From Osher Doctorow

Is there any really Local probability? Yes. I discuss these below.

Let's look at statistical dependence, which is a mainstream field in
mathematical probability-statistics. The expression:

1) F(x, y) - FX(x)FY(y)

is the main object of study in this field, where F(x, y) is the joint
cumulative distribution function of random variables X and Y at (x, y)
and where FX(x) is the (marginal) cumulative distribution function of X
at x. These are all local.

Another mainstream subfield of mathematical probability-statistics is
the study of probability distributions of random variables, which
includes: (a) probability density (pdfs) or mass functions, (b)
cumulative distribution functions (cdfs), (c) characteristic functions
(cfs), (d) probability generating functions, (e) moment generating
functions, (f) moments, (g) comparing different distributions with
regard to efficiency, sufficiency, unbiasedness, etc. These are all
local.

Maximum likelihood methods in statistics involve pdfs entirely and are
very important in statistical hypothesis testing. These are local.

Goodness of fit methods (including chi-square) are a major subfield of
probability-statistics entirely concerned with pdfs or cdfs which are
of course local.

Reliability in engineering is entirely local and involves cdfs and 1 -
cdf expressions.

Stochastic inequalities and majorization are a branch of
probability-statistics and are local.

Probable Influence (PI) is entirely local.

Large Deviations are usually local unless emphasis is on the large
deviations of means/aggregates.

Quality control is mostly local and involves confidence intervals which
are also local.

Estimation of population parameters (constants) by sample statistics is
local except when expectations (mean) and similar types of quantities
are involved. Estimation is a large branch of mathematical
probability-statistics.

Order statistics (maxima, minima, medians, etc.) are a branch of
mathematical probability-statistics which are mostly studied locally,
and are an important branch.

Osher Doctorow