides
where there are simply third alternatives (past incompleteness).

Such notions of infinitesimal probability instead of a sum of
measure zero events being impossible, has in a usual consideration
about the natural integers at uniform random as considered in
one of the essays above: that surprisingly there is more than
one pdf about this distribution.

https://groups.google.com/d/topic/sci.math/8B8hPWpDooo/discussion

That there's a similar arrangement for U [0,1] (the distribution)
may be interesting.

Ah - only gibberish detected -
sorry - it can't be much more simple.

It might help the reader to decode some of Burse's usage,
Burse's box is a reference to some comments about his style
of argument, Burse's blisters is about the mathematical
infinitesimal: as Cantor referred to them as cholera bacilli,
back in the times when the flu was a regular generational plague,
Burse files my mention of infinitesimals under a virus, while
Burse's amoebae are protozoans about the reals being larger
than the standard reals, a term he coined one day.

"Santa Clause" might be seen as generous,
while the ekpyrotic (vis-a-vis, the ergodic) universe,

https://en.wikipedia.org/wiki/Ekpyrotic_universe

proposes at least an infinite past and future for the universe.
(Or, time goes back forever and space goes on forever.)

I would infer as a reference to how in physics I noted that
the universe's origins are both, at once, Steady State and
Big Bang. (Or, maybe it's a reference to something else).
I.e., a generous and even in-group's reading might find
meaningful usage of the terms, that are otherwise disjoint
or wrong.

That might help the reader, it might not. It might help the
reader at least to point out that Burse is sometimes a
silly person and sometimes informal. (Or, "Burse might
be a genius: there are limits.")

The infinitesimal in probabilities usually refers to a notion
that some events have probability zero because they are
not events (statistical events), others from continuous distributions
have measure zero (but are not empty), where "almost everywhere"
is used to refer to measure one, as the complement of the set of
measure zero events has, in the set of possible events. The point
is that they are not impossible, these events, but without some
means of summing together all the probabilities of the events
and finding that they equal one, the whole of them, the usual
notions that the area or integral of a p.d.f. equals one wouldn't
be satisfied. (We know real analysis uses countable additivity.)

So, I noted that the sweep function a.k.a. EF the natural/unit
equivalency function, f(n/d) = n/d, n->d, d->oo, which is very
simple and very simply modeled by real functions, via inspection
has all these relevant properties to do with functions that
describe distributions as not-a-real-function, has "real infinitesimals".

(Newton and Leibniz and many others would point at this function
and say "ah, that's my function, too". That it's integrable and
has area one instead of 1/2 I found this.)

The domain of this function is the natural integers,
the range of this function is [0,1],
the range is a continuous domain,
and this function in the setting of uncountability results
does _not_ find the resulting model of a continuum uncountable,
uniquely among functions. (Or, "Cantor proves the line is drawn.")

(It was also noted in the referenced thread that like the exponential
function which falls under differential operators, another peculiar
unique feature of this continuity model is that it's its own
derivative and anti-derivative. This might be a fact only relevant
to those familiar with the systems of differential equations.)

Then, the referenced papers as work to formalize notions of
the infinitesimal, here particularly for probability theory,
have that more-or-less they either eventually point at this
prototype of a line-drawing continuous domain, or: don't.
I.e., toward completeness, and a definition of "line continuity"
and another of "signal continuity" besides the day's "Dedekind's
field continuity", which is the only one offered by the usual
curriculum, the Equivalency Function is a central object in mathematics.

"We already talked about Mochizuki here
and about Teichmuller spaces as about
Groethendieck universes here about
Frobenius and a "prime at infinity", and
Mochizuki's uniformization to the p-adics
from the integers with a prime at infinity.

It's got nothing to do with breaking or
changing the rules, it's about transforms
between systems, not the bait-and-switch.

That is to say, it's built way high above
standard numbers and the Archimedean,
and it's still there, not having inconstancy
in definition.

Inconstancy: kind of like inconsistency,
but in a variety of senses, worse. "

"I study Burns as a model of professionalism...".

"Mochizuki's group theoretic results
about abc conjecture up in Teichmuller,
here for example "so complicated",
don't allow HP to share "just because
it's so complicated that HP can't be
bothered to maintain consistency". "

"That's not to say nonstandard models
of the integers don't have reason for
their existence and properties, or that
various models of effectively the integers
don't have the varieties of their objects
in the nonstandard as about the quest of
the integer continuum for number theory,
and it's not necessarily to say that Cohen's
forcing models M and the other M aren't a
bait-and-switch, it's just that the above are
examples of illustrated fallacies, this forum
is about logic, there are right answers,
and those are not them.

Statements about arithmetic that would
establish consistency of arithmetic so might
be a Goedel sentence, may also simply enough
point to the extra-standard instead of the
anti-standard."

"Your "uncountably many", with
"almost all" of them wrong, is,
not sufficient that there's
anything to contradict, at all.

Because it's already wrong. "

"I appreciated "it's a pinata,
not a theory. And it's his party." "

""S" isn't just a notation that you can
purpose to your own device (or corrupt),
here it's the Peano's Successor function
and the only meaningful ("true") interpretation
of "substring_1" is Predecessor. "

https://groups.google.com/d/msg/sci.logic/vrr0ltxCi2U/XKky7w-fCwAJ

"(That also pretty well dispatched
"model structure language theory"
as a poor translation of a model-
theoretic discourse of Shoenfield.)"

https://groups.google.com/d/msg/sci.logic/XFR2K6rNunI/K3y5F3rhmvcJ

https://en.wikipedia.org/wiki/Abc_conjecture

Where a, b, c are co-prime and a + b = c and d is the product
of distinct factors of abc, d <= abc, d/c <=ab, c/d >= 1/ab.

d is much smaller than abc when either a and b, or c,
are high powers of small primes.